ALBERT

Description: In the present experimental work, the behavior of laminar liquid jet in its own vapor as well as supercritical fluid environment is conducted. Also the study of liquid jet injection into nitrogen (N 2 ) environment is carried out at supercritical conditions. It is expected that the injected liquid jet would undergo thermodynamic transition to the chamber condition and this would alter the behavior of the injected jet. Moreover at such conditions there is a strong dependence between thermodynamic and fluid dynamic processes. Thus the thermodynamic transition has its effect on the initial instability as well as the breakup nature of the injected liquid jet. In the present study, the interfacial disturbance wavelength, breakup characteristics, and mixing behavior are analysed for the fluoroketone liquid jet that is injected into N 2 environment as well as into its own vapor at subcritical to supercritical conditions. It is observed that at subcritical chamber conditions, the injected liquid jet exhibits classical liquid jet characteristics with Rayleigh breakup at lower Weber number and Taylor breakup at higher Weber number for both N 2 and its own environment. At supercritical chamber conditions with its own environment, the injected liquid jet undergoes sudden thermodynamic transition to chamber conditions and single phase mixing characteristics is observed. However, the supercritical chamber conditions with N 2 as ambient fluid does not have significant effect on the thermodynamic transition of the injected liquid jet.

Description: The acoustic signature of an acoustically compact tandem airfoil setup in uniform high-Reynolds number flow is investigated. The upstream airfoil is considered rigid and is actuated at its leading edge with small-amplitude harmonic pitching motion. The downstream airfoil is taken passive and elastic, with its motion forced by the vortex-street excitation of the upstream airfoil. The non-linear near-field description is obtained via potential thin-airfoil theory. It is then applied as a source term into the Powell-Howe acoustic analogy to yield the far-field dipole radiation of the system. To assess the effect of downstream-airfoil elasticity, results are compared with counterpart calculations for a non-elastic setup, where the downstream airfoil is rigid and stationary. Depending on the separation distance between airfoils, airfoil-motion and airfoil-wake dynamics shift between in-phase (synchronized) and counter-phase behaviors. Consequently, downstream airfoil elasticity may act to amplify or suppress sound through the direct contribution of elastic-airfoil motion to the total signal. Resonance-type motion of the elastic airfoil is found when the upstream airfoil is actuated at the least stable eigenfrequency of the downstream structure. This, again, results in system sound amplification or suppression, depending on the separation distance between airfoils. With increasing actuation frequency, the acoustic signal becomes dominated by the direct contribution of the upstream airfoil motion, whereas the relative contribution of the elastic airfoil to the total signature turns negligible.

Description: Bubble size distributions in cloud cavitation are important in cavitating flows. In this study, a numerical model was developed to study the evolution of the internal structure of cloud cavitation. The model includes (1) an evolution equation of bubble number density, which considers the bubble breakup effect and (2) the multiphase Reynolds-averaged Navier–Stokes equations with a modified cavitation model for background cavitating flows. The proposed model was validated with a flow over a projectile. Results show that the numerical model can predict the evolution of the internal structure of cloud cavitation. Comparisons of the proposed model and Singhal model were discussed. The effects of re-entrant jet and bubble number density on cavitating flows were also investigated.

Description: This paper presents two key contributions; the first concerns the development of analytical expressions for the axial and transverse acoustic radiation forces exerted on a 2D rigid elliptical cylinder placed in the field of plane progressive, quasi-standing, or standing waves with arbitrary incidence. The second emphasis is on the acoustic radiation torque per length. The rigid elliptical cylinder case is important to be considered as a first-order approximation of the behavior of a cylindrical fluid column trapped in air because of the significant acoustic impedance mismatch at the particle boundary. Based on the rigorous partial-wave series expansion method in cylindrical coordinates, non-dimensional acoustic radiation force and torque functions are derived and defined in terms of the scattering coefficients of the elliptic cylinder. A coupled system of linear equations is obtained after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid and solved numerically by matrix inversion after performing a single numerical integration procedure. Computational results for the non-dimensional force components and torque, showing the transition from the progressive to the (equi-amplitude) standing wave behavior, are performed with particular emphasis on the aspect ratio a / b , where a and b are the semi-axes of the ellipse, the dimensionless size parameter, as well as the angle of incidence ranging from end-on to broadside incidence. The results show that the elliptical geometry has a direct influence on the radiation force and torque, so that the standard theory for circular cylinders (at normal incidence) leads to significant miscalculations when the cylinder cross section becomes non-circular. Moreover, the elliptical cylinder experiences, in addition to the acoustic radiation force, a radiation torque that vanishes for the circular cylinder case. The application of the formalism presented here may be extended to other 2D surfaces of arbitrary shape, such as Chebyshev cylindrical particles with a small deformation, stadiums (with oval shape), or other non-circular geometries.

Description: The Wegner estimate for the Hamiltonian of the Anderson model for the special Gaussian random magnetic field is extended to more general magnetic fields. The Lifshitz tail upper bounds of the integrated density of states as analyzed by Nakamura are reviewed and extended so that Gaussian random magnetic fields can be treated. By these and multiscale analysis, the Anderson localization at low energies is proven.

Description: Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su (1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them is obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.

Description: We consider the p -Laplacian problem − ε p Δ p u + V ( x ) u p − 2 u = f ( u ) , u ∈ W 1 , p ( R N ) , where p ∈ (1, N ) and f ( s ) is of critical growth. In this paper, we construct a single peak solution around an isolated component of the positive local minimum points of V as ε → 0 with a general nonlinearity f . In particular, the monotonicity of f ( s )/ s p −1 and the so-called Ambrosetti-Rabinowitz condition are not required.

Description: It is shown that the initial value problem for an integrable Novikov system is well-posed in Sobolev spaces H s , s 〉 3/2, in the sense of Hadamard. Furthermore, it is proved that the dependence on initial data is sharp, i.e., the data-to-solution map is continuous but not uniformly continuous. Also, peakon traveling wave solutions are used to prove that the solution map is not uniformly continuous in H s for s 〈 3/2.

Description: Our discussion here mainly focuses on the formation of singularities for solutions to the N -dimensional Euler-Poisson equations with attractive forces, in radial symmetry. Motivated by the integration method of Yuen, we prove two blow-up results under the conditions that the solutions have compact radius R ( t ) or have no compact support restriction, which generalize the ones Yuen obtained in 2011 [M. W. Yuen, “Blowup for the C 1 solution of the Euler-Poisson equations of gaseous stars in R N ,” J. Math. Anal. Appl. 383 , 627-633 (2011)].

Description: A new variational method is proposed to calculate the evolution of liquid film and liquid droplet moving on a solid substrate. A simple time evolution equation is obtained for the contact angle of a liquid film that starts to move on a horizontal substrate. The equation indicates the dynamical transition at the receding side and the ridge formation at the advancing side. The same method is applied for the evolution of a droplet that starts to move on an inclined solid surface, and again the characteristic shape change of the droplet is obtained by solving a simple ordinary differential system. We will show that this method has a potential application to a wide class of problems of droplets moving on a substrate.

Description: The pressure-driven Stokes flow through a plane channel with arbitrary wall separation having a continuous pattern of sinusoidally varying slippage of arbitrary wavelength and amplitude on one/both walls is modelled semi-analytically. The patterning direction is transverse to the flow. In the special situations of thin and thick channels, respectively, the predictions of the model are found to be consistent with lubrication theory and results from the literature pertaining to free shear flow. For the same pattern-averaged slip length, the hydraulic permeability relative to a channel with no-slip walls increases as the pattern wave-number, amplitude, and channel size are decreased. Unlike discontinuous wall patterns of stick-slip zones studied elsewhere in the literature, the effective slip length of a sinusoidally patterned wall in a confined flow continues to scale with both channel size and the pattern-averaged slip length even in the limit of thin channel size to pattern wavelength ratio. As a consequence, for sufficiently small channel sizes, the permeability of a channel with sinusoidal wall slip patterns will always exceed that of an otherwise similar channel with discontinuous patterns on corresponding walls. For a channel with one no-slip wall and one patterned wall, the permeability relative to that of an unpatterned reference channel of same pattern-averaged slip length exhibits non-monotonic behaviour with channel size, with a minimum appearing at intermediate channel sizes. Approximate closed-form estimates for finding the location and size of this minimum are provided in the limit of large and small pattern wavelengths. For example, if the pattern wavelength is much larger than the channel thickness, exact results from lubrication theory indicate that a worst case permeability penalty relative to the reference channel of ∼23% arises when the average slip of the patterned wall is ∼2.7 times the channel size. The results from the current study should be applicable to microfluidic flows through channels with hydrophobized/super-hydrophobic surfaces.

