ALBERT

Description: A fully nonlinear solution for bi-chromatic progressive waves in water of finite depth in the framework of the homotopy analysis method (HAM) is derived. The bi-chromatic wave field is assumed to be obtained by the nonlinear interaction of two monochromatic wave trains that propagate independently in the same direction before encountering. The equations for the mass, momentum, and energy fluxes based on the accurate high-order homotopy series solutions are obtained using a discrete integration and a Fourier series-based fitting. The conservation equations for the mean rates of the mass, momentum, and energy fluxes before and after the interaction of the two nonlinear monochromatic wave trains are proposed to establish the relationship between the steady-state bi-chromatic wave field and the two nonlinear monochromatic wave trains. The parametric analysis on ε 1 and ε 2 , representing the nonlinearity of the bi-chromatic wave field, is performed to obtain a sufficiently small standard deviation S d , which is applied to describe the deviation from the conservation state ( S d = 0) in terms of the mean rates of the mass, momentum, and energy fluxes before and after the interaction. It is demonstrated that very small standard deviation from the conservation state can be achieved. After the interaction, the amplitude of the primary wave with a lower circular frequency is found to decrease; while the one with a higher circular frequency is found to increase. Moreover, the highest horizontal velocity of the water particles underneath the largest wave crest, which is obtained by the nonlinear interaction between the two monochromatic waves, is found to be significantly higher than the linear superposition value of the corresponding velocity of the two monochromatic waves. The present study is helpful to enrich and deepen the understanding with insight to steady-state wave-wave interactions.

Description: A numerical investigation of the vortex-induced vibration (VIV) in a side-by-side circular cylinder arrangement has been performed in a two-dimensional laminar flow environment. One of the cylinders is elastically mounted and only vibrates in the transverse direction, while its counterpart remains stationary in a uniform flow stream. When the gap ratio is sufficiently small, the flip-flopping phenomenon of the gap flow can be an additional time-dependent interference to the flow field. This phenomenon was reported in the experimental work of Bearman and Wadcock [“The interaction between a pair of circular cylinders normal to a stream,” J. Fluid Mech. 61 (3), 499–511 (1973)] in a side-by-side circular cylinder arrangement, in which the gap flow deflects toward one of the cylinders and switched its sides intermittently. Albeit one of the two cylinders is free to vibrate, the flip-flop of a gap flow during VIV dynamics can still be observed outside the lock-in region. The exact moments of the flip-flop phenomenon due to spontaneous symmetry breaking are observed in this numerical study. The significant characteristic vortex modes in the near-wake region are extracted via dynamic modal analysis and the interference between the gap flow and VIV is found to be mutual. In a vibrating side-by-side arrangement, the lock-in region with respect to reduced velocity becomes narrower due to the interference from its stationary counterpart. The frequency lock-in occurs and ends earlier than that of an isolated vibrating circular cylinder subjected to an identical flow environment. Similar to a tandem cylinder arrangement, in the post-lock-in region, the maximum vibration amplitudes are escalated compared with those of an isolated circular cylinder configuration. On the other hand, subjected to the influence from VIV, the biased gap flow deflects toward the vibrating cylinder quasi-stably during the frequency lock-in process. This behavior is different from the reported bi-stable regime in a stationary side-by-side arrangement. The analyses show that the flip-flop is associated with a characteristic low flip-flopping frequency, which is dependent upon the values of gap ratio, Reynolds number and the symmetry of the gap flow strength in a time-averaged sense. The disappearance of the flip-flop during the frequency lock-in of vibrating side-by-side arrangements is further investigated through a critical-point concept and a critical vortex merging distance.

Description: The non-isothermal extrudate swell of a high molecular weight high-density polyethylene (HDPE) in long capillary and slit dies is studied numerically (ANSYS POLYFLOW ® ) using an integral K-BKZ constitutive model including crystallization kinetics, determined experimentally. The Nakamura model is used for crystallization of the HDPE, where the crystallization rate parameter is evaluated by using the well-known Ziabicki equation. This non-isothermal extrudate swell phenomenon is simulated using the pseudo-time integral K-BKZ model with the Wagner damping function along with the differential form of the Nakamura model to account for the crystallization of the extrudate. The swell measurements were carried out under non-isothermal conditions by extruding the polymer melt at 200 °C through long capillary and slit dies to ambient air at 25 °C, 110 °C, and 200 °C. The numerical results are found to be in excellent agreement with experimental observations.

Description: The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers (Re T ) ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos while increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun, C. K. and Ding, E.-J., “Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state,” Phys. Fluids 15 , 1612 (2003)]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.

Description: This is a review of results from studies of the effect of artificially restricted geometry (the size effect) on the superconducting properties of nanoparticles of low-melting metals (Hg, Pb, Sn, In). Restricted geometrical conditions are created by embedding molten metals under high pressure into nanoporous matrices of two types: channel structures based on chrysotile asbestos and porous alkali-borosilicate glasses. Chrysotile asbestos is a system of parallel nanotubes with channel diameters ranging from 2 to 20 nm and an aspect ratio (channel length to diameter) of up to 10 7 . The glasses are a random dendritic three-dimensional system of interconnected channels with a technologically controllable mean diameter of 2–30 nm. Temperature dependences of the resistance and heat capacity in the region of the superconducting transition and the dependences of the critical temperature on the mean pore diameter are obtained. The critical magnetic fields are also determined.

Description: The electronic structure of FeSe, the simplest iron-based superconductor (Fe-SC), conceals a potential of dramatic increase of T c that realizes under pressure or in a single layer film. This is also the system where nematicity, the phenomenon of a keen current interest, is most easy to study since it is not accompanied by the antiferromagnetic transition like in all other Fe-SC's. Here we overview recent experimental data on electronic structure of FeSe-based superconductors: isovalently doped crystals, intercalates, and single layer films, trying to clarify its topology and possible relation of this topology to superconductivity. We argue that the marked differences between the experimental and calculated band structures for all FeSe compounds can be described