Description: The rotation and an axial gradient of temperature drive the meridional circulation of a fluid filling a sealed cylindrical container. This numerical study explains why the flow remains stable up to the Grashof number Gr around 10 11 ; Gr characterizes the circulation strength. The shear-layer instability, occurring in a rotating pipe for small values of the Prandtl number Pr [M. A. Herrada and V. N. Shtern, “Stability of centrifugal convection in a rotating pipe,” Phys. Fluids 27 , 064106 (2015)], is suppressed here even for the cylinder length-to-radius ratio being ten. The cold end disk enhances the fluid circulation near the sidewall and diminishes it near the axis. The inflection point in the radial profile of axial velocity shifts to the sidewall vicinity where the stable centrifugal stratification and the no-slip condition prevent the disturbance growth. The cases Pr = 0, 0.015 (mercury), 0.7 (air), and 5.8 (water) are particularly analyzed. At Pr 〉 0, the stable density stratification develops and helps to suppress the disturbances. The obtained results are of fundamental interest and might be important for the development of efficient heat exchangers.

Description: This paper investigates the effects of surface roughness on nanoflows using molecular dynamics simulations. A fractal model is employed to model wall roughness, and simulations are performed for liquid argon confined by two solid walls. It is shown that the surface roughness reduces the velocity in the proximity of the walls with the reduction being accentuated when increasing the roughness depth and wettability of the solid wall. It also makes the flow three-dimensional and anisotropic. In flows over idealized smooth surfaces, the liquid forms parallel, well-spaced layers, with a significant gap between the first layer and the solid wall. Rough walls distort the orderly distribution of fluid layers resulting in an incoherent formation of irregularly shaped fluid structures around and within the wall cavities.

Description: The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the non-classical physics, and whether the second-order non-Navier-Fourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method. Peculiar behaviors (non-uniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23 (1), 012002 (2011)]) were re-examined using atomic-level MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the second-order non-Navier-Fourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the non-Navier-Fourier constitutive laws are essential for describing non-zero normal stress and tangential heat flux, while the classical and non-classical laws remain similar for shear stress and normal heat flux.

Description: An exact solution is found for laminar fluid flow along the grooves of a family of surfaces whose shape is given by the Lambert W-function. This simple solution allows for the slip length in the direction parallel to the grooves to be calculated exactly. With this analytical model, we establish the regime of validity for a previously untested perturbation theory intended for calculating the surface mobility tensor of arbitrary periodic surfaces, finding that it compares well to the exact expression for nearly all choices of parameters of the conformal map. To test this perturbation theory further, the mobility tensor is evaluated for a simple sinusoidal surface for flow both parallel and perpendicular to the grooves, finding that the perturbation theory is less accurate in the latter of these two cases.

Description: This paper investigates the bubbling behaviors induced by gas-liquid mixture permeating through porous medium (PM), which was observed in developing immersion lithography system and was found having great differences with traditional bubbling behaviors injected with only gas phase through the PM. An experimental setup was built up to investigate the bubbling characteristics affected by the mixed liquid phase. Both the flow regimes of gas-liquid mixture in micro-channel (upstream of the PM) and the bubbling flow regimes in water tank (downstream of the PM) were recorded synchronously by high-speed camera. The transitions between the flow regimes are governed by gas and liquid Weber numbers. Based on the image analysis, the characteristic parameters of bubbling region, including the diameter of bubbling area on PM surface, gas-phase volume flux, and dispersion angle of bubbles in suspending liquid, were studied under different proportions of gas and liquid flow rate. Corresponding empirical correlations were developed to describe and predict these parameters. Then, the pertinent bubble characteristics in different bubbling flow regimes were systematically investigated. Specifically, the bubble size distribution and the Sauter mean diameter affected by increasing liquid flow rate were studied, and the corresponding analysis was given based on the hydrodynamics of bubble-bubble and bubble-liquid interactions. According to dimensionless analysis, the general prediction equation of Sauter mean diameter under different operating conditions was proposed and confirmed by experimental data. The study of this paper is helpful to improve the collection performance of immersion lithography and aims to reveal the differences between the bubbling behaviors on PM caused by only gas flow and gas-liquid mixture flow, respectively, for the researches of fluid flow.

Description: We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects of gravity, viscosity, rotation, surface tension, and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids, the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes change with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers.

Description: A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.

Description: New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.

Description: In this work, the interfacial instability and transition of a two-fluid flow from a stratified state to large amplitude waves or slugs is considered. By combining an asymptotic approximation of the linear Orr-Sommerfeld analysis with nonlinear resonant wave interaction theory, a novel nonlinear slug-transition criterion is derived. This criterion corresponds to a bounding condition on the upper fluid’s velocity in order to limit the amount of energy (provided by the linear instability) which is transferred to long waves through resonant wave interactions. It is proposed that such a condition can predict the formation of large-amplitude long waves and/or slugs. Quantitative comparisons of the onset of slugging are made between the prediction by the nonlinear transition criterion and the experimental measurements carried out in a horizontal square channel. Good agreement is observed. An additional heuristic model is developed which generalizes the transition criterion to flow through horizontal pipes. Comparisons are made for flows through different pipe diameters and over a wide range of fluid properties. Good agreement between the present theoretical predictions and the experimental measurements is also observed.

Description: In this paper, we provide a new method for establishing the blowup of C 2 solutions for the pressureless Euler-Poisson system with attractive forces for R N ( N ≥ 2) with ρ (0, x 0 ) 〉 0 and Ω 0 i j ( x 0 ) = 1 2 ∂ i u j ( 0 , x 0 ) − ∂ j u i ( 0 , x 0 ) = 0 at some point x 0 ∈ R N . By applying the generalized Hubble transformation   div   u ( t , x 0 ( t ) ) = N a ̇ ( t ) a ( t ) to a reduced Riccati differential inequality derived from the system, we simplify the inequality into the Emden equation a ̈ ( t ) = − λ a ( t ) N − 1 , a ( 0 ) = 1 , a ̇ ( 0 ) =   div   u ( 0 , x 0 ) N . Known results on its blowup set allow us to easily obtain the blowup conditions of the Euler-Poisson system.

Description: Using a sharp Gagliardo-Nirenberg type inequality, well-posedness issues of the initial value problem for a fractional inhomogeneous Schrödinger equation are investigated.

Description: The paper focuses on studying the Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales. First, the Hamilton equations of nonholonomic nonconservative systems on time scales are established, which is based on the Lagrange equations for nonholonomic systems on time scales. Then, based upon the quasi-invariance of Hamilton action of systems under the infinitesimal transformations with respect to the time and generalized coordinate on time scale, the Noether identity and the conserved quantity of nonholonomic nonconservative systems on time scales are obtained. Finally, an example is presented to illustrate the application of the results.

Description: Cavities behind a surface irregularity appear in vortices drifting downstream of it. Cavitation can occur there substantially earlier than over smooth surfaces of the same bodies. Cavitation inception and desinence behind surface irregularities have been intensively studied in the course of water tunnel experiments several decades ago, but no corresponding quantitative theoretical (numerical) analysis was reported. This numerical study is aimed at elaboration of a general approach to the prediction of cavitation desinence numbers for various irregularities over various surfaces and on determination of the major factors influencing these numbers in both computations and experiments. The developed multi-level computational method employs diverse models for flow zones of diverse scale. The viscous-inviscid interaction approach is used for the flow around irregularities submerged (or partially submerged) in the turbulent boundary layer. Combinations of the semi-empirical and asymptotic analyses are used for vortices and cavities in their cores. The computational method is validated with various known experimental data.

Description: Experiments are conducted in a linear stratified fluid with a momentum source modeled via a nozzle jet moving horizontally. The generation mechanism of the quasi-two-dimensional dipolar vortex streets is investigated and their evolution characteristics are analyzed. Observation shows that the formation of a dipolar vortex street requires a nonzero motion of the nozzle in addition to conditions of the Reynolds and Froude number ( Re , Fr ). The ( Re , Fr ) condition that the dipolar vortex streets can be generated is determined via experimental measurements. The explanation for the absence of such a vortex street can be the low energy of the jet and the strong body-effect disturbance of the solid nozzle. The dependence of the vortex street dimensionless formation time τ and the Strouhal number St on the Froude number Fr or the Reynolds number Re is analyzed. This analysis shows that τ and St appear to be independent of Re and approximately have power-law relations with Fr via data fitting. The exponents of Fr in the two power-law functions are −0.27 for τ and −0.21 for St , while the constant coefficients are 65 and 0.21.

Description: A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by converging-diverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, “Effective correlation of apparent gas permeability in tight porous media,” Transp. Porous Media 82 , 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model.

Description: General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

Description: The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called singular eigenfunctions. In this paper, we explore the singular-eigenfunction approach in flatland or two-dimensional space.

Description: Pinch-off of axisymmetric vortex pairs generated by flow between concentric cylinders with radial separation Δ R was studied numerically and compared with planar vortex dipole behavior. The axisymmetric case approaches planar vortex dipole behavior in the limit of vanishing Δ R . The flow was simulated at a jet Reynolds number of 1000 (based on Δ R and the jet velocity), jet pulse length-to-gap ratio ( L Δ R ) in the range 10–20, and gap-to-outer radius ratio ( Δ R R o ) in the range 0.01-0.1. Contrary to investigations of strictly planar flows, vortex pinch-off was observed for all gap sizes investigated. This difference was attributed to the less constrained geometry considered, suggesting that even very small amounts of vortex line curvature and/or vortex stretching may disrupt the absence of pinch-off observed in strictly planar vortex dipoles.

Description: We study the late time flow structure of Richtmyer-Meshkov instability. Recent numerical work [F. J. Cherne et al. “On shock driven jetting of liquid from non-sinusoidal surfaces into a vacuum,” J. Appl. Phys. 118 , 185901 (2015)] has suggested a self-similar collapse of the development of this instability at late times, independent of the initial surface profile. Using the form of collapse suggested, we derive an analytic expression for the mass-velocity relation in the spikes, and a global theory for the late time flow structure. We compare these results with fluid dynamical simulation.

Description: The BPS Skyrme model is a model containing an SU (2)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU (2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here that in the BPS Skyrme model such solutions exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.

Description: Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.

Description: Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N -vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.

Description: Computer simulations are performed to study translational motion and deformation of a liquid column or jet, in a plane perpendicular to its axis, due to a transverse electric field. A front tracking/finite difference scheme is used in conjunction with the Taylor-Melcher leaky dielectric theory to solve the governing equations. The column is confined within a rectangular channel, wall-bounded in the vertical direction and periodic in the horizontal direction. It is shown that perfect dielectric columns move toward electrode wall of shorter initial distance, but the leaky dielectric columns may move toward or away from it, depending on the relative importance of the ratios (drop fluid to suspending fluid) of their electric permittivity and conductivity. Furthermore, the degree of interface deformation might increase or decrease with the initial separation distance from the shorter electrode wall due to the same factor. Scaling arguments are used to discern the correlation between the translational velocity and the initial separation distance from the electrodes.

Description: In this paper, we study the existence of positive solution for the following class of fractional elliptic equation ϵ 2 s ( − Δ ) s u + V ( z ) u = λ u q − 2 u + u 2 s ∗ − 2 u in R N , where ϵ , λ 〉 0 are positive parameters, q ∈ ( 2 , 2 s ∗ ) , 2 s ∗ = 2 N N − 2 s , N 〉 2 s , s ∈ ( 0 , 1 ) , ( − Δ ) s u is the fractional Laplacian, and V is a saddle-like potential. The result is proved by using minimizing method constrained to the Nehari manifold. A special minimax level is obtained by using an argument made by Benci and Cerami.

Description: We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general equation of state (EOS) of Mie-Grüneisen type. In addition, we suppose that the viscosity coefficients may decay to zero for large values of the temperature. We show the existence of global-in-time weak solution, derive a relative energy inequality, and compare the weak solutions with strong one emanating from the same initial data—the weak strong uniqueness property.

Description: A series of three-dimensional numerical simulations on thermal-solutal capillary-buoyancy flow in an annular pool were carried out. The pool was filled with silicon-germanium melt with an initial silicon mass fraction of 1.99%. The Prandtl number and the Lewis number of the working fluid are 6.37 × 10 −3 and 2197.8, respectively. Both the radial temperature gradient and the solute concentration gradient were applied to the annular pool. The capillary ratio was assumed to be −1, which means that the solutal and thermal capillary effects were equal and opposite. Results show that the thermal-solutal capillary-buoyancy flow always occurs at this special case with the capillary ratio of −1, and even in a shallow annular pool with an aspect ratio of 0.05. With the increase of the thermal Marangoni number, four kinds of flow patterns appear orderly, including concentric rolls, petal-like, spoke, and rosebud-like patterns. These flow patterns are strongly influenced by the local interaction between the solutal and thermal capillary effects and the vertical solute concentration gradient near the outer cylinder. A small vortex driven by the dominant solutal capillary effect emerges near the inner cylinder, which is different from the flow pattern in a pure fluid. In addition, the critical thermal Marangoni number of the initial three-dimensional flow decreases with the increase of the aspect ratio of the annular pool.

Description: In this paper we apply the short-wavelength perturbation method to derive instability criteria for the three-dimensional nonlinear Pollard geophysical waves. We show that these waves are linearly unstable when the wave steepness exceeds a certain threshold.

Description: Recent advances in numerical methods coupled with the substantial enhancements in computing power and the advent of high performance computing have presented first principle, high fidelity simulation as a viable tool in the prediction and analysis of spray atomization processes. The credibility and potential impact of such simulations, however, has been hampered by the relative absence of detailed validation against experimental evidence. The numerical stability and accuracy challenges arising from the need to simulate the high liquid-gas density ratio across the sharp interfaces encountered in these flows are key reasons for this. In this work we challenge this status quo by presenting a numerical model able to deal with these challenges, employing it in simulations of liquid jet in crossflow atomization and performing extensive validation of its results against a carefully executed experiment with detailed measurements in the atomization region. We then proceed to the detailed analysis of the flow physics. The computational model employs the coupled level set and volume of fluid approach to directly capture the spatiotemporal evolution of the liquid-gas interface and the sharp-interface ghost fluid method to stably handle high liquid-air density ratio. Adaptive mesh refinement and Lagrangian droplet models are shown to be viable options for computational cost reduction. Moreover, high performance computing is leveraged to manage the computational cost. The experiment selected for validation eliminates the impact of inlet liquid and gas turbulence and focuses on the impact of the crossflow aerodynamic forces on the atomization physics. Validation is demonstrated by comparing column surface wavelengths, deformation, breakup locations, column trajectories and droplet sizes, velocities, and mass rates for a range of intermediate Weber numbers. Analysis of the physics is performed in terms of the instability and breakup characteristics and the features of downstream flow recirculation, and vortex shedding. Formation of “Λ” shape windward column waves is observed and explained by the combined upward and lateral surface motion. The existence of Rayleigh-Taylor instability as the primary mechanism for the windward column waves is verified for this case by comparing wavelengths from the simulations to those predicted by linear stability analyses. Physical arguments are employed to postulate that the type of instability manifested may be related to conditions such as the gas Weber number and the inlet turbulence level. The decreased column wavelength with increasing Weber number is found to cause enhanced surface stripping and early depletion of liquid core at higher Weber number. A peculiar “three-streak-two-membrane” liquid structure is identified at the lowest Weber number and explained as the consequence of the symmetric recirculation zones behind the jet column. It is found that the vortical flow downstream of the liquid column resembles a von Karman vortex street and that the coupling between the gas flow and droplet transport is weak for the conditions explored.

Description: Linear stability of the stratified gas-liquid and liquid-liquid plane-parallel flows in the inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict the parameter regions in which the stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in the inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid to the multiple solution regions to reveal the feasibility of the non-unique stable stratified configurations in inclined channels. The stability boundaries of each branch of the steady state solutions are presented on the flow pattern map and are accompanied by the critical wavenumbers and the spatial profiles of the most unstable perturbations. Instabilities of different nature are visualized by the streamlines of the neutrally stable perturbed flows, consisting of the critical perturbation superimposed on the base flow. The present analysis confirms the existence of two stable stratified flow configurations in a region of low flow rates in the countercurrent liquid-liquid flows. These configurations become unstable with respect to the shear mode of instability. It was revealed that in slightly upward inclined flows the lower and middle solutions for the holdup are stable in the part of the triple solution region, while the upper solution is always unstable. In the case of downward flows, in the triple solution region, none of the solutions are stable with respect to the short-wave perturbations. These flows are stable only in the single solution region at low flow rates of the heavy phase, and the long-wave perturbations are the most unstable ones.

Description: In the present study, we are interested in the Davey-Stewartson equations (DSE) that model packets of surface and capillary-gravity waves. We focus on the elliptic-elliptic case, for which it is known that DSE may develop a finite-time singularity. We propose three systems of non-viscous regularization to the DSE in a variety of parameter regimes under which the finite-time blow-up of solutions to the DSE occurs. We establish the global well-posedness of the regularized systems for all initial data. The regularized systems, which are inspired by the α -models of turbulence and therefore are called the α -regularized DSE, are also viewed as unbounded, singularly perturbed DSE. Therefore, we also derive reduced systems of ordinary differential equations for the α -regularized DSE by using the modulation theory to investigate the mechanism with which the proposed non-viscous regularization prevents the formation of the singularities in the regularized DSE. This is a follow-up of the work [Cao et al. , Nonlinearity 21 , 879–898 (2008); Cao et al. , Numer. Funct. Anal. Optim. 30 , 46–69 (2009)] on the non-viscous α -regularization of the nonlinear Schrödinger equation.

Description: In this study, we report the effects of a uniform stationary magnetic field on the flow of ferrofluid (FF) inside a boundary driven cavity. A coupled set of conservation equations for the flow field, the Maxwell’s magnetostatic equations, and the constitutive magnetization equation are solved numerically. The non-dimensional groups primarily influencing the phenomenon are first systematically identified through the normalization of the complete set of equations. We find the magnetization relaxation effects, under the stationary uniform field, to be flow restrictive in nature. The misalignment between the local magnetic field and the magnetization suppresses the vorticity field in the cavity, shifts the primary central vortex, and reduces the average shear stress at the boundaries. As a consequence, it becomes apparent that at a given Reynolds number, the application of uniform magnetic field can reduce the shear drag at the boundaries of the cavity, of course at an expense of reduced flow rate in their vicinity. Our study uniquely reveals that the relaxation time effects are dominant in the regions of ferrofluid flow where the change in the magnitude of the vorticity takes place over a length scale which is much smaller than the characteristic length scale of the flow geometry. Depending on the magnitudes of influencing parameters, the solution exhibits anomalous characteristics, such as creeping and saturating behavior.

Description: We study an important system of Schrödinger equations with linear and nonlinear couplings arising from Bose-Einstein condensates. We use the Nehari manifold to prove the existence of a ground state solution; moreover, we give the sign of the solutions depending on linear coupling; by using index theory and Nehari manifold, we prove that there exist infinitely many positive bound state solutions.

Description: It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.

Description: We consider Landau Hamiltonians with a weak coupling random electric potential of breather type. Under appropriate assumptions we prove a Wegner estimate. It implies the Hölder continuity of the integrated density of states. The main challenge is the problem how to deal with non-linear dependence on the random parameters.

Description: Using a conservative level set method we investigate the deformation behavior of isolated spherical fluid drops in a fluid channel subjected to simple shear flows, accounting the following three non-dimensional parameters: (1) degree of confinement ( W c = 2 a / h , where a is the drop radius and h is the channel thickness); (2) viscosity ratio between the two fluids ( λ = μ d / μ m , where μ d is the drop viscosity and μ m is the matrix viscosity); and (3) capillary number ( Ca ). For a given W c , a drop steadily deforms to attain a stable geometry (Taylor number and inclination of its long axis to the shear direction) when Ca 〈 0.3. For Ca 〉 0.3, the deformation behavior turns to be unsteady, leading to oscillatory variations of both its shape and orientation with progressive shear. This kind of unsteady deformation also occurs in a condition of high viscosity ratios ( λ 〉 2). Here we present a detailed parametric analysis of the drop geometry with increasing shear as a function of W c , Ca , and λ . Under a threshold condition, deforming drops become unstable, resulting in their breakup into smaller droplets. We recognize three principal modes of breakup: Mode I (mid-point pinching), Mode II (edge breakup), and Mode III (homogeneous breakup). Each of these modes is shown to be most effective in the specific field defined by Ca and λ . Our study also demonstrates the role of channel confinement ( W c ) in controlling the transition of Mode I to III. Finally, we discuss implications of the three modes in determining characteristic drop size distributions in multiphase flows.

Description: A novel hydrodynamic model for the threshold of cohesionless sediment particle motion under a steady unidirectional streamflow is presented. The hydrodynamic forces (drag and lift) acting on a solitary sediment particle resting over a closely packed bed formed by the identical sediment particles are the primary motivating forces. The drag force comprises of the form drag and form induced drag. The lift force includes the Saffman lift, Magnus lift, centrifugal lift, and turbulent lift. The points of action of the force system are appropriately obtained, for the first time, from the basics of micro-mechanics. The sediment threshold is envisioned as the rolling mode, which is the plausible mode to initiate a particle motion on the bed. The moment balance of the force system on the solitary particle about the pivoting point of rolling yields the governing equation. The conditions of sediment threshold under the hydraulically smooth, transitional, and rough flow regimes are examined. The effects of velocity fluctuations are addressed by applying the statistical theory of turbulence. This study shows that for a hindrance coefficient of 0.3, the threshold curve (threshold Shields parameter versus shear Reynolds number) has an excellent agreement with the experimental data of uniform sediments. However, most of the experimental data are bounded by the upper and lower limiting threshold curves, corresponding to the hindrance coefficients of 0.2 and 0.4, respectively. The threshold curve of this study is compared with those of previous researchers. The present model also agrees satisfactorily with the experimental data of nonuniform sediments.

Description: We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel direction, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuation-dissipation theorem we compute the Brownian motion of the particle, finding a long-lasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed point-particle approximation via boundary-integral simulations for a truly extended particle. They are found to be in excellent agreement with the analytical predictions.

Description: This article reports an unbiased analysis for the water based rod shaped alumina nanoparticles by considering both the homogeneous and non-homogeneous nanofluid models over the coupled nanofluid-surface interface. The mechanics of the surface are found for both the homogeneous and non-homogeneous models, which were ignored in previous studies. The viscosity and thermal conductivity data are implemented from the international nanofluid property benchmark exercise. All the simulations are being done by using the experimentally verified results. By considering the homogeneous and non-homogeneous models, the precise movement of the alumina nanoparticles over the surface has been observed by solving the corresponding system of differential equations. For the non-homogeneous model, a uniform temperature and nanofluid volume fraction are assumed at the surface, and the flux of the alumina nanoparticle is taken as zero. The assumption of zero nanoparticle flux at the surface makes the non-homogeneous model physically more realistic. The differences of all profiles for both the homogeneous and nonhomogeneous models are insignificant, and this is due to small deviations in the values of the Brownian motion and thermophoresis parameters.

Description: We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator (−Δ) 1/2 , whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral data for lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled E ( k , l ) series. For each orbital label l = 0, 1, 2, …, the label k = 1, 2, … enumerates consecutive l th series eigenvalues. Each of them is 2 l + 1-degenerate. The l = 0 eigenvalues series E ( k ,0) are identical with the set of even labeled eigenvalues for the d = 1 Cauchy well: E ( k ,0) ( d = 3) = E 2 k ( d = 1). Likewise, the eigenfunctions ψ ( k ,0) ( d = 3) and ψ 2 k ( d = 1) show affinity. We have identified the generic functional form of eigenfunctions of the spherical well which appear to be composed of a product of a solid harmonic and of a suitable purely radial function. The method to evaluate (approximately) the latter has been found to follow the universal pattern which effectively allows to skip all, sometimes involved, intermediate calculations (those were in usage, while computing the eigenvalues for l ≤ 3).

Description: The aim of this paper is to prove the existence of a new symmetric family of periodic solutions of the generalized van der Waals Hamiltonian. In fact, we prove the existence of several families of first kind symmetric periodic solutions as continuation of circular orbits of the Kepler problem in the spatial case.

Description: The flow in an annulus driven by the axial movement of one of the cylinders has been studied. The stationary cylinder has been fitted with axisymmetric ribs resulting in the appearance of the centrifugal-force-driven instability which leads to the formation of axial vortices. The critical stability conditions have been determined for a wide range of geometries of practical interest; these conditions include the critical Reynolds number as well as the best vortex packing. It has been shown that a sufficiently large increase of the ribs’ wavelength leads to a flow stabilization as the flow becomes nearly rectilinear, thus reducing the strength of the centrifugal force field. It has also been demonstrated that a sufficiently large decrease of the ribs’ wavelength similarly results in the flow stabilization as the stream lifts up above the ribs’ peaks and becomes more rectilinear. Reduction of the annulus’ radius leads to qualitatively different flow responses depending on the position of the moving cylinder. The critical Reynolds number is reduced and the range of the ribs’ wave numbers capable of inducing the instability is increased when the outer cylinder drives the flow. The trend is reversed when the inner cylinder drives the flow. Conditions when the ribbed cylinder is unable to induce any instability and, thus, behaves as a hydraulically smooth cylinder have been identified.

Description: Transformation from annular to droplet flow is investigated for co-current, upward gas-liquid flow through a cylindrical tube using grid based volume of fluid framework. Three transitional routes, namely, orificing, rolling, and undercutting are observed for flow transformation at different range of relative velocities between the fluids. Physics behind these three exclusive phenomena is described using circulation patterns of gaseous phase in the vicinity of a liquid film which subsequently sheds drop leading towards transition. Orifice amplitude is found to grow exponentially towards the core whereas it propagates in axial direction in a parabolic path. Efforts have been made to fit the sinusoidal profile of wave structure with the numerical interface contour at early stages of orificing. Domination of gas inertia over liquid flow has been studied in detail at the later stages to understand the asymmetric shape of orifice, leading towards lamella formation and droplet generation. Away from comparative velocities, circulations in the dominant phase dislodge the drop by forming either a ligament (rolling) or a bag (undercut) like protrusion in liquid. Study of velocity patterns in the plane of droplet dislodge reveals the underlying physics behind the disintegration and its dynamics at the later stages. Using numerical phase distributions, rejoining of dislodged droplet with liquid film as post-rolling consequences has been also proposed. A flow pattern map showing the transitional boundaries based on the physical mechanism is constructed for air-water combination.

Description: A rigorous and systematic computational and theoretical study, the first of its kind, for the laminar natural convective flow above rectangular horizontal surfaces of various aspect ratios ϕ (from 1 to ∞) is presented. Two-dimensional computational fluid dynamic (CFD) simulations (for ϕ → ∞) and three-dimensional CFD simulations (for 1 ≤ ϕ 〈 ∞) are performed to establish and elucidate the role of finiteness of the horizontal planform on the thermo-fluid-dynamics of natural convection. Great care is taken here to ensure grid independence and domain independence of the presented solutions. The results of the CFD simulations are compared with experimental data and similarity theory to understand how the existing simplified results fit, in the appropriate limiting cases, with the complex three-dimensional solutions revealed here. The present computational study establishes the region of a high-aspect-ratio planform over which the results of the similarity theory are approximately valid, the extent of this region depending on the Grashof number. There is, however, a region near the edge of the plate and another region near the centre of the plate (where a plume forms) in which the similarity theory results do not apply. The sizes of these non-compliance zones decrease as the Grashof number is increased. The present study also shows that the similarity velocity profile is not strictly obtained at any location over the plate because of the entrainment effect of the central plume. The 3-D CFD simulations of the present paper are coordinated to clearly reveal the separate and combined effects of three important aspects of finiteness: the presence of leading edges, the presence of planform centre, and the presence of physical corners in the planform. It is realised that the finiteness due to the presence of physical corners in the planform arises only for a finite value of ϕ in the case of 3-D CFD simulations (and not in 2-D CFD simulations or similarity theory). The presence of physical corners is related here to several significant aspects of the solution—the conversion of in-plane velocity to out-of-plane velocity near the diagonals, the star-like non-uniform distribution of surface heat flux on heated planforms, the three-dimensionality of the temperature field, and the complex spatial structure of the velocity iso-surfaces. A generic theoretical correlation for the Nusselt number is deduced for the averaged surface heat flux for various rectangular surfaces (1 ≤ ϕ 〈 ∞) over a wide range of Grashof number. Innovative use of numerical visualization images is made to generate a comprehensive, quantitative understanding of the physical processes involved.

Description: The dielectrophoresis of a surfactant-laden viscous drop in the presence of non-uniform DC electric field is investigated analytically and numerically. Considering the presence of bulk-insoluble surfactants at the drop interface, we first perform asymptotic solution for both low and high surface Péclet numbers, where the surface Péclet number signifies the strength of surface convection of surfactants as compared to the diffusion at the drop interface. Neglecting fluid inertia and interfacial charge convection effects, we obtain explicit expression for dielectrophoretic drop velocity for low and high Péclet numbers by assuming small deviation of drop shape from sphericity and small deviation of surfactant concentration from the equilibrium uniform distribution. We then depict a numerical solution, assuming spherical drop, for arbitrary values of Péclet number. Our analyses demonstrate that the asymptotic solution shows excellent agreement with the numerical solution in the limiting conditions of low and high Péclet numbers. The present analysis shows that the flow-induced redistribution of the surfactants at the drop interface generates Marangoni stress, owing to the influence of the surfactant distribution on the local interfacial tension, at the drop interface and significantly alters the drop velocity at steady state. For a perfectly conducting/dielectric drop suspended in perfectly dielectric medium, Marangoni stress always retards the dielectrophoretic velocity of the drop as compared with a surfactant-free drop. For a leaky dielectric drop suspended in another leaky dielectric medium, in the low Péclet number limit, depending on the electrical conductivity and permittivity of both the liquids, the Marangoni stress may aid or retard the dielectrophoretic velocity of the drop. The Marangoni stress also has the ability to move the drop in the opposite direction as compared with a surfactant-free drop. This non-intuitive reverse motion of the drop is observed for drops with less viscosity and for particular values of electrical conductivity and permittivity ratios. In the high Péclet number limit, the surfactants completely immobilize the fluid velocity at the drop interface. As a result, the drop behaves like a solid sphere. Further, it is also demonstrated that the flow-induced non-uniform distribution of surfactants always increases the deformation of the drop as compared with a uniformly coated drop which is due to the decreased (or increased) interfacial tension near the poles of the drop for prolate (or oblate) type deformation.

Description: The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ℂ d 1 ⊗ ℂ d 2 are locally unitary equivalent in connection with trace identities, Kronecker pencils, Albert determinants and Smith normal forms.

Description: The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.

Description: Although shear banding is a ubiquitous phenomenon observed in soft materials, the mechanisms that give rise to shear-band formation are not always the same. In this work, we develop a new two-fluid model for semi-dilute entangled polymer solutions using the generalized bracket approach of nonequilibrium thermodynamics. The model is based on the hypothesis that the direct coupling between polymer stress and concentration is the driving mechanism of steady shear-band formation. To obtain smooth banded profiles in the two-fluid framework, a new stress-diffusive term is added to the time evolution equation for the conformation tensor. The advantage of the new model is that the differential velocity is treated as a state variable. This allows a straightforward implementation of the additional boundary conditions arising from the derivative diffusive terms with respect to this new state variable. To capture the overshoot of the shear stress during the start of a simple shear flow, we utilize a nonlinear Giesekus relaxation. Moreover, we include an additional relaxation term that resembles the term used in the Rouse linear entangled polymer model to account for convective constraint release and chain stretch to generate the upturn of the flow curve at large shear rates. Numerical calculations performed for cylindrical Couette flow confirm the independency of the solution from the deformation history and initial conditions. Furthermore, we find that stress-induced migration is the responsible diffusive term for steady-state shear banding. Because of its simplicity, the new model is an ideal candidate for the use in the simulation of more complex flows.

Description: A typical experiment to measure monolayer surface rheological properties consists of two parallel, slightly immersed, moving solid barriers that compress and expand a shallow liquid layer that contains the surfactant monolayer in its free surface. The area between the barriers controls the surfactant concentration, which is frequently assumed as spatially constant. In order to minimize the fluid dynamics and other non-equilibrium effects, the barriers motion is very slow. Nevertheless, the surfactant concentration dynamics exhibit some unexpected features such as irreversibility, suggesting that the motion is not slow enough. We present a long wave theory that takes into account the fluid dynamics in the bulk phase coupled to the free surface elevation. In addition, apparent irreversibility is also discussed that may result from artifacts associated with the menisci dynamics when surface tension is measured using a Wilhelmy plate. Instead, additional, purely chemical, non-equilibrium effects are ignored. Results from this theory are discussed for varying values of the parameters, which permit establishing specific predictions on experiments. On the other hand, these results compare fairly well with the available experimental observations, at least qualitatively. The overall conclusion is that the fluid dynamics should not be ignored in the analysis of these experimental devices.

Description: We study the resonances of a forced turbulent wake past a flat-based bluff body using symmetric and antisymmetric actuation modes. The natural, unforced wake flow exhibits broadband dynamics superimposed on oscillatory motions linked to the reminiscent laminar Bénard-von Kármán instability in the turbulent flow. Harmonic and subharmonic resonances can be controlled by the phase relationship of periodic forcing and are linked to the symmetry properties of vortex shedding. Symmetric forcing leads to a strong subharmonic amplification of vortex shedding in the wake, but no harmonic excitation. The robustness of the subharmonic resonance is confirmed at different Reynolds numbers. Antisymmetric actuation, however, promotes a harmonic resonance with very similar wake and drag features.

Description: The spatial and orientational behaviour of fibres within a suspension influences the rheological and mechanical properties of that suspension. An Eulerian-Lagrangian framework to simulate the behaviour of fibres in turbulent flows is presented. The framework is intended for use in simulations of non-spherical particles with high Reynolds numbers, beyond the Stokesian regime, and is a computationally efficient alternative to existing Stokesian models for fibre suspensions in turbulent flow. It is based on modifying available empirical drag correlations for the translation of non-spherical particles to be orientation dependent, accounting for the departure in shape from a sphere. The orientational dynamics of a particle is based on the framework of quaternions, while its rotational dynamics is obtained from the solution of the Euler equation of rotation subject to external torques on the particle. The fluid velocity and turbulence quantities are obtained using a very high-resolution large eddy simulation with dynamic calibration of the sub-grid scale energy containing fluid motions. The simulation matrix consists of four different fibre Stokes numbers ( St = 1, 5, 25, and 125) and five different fibre aspect ratios (λ = 1.001, 3, 10, 30, and 50), with results considered at four distances from a channel wall (in the viscous sub-layer, buffer, and fully turbulent regions), which are taken as a measure of the flow velocity gradient, all at a constant fibre to fluid density ratio ( ρ p / ρ = 760) and shear Reynolds number Re τ = 150. The simulated fibre orientation, concentration, and streakiness confirm previous experimentally observed characteristics of fibre behaviour in turbulence, and that of direct numerical simulations of fibres in Stokesian, or creeping flow, regimes. The fibres exhibit translational motion similar to spheres, where they tend to accumulate in the near-wall (viscous sub-layer and buffer) region and preferentially concentrate in regions of low-speed streaks. The current results further demonstrate that the fibres’ translational dynamics, in terms of preferential concentration, is strongly dependent on their inertia and less so on their aspect ratio. However, the contrary is the case for the fibre alignment distribution as this is strongly dependent on the fibre aspect ratio and velocity gradient, and only moderately dependent on particle inertia. The fibre alignment with the flow direction is found to be mostly anisotropic where the velocity gradient is large (i.e., viscous sub-layer and buffer regions), but is virtually non-existent and isotropic where the turbulence is near-isotropic (i.e., channel centre). The present investigation highlights that the level of fibre alignment with the flow direction reduces as a fibre’s inertia decreases, and as the shape of the fibre approaches that of a sphere. Short fibres, and especially near-spherical λ = 1.001 particles, are found to exhibit isotropic orientation with respect to all directions, whilst sufficiently long fibres align themselves parallel to the flow direction, and orthogonal to the other two co-ordinate directions, and the vorticity and flow velocity gradient directions.

Description: In this study, we attempt to bring out a generalized formulation for electro-osmotic flows over inhomogeneously charged surfaces in presence of non-electrostatic ion-ion interactions. To this end, we start with modified electro-chemical potential of the individual species and subsequently use it to derive modified Nernst-Planck equation accounting for the ionic fluxes generated because of the presence of non-electrostatic potential. We establish what we refer to as the Poisson-Helmholtz-Nernst-Planck equations, coupled with the Navier-Stokes equations, to describe the complete transport process. Our analysis shows that the presence of non-electrostatic interactions between the ions results in an excess body force on the fluid, and modifies the osmotic pressure as well, which has hitherto remained unexplored. We further apply our analysis to a simple geometry, in an effort to work out the Smoluchowski slip velocity for thin electrical double layer limits. To this end, we employ singular perturbation and develop a general framework for the asymptotic analysis. Our calculations reveal that the final expression for slip velocity remains the same as that without accounting for non-electrostatic interactions. However, the presence of non-electrostatic interactions along with ion specificity can significantly change the quantitative behavior of Smoluchowski slip velocity. We subsequently demonstrate that the presence of non-electrostatic interactions may significantly alter the effective interfacial potential, also termed as the “Zeta potential.” Our analysis can potentially act as a guide towards the prediction and possibly quantitative determination of the implications associated with the existence of non-electrostatic potential, in an electrokinetic transport process.

Description: In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac–Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.

Description: An adaptation of the Wentzel–Kramers–Brilluoin method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between the phase σ ( r → ) of a wave function exp i ħ σ ( r → ) and its respective Wigner function is derived. Formulas to calculate the Wigner function of a product and of a superposition of wave functions are proposed. Properties of a Wigner function of interfering states are also investigated. Examples of this quasi–classical approximation in deformation quantization are analysed. A strict form of the Wigner function for states represented by tempered generalised functions has been derived. Wigner functions of unbound states in the Poeschl–Teller potential have been found.

Description: Supercooled large droplet (SLD), which can cause abnormal icing, is a well-known issue in aerospace engineering. Although efforts have been exerted to understand large droplet impact dynamics and the supercooled feature in the film/substrate interface, respectively, the thermodynamic effect during the SLD impact process has not received sufficient attention. This work conducts experimental studies to determine the effects of drop size on the thermodynamics for supercooled large droplet impingement. Through phenomenological reproduction, the rapid-freezing characteristics are observed in diameters of 400, 800, and 1300 μ m. The experimental analysis provides information on the maximum spreading rate and the shrinkage rate of the drop, the supercooled diffusive rate, and the freezing time. A physical explanation of this unsteady heat transfer process is proposed theoretically, which indicates that the drop size is a critical factor influencing the supercooled heat exchange and effective heat transfer duration between the film/substrate interface. On the basis of the present experimental data and theoretical analysis, an impinging heating model is developed and applied to typical SLD cases. The model behaves as anticipated, which underlines the wide applicability to SLD icing problems in related fields.

Description: Quantum Stein’s lemma is a cornerstone of quantum statistics and concerns the problem of correctly identifying a quantum state, given the knowledge that it is one of two specific states ( ρ or σ ). It was originally derived in the asymptotic i.i.d. setting, in which arbitrarily many (say, n ) identical copies of the state ( ρ ⊗ n or σ ⊗ n ) are considered to be available. In this setting, the lemma states that, for any given upper bound on the probability α n of erroneously inferring the state to be σ , the probability β n of erroneously inferring the state to be ρ decays exponentially in n , with the rate of decay converging to the relative entropy of the two states. The second order asymptotics for quantum hypothesis testing, which establishes the speed of convergence of this rate of decay to its limiting value, was derived in the i.i.d. setting independently by Tomamichel and Hayashi, and Li. We extend this result to settings beyond i.i.d. Examples of these include Gibbs states of quantum spin systems (with finite-range, translation-invariant interactions) at high temperatures, and quasi-free states of fermionic lattice gases.

Description: We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of temperature and dissipation strength.

Description: In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.

Description: A functional realization of the Lie algebra s l 3 , R as a Vessiot–Guldberg–Lie algebra of second order differential equation (SODE) Lie systems is proposed. It is shown that a minimal Vessiot–Guldberg–Lie algebra L V G is obtained from proper subalgebras of s l 3 , R for each of the SODE Lie systems of this type by particularization of one functional and two scalar parameters of the s l 3 , R -realization. The relation between the various Vessiot–Guldberg–Lie algebras by means of a limiting process in the scalar parameters further allows to define a notion of contraction of SODE Lie systems.

Description: We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.

Description: Precession has been proposed as an alternative power source for planetary dynamos. Previous hydrodynamic simulations suggested that precession can generate very complex flows in planetary liquid cores [Y. Lin, P. Marti, and J. Noir, “Shear-driven parametric instability in a precessing sphere,” Phys. Fluids 27 , 046601 (2015)]. In the present study, we numerically investigate the magnetohydrodynamics of a precessing sphere. We demonstrate precession driven dynamos in different flow regimes, from laminar to turbulent flows. In particular, we highlight the magnetic field generation by large scale cyclonic vortices, which has not been explored previously. In this regime, dynamos can be sustained at relatively low Ekman numbers and magnetic Prandtl numbers, which paves the way for planetary applications.

Description: A mathematical model for the dip coating process has been developed for cylindrical geometries with non-Newtonian fluids. This investigation explores the effects of the substrate radius and hydrodynamic behavior of the non-Newtonian viscous fluid on the resulting thin film on the substrate. The coating fluid studied, Dymax 1186-MT, is a resin for fiber optics and used as a matrix to suspend 1 vol. % titanium dioxide particles. The coating substrate is a 100 μ m diameter fiber optic diffuser. Ellis viscosity model is applied as a non-Newtonian viscous model for coating thickness prediction, including the influence of viscosity in low shear rates that occurs near the surface of the withdrawal film. In addition, the results of the Newtonian and power law models are compared with the Ellis model outcomes. The rheological properties and surface tension of fluids were analyzed and applied in the models and a good agreement between experimental and analytical solutions was obtained for Ellis model.

Description: Direct numerical simulations (DNS) are used to systematically study the development and establishment of turbulence when the flow is initialized with concentrated regions of intense kinetic energy. This resembles both active and passive grids which have been extensively used to generate and study turbulence in laboratories at different Reynolds numbers and with different characteristics, such as the degree of isotropy and homogeneity. A large DNS database was generated covering a wide range of initial conditions with a focus on perturbations with some directional preference, a condition found in active jet grids and passive grids passed through a contraction as well as a new type of active grid inspired by the experimental use of lasers to photo-excite the molecules that comprise the fluid. The DNS database is used to assert under what conditions the flow becomes turbulent and if so, the time required for this to occur. We identify a natural time scale of the problem which indicates the onset of turbulence and a single Reynolds number based exclusively on initial conditions which controls the evolution of the flow. It is found that a minimum Reynolds number is needed for the flow to evolve towards fully developed turbulence. An extensive analysis of single and two point statistics, velocity as well as spectral dynamics and anisotropy measures is presented to characterize the evolution of the flow towards realistic turbulence.

Description: We study the Schrödinger operator with a constant magnetic field in the exterior of a compact domain in Euclidean space. Functions in the domain of the operator are subject to a boundary condition of the third type (a magnetic Robin condition). In addition to the Landau levels, we obtain that the spectrum of this operator consists of clusters of eigenvalues around the Landau levels and that they do accumulate to the Landau levels from below. We give a precise asymptotic formula for the rate of accumulation of eigenvalues in these clusters, which is independent of the boundary condition.

Description: We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.

Description: We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.

Description: This study is concerned with the investigation of two-vortex systems (2VS) of various strengths that are released near the ground and evolve in the presence of a turbulent crosswind. We analyze the physics of the vortices interactions with the turbulent wind and with the ground during the rebound phase, and that lead to the fully developed turbulent flow and interactions. The transport and decay of the vortices are also analyzed. The turbulent wind itself is obtained by direct numerical simulation using a half channel flow. The flow is then supplemented with the 2VS, using vortices with a circulation distribution that is representative of vortices after roll-up of a near wake. The vortex strengths, Γ 0 , are such that Re Γ = Γ 0 / ν = 2.0 × 10 4 for the baseline; there is then a case with twice weaker vortices, and a case with twice stronger vortices. The simulations are run in wall-resolved Large Eddy Simulation (LES) mode. The baseline is in line with the wall-resolved LES study of a similar case [A. Stephan et al. , “Aircraft wake-vortex decay in ground proximity—Physical mechanisms and artificial enhancement,” J. Aircr. 50 (4), 1250–1260 (2013)]. They highlighted the significant effect that the near-wall streaks of the wind have on the development of instabilities in the secondary vortices, and the ensuing turbulence. Our analysis complements theirs by also showing the significant effect that the wind turbulent structures, away from the ground and that are stretched by the primary vortices, also have on the destabilization of the secondary vortices. Comparisons are also made with the most recent study [F. N. Holzäpfel et al. , “Wind impact on single vortices and counter-rotating vortex pairs in ground proximity,” in 7th AIAA Atmospheric and Space Environments Conference, AIAA Aviation (American Institute of Aeronautics and Astronautics, 2015)], where Re Γ = 2.0 × 10 4 for all cases and where it is the wind intensity that is varied. Diagnostics on the vortex trajectories and circulation decay are provided, for the mean and for the envelopes of behaviour. The results are discussed and compared with the recent literature. In particular, for the case with relatively twice stronger wind relative to the vortices, the upwind vortex quickly looses its coherence when it comes closest to the ground and does not rebound; the physics of that are explained by a long wave instability excited by the turbulent wind. Finally, a case where the baseline wake is released at a lower altitude is also studied, to support an analysis on what is the proper length scale to use, and initial time, when comparing results of wakes released at different altitudes: indeed, when normalized using those quantities, the trajectory and decay curves of this case are seen to collapse very well with those of the baseline.

Description: Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincaré duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincaré duality for the new cohomology groups.

Description: We introduce the notion of a universal odd generalized Poisson superalgebra associated with an associative algebra A , by generalizing a construction made in the work of De Sole and Kac [Jpn. J. Math. 8 , 1–145 (2013)]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n -Nambu-Poisson algebras over an algebraically closed field of characteristic zero.

Description: Phototaxis is a directed swimming response dependent upon the light intensity sensed by microorganisms. Positive (negative) phototaxis denotes the motion directed towards (away from) the source of light. In this paper, we simulate numerically penetrative phototactic bioconvection in a non-scattering suspension of phototactic algae in the non-linear regime. The suspension is confined by a stress-free top boundary, and rigid bottom and lateral boundaries. The algae receive light from the source directly above it and thus they swim vertically upward by neglecting the effects of scattering. We use the phototaxis model proposed by Vincent and Hill [“Bioconvection in a suspension of phototactic algae,” J. Fluid Mech. 327 , 343 (1996)] to investigate the onset of bioconvection in two dimensions using the stream function-vorticity formulation. The critical conditions from the onset of bioconvection are used to study the effects of different governing parameters on the structure and stability of the obtained solutions. The resulting bioconvective patterns differ qualitatively from those found by Ghorai and Hill [“Penetrative phototactic bioconvection,” Phys. Fluids 17 , 074101 (2005)] at some particular swimming velocity of microorganisms due to rigid lateral walls. A significant stabilizing effect on suspension has been also observed due to lateral rigid walls for some governing parameters.

Description: This paper presents two sets of analytical exact solutions for collisionless gas flows from a planar exit, impinging at an inclined flat plate. These analytical results are obtained by using gaskinetic theories. The first set of solutions are for a diffuse reflective plate surface, and the other set of solutions are for a specular reflective plate surface. A virtual nozzle exit is adopted to aid analyzing the specular reflective plate scenario. New formulas for plate surface properties, including velocity slips, pressure, shear stress, and heat flux distributions, are provided. For both problems, the flowfield exact solutions are investigated as well. Numerical simulations with the direct simulation Monte Carlo method are performed to validate these new analytical results, and good agreement is obtained for flows with high Knudsen numbers. The results consider effects from many factors, such as the plate inclination angle, geometry ratios, and exit gas and plate properties (such as exit gas bulk density, gas speed ratio, and exit gas and plate temperatures). Compared with past work, these new solutions are more comprehensive and practical. The results also illustrate that if the plate is quite close to the nozzle exit, it is improper to adopt the traditional treatments of a point source and a simple cosine function.

Description: In this work, we study the flow of a conducting fluid inside a two-dimensional square domain. The problem is solved by using a variational multiscale finite element approach. The study focuses on a high magnetic interaction parameter range and high Reynolds number. Under the imposition of a high magnetic field, the flow gets regularized, but fast transient phenomena take place, which could lead to numerical errors. An expression to compute the maximum time step that guarantees convergence in explicit schemes is proposed and validated through numerical tests.

Description: The higher-order superintegrability of the two-dimensional isotonic oscillator (noncentral oscillator with inversely quadratic nonlinearities also known as caged anisotropic oscillator) with rational ratio of frequencies is directly related with the existence of some complex functions with interesting Poisson bracket properties. First the properties of these functions are studied and then it is proved that these complex functions determine the existence of a bi-Hamiltonian complex structure. In the second part several real symplectic structures are obtained and the properties of the recursion operators are studied.

Description: We study finite W -algebras associated to even regular (principal) nilpotent elements for the family of simple exceptional Lie superalgebras D (2, 1; α ) and for the universal central extension of

Description: As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.

Description: The objective of this investigation is to study the influence of superheat temperature and applied uniform electric field across the liquid-vapor interface during film boiling using a coupled level set and volume of fluid algorithm. The hydrodynamics of bubble growth, detachment, and its morphological variation with electrohydrodynamic forces are studied considering the medium to be incompressible, viscous, and perfectly dielectric at near critical pressure. The transition in interfacial instability behavior occurs with increase in superheat, the bubble release being periodic both in space and time. Discrete bubble growth occurs at a smaller superheat whereas vapor columns form at the higher superheat values. Destabilization of interfacial motion due to applied electric field results in decrease in bubble separation distance and increase in bubble release rate culminating in enhanced heat transfer rate. A comparison of maximum bubble height owing to application of different intensities of electric field is performed at a smaller superheat. The change in dynamics of bubble growth due to increasing superheat at a high intensity of electric field is studied. The effect of increasing intensity of electric field on the heat transfer rate at different superheats is determined. The boiling characteristic is found to be influenced significantly only above a minimum critical intensity of the electric field.

Description: In the present study, we conduct unsteady three-dimensional simulations of flows around a helically twisted elliptic (HTE) cylinder at the Reynolds numbers of 100 and 3900, based on the free-stream velocity and square root of the product of the lengths of its major and minor axes. A parametric study is conducted for Re = 100 by varying the aspect ratio ( AR ) of the elliptic cross section and the helical spanwise wavelength ( λ ). Depending on the values of AR and λ , the flow in the wake contains the characteristic wavelengths of λ , 2 λ , 6 λ , or even longer than 60 λ , showing a wide diversity of flows in the wake due to the shape change. The drag on the optimal (i.e., having lowest drag) HTE cylinder ( AR = 1.3 and λ = 3.5 d ) is lower by 18% than that of the circular cylinder, and its lift fluctuations are zero owing to complete suppression of vortex shedding in the wake. This optimal HTE configuration reduces the drag by 23% for Re = 3900 where the wake is turbulent, showing that the HTE cylinder reduces the mean drag and lift fluctuations for both laminar and turbulent flows.

Description: The tunnel noise in a Mach 5.9 Ludwieg tube is determined by two methods, a newly developed cone-probe-DNS method and a reliable hot-wire-Pitot-probe method. The new method combines pressure and heat flux measurements using a cone probe and direct numerical simulation (DNS). The modal analysis is based on transfer functions obtained by the DNS to link the measured quantities to the tunnel noise. The measurements are performed for several unit-Reynolds numbers in the range of 5 ⋅ 10 6 ≤ Re/m ≤ 16 ⋅ 10 6 and probe positions to identify the sensitivities of tunnel noise. The DNS solutions show similar response mechanisms of the cone probe to incident acoustic and entropy waves which leads to high condition numbers of the transfer matrix such that a unique relationship between response and source mechanism can be only determined by neglecting the contribution of the non-acoustic modes to the pressure and heat flux fluctuations. The results of the cone-probe-DNS method are compared to a modal analysis based on the hot-wire-Pitot-probe method which provides reliable results in the frequency range less than 50 kHz. In this low frequency range the findings of the two different mode analyses agree well. At higher frequencies, the newly developed cone-probe-DNS method is still valid. The tunnel noise is dominated by the acoustic mode, since the entropy mode is lower by one order of magnitude and the vorticity mode can be neglected. The acoustic mode is approximately 0.5% at 30 kHz and the cone-probe-DNS data illustrate the acoustic mode to decrease and to asymptotically approach 0.2%.

Description: The propagation of high-frequency sound waves in binary gas mixtures flowing through microchannels is investigated by using the linearized Boltzmann equation based on a Bhatnagar-Gross-Krook (BGK)-type approach and diffuse reflection boundary conditions. The results presented refer to mixtures whose constituents have comparable molecular mass (like Ne-Ar) as well as to disparate-mass gas mixtures (composed of very heavy plus very light molecules, like He-Xe). The sound wave propagation model considered in the present paper allows to analyze the precise nature of the forced-sound modes excited in different gas mixtures.

Description: In this work, a transition scenario is demonstrated, in which most of the stages are followed analytically. The transition is initiated by the linear transient growth mechanism in plane Poiseuille flow subjected to an infinitesimally small secondary disturbance. A novel analytical approximation of the linear transient growth mechanism enables us to perform a secondary linear stability analysis of the modified base-flow. Two possible routes to transition are highlighted here, both correspond to a small secondary disturbance superimposed on a linear transient growth. The first scenario is initiated by four decaying odd normal modes which form a counter-rotating vortex pair; the second is initiated by five even decaying modes which form a pair of counter-rotating pairs. The approximation of the linear transient growth stage by a combination of minimal number of modes allows us to follow the transition stages analytically by employing the multiple time scale method. In particular, the secondary instability stage is followed analytically using linear tools, and is verified by obtaining transition in a direct numerical simulation initiated by conditions dictated by the transient growth analytical expressions. Very good agreement is observed, verifying the theoretical model. The similarities between the two transition routes are discussed and the results are compared with similar results obtained for plane Couette flow.

Description: A one-dimensional electrified viscoelastic model is built to study the nonlinear behavior of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field. The equations are solved numerically using an implicit finite difference scheme together with a boundary element method. The electrified viscoelastic jet is found to evolve into a beads-on-string structure in the presence of the radial electric field. Although the radial electric field greatly enhances the linear instability of the jet, its influence on the decay of the filament thickness is limited during the nonlinear evolution of the jet. On the other hand, the radial electric field induces axial non-uniformity of the first normal stress difference within the filament. The first normal stress difference in the center region of the filament may be greatly decreased by the radial electric field. The regions with/without satellite droplets are illuminated on the χ (the electrical Bond number)- k (the dimensionless wave number) plane. Satellite droplets may be formed for larger wave numbers at larger radial electric fields.

Description: The spectra of turbulent heat flux H( k ) in Rayleigh-Bénard convection with and without uniform rotation are presented. The spectrum H( k ) scales with wave number k as ∼ k −2 . The scaling exponent is almost independent of the Taylor number Ta and Prandtl number Pr for higher values of the reduced Rayleigh number r (〉10 3 ). The exponent, however, depends on Ta and Pr for smaller values of r (

Description: We report on the rebound of high velocity continuous water droplet streams from the surface of an immiscible oil pool. The droplets have diameters and velocities of less than 90 μ m and 15 m/s, respectively, and were created at frequencies up to 60 kHz. The impact and rebound of continuous droplet streams at this scale and velocity have been largely unexplored. This regime bridges the gap between single drop and jet impacts. The impinging droplets create a divot at the surface of the oil pool that had a common characteristic shape across a wide-range of droplet and oil properties. After impact, the reflected droplets maintain the same uniformity and periodicity of the incoming droplets but have significantly lower velocity and kinetic energy. This was solely attributed to the generation of a flow induced in the viscous oil pool by the impacting droplets. Unlike normally directed impact of millimeter-scale droplets with a solid surface, our results show that an air film does not appear to be maintained beneath the droplets during impact. This suggests direct contact between the droplets and the surface of the oil pool. A ballistic failure limit, correlated with the Weber number, was identified where the rebound was suppressed and the droplets were driven through the oil surface. A secondary failure mode was identified for aperiodic incoming streams. Startup effects and early time dynamics of the rebounding droplet stream were also investigated.

Description: We investigate the spectrum of the self-similar Laplacian, which generates the so-called “ pq random walk” on the integer half-line ℤ + . Using the method of spectral decimation, we prove that the spectral type of the Laplacian is singularly continuous whenever p ≠ 1 2 . This serves as a toy model for generating singularly continuous spectrum, which can be generalized to more complicated settings. We hope it will provide more insight into Fibonacci-type and other weakly self-similar models.

Description: In this paper, we study Lie super-bialgebra and quantization of the super Virasoro algebra, whose even part is the centerless twisted Heisenberg-Virasoro algebra. By using some Liu-Pei-Zhu’s results, we prove that all Lie super-bialgebra structures on the super Virasoro algebra are triangular coboundary. Furthermore, we quantize the super Virasoro algebra by the Drinfel’d twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras.

Description: The method of pulsed liquid superheating in a tension wave that forms when a compression pulse is reflected from the liquid free surface has been used to investigate the kinetics of spontaneous cavitation in liquid nitrogen. The limiting tensile stress p n of nitrogen corresponding to nucleation rates J = 10 20 − 10 22 s −1 m −3 and the slope of the temperature dependence of the nucleation rate G T = d ln J / dT have been determined by experiment. The results of experiments are compared with classical nucleation theory (CNT) and a modified classical nucleation theory (MCNT), which takes into account the size dependence of the properties of a critical bubble. It has been noted that experimental data are in better agreement with the results of MCNT than with those of CNT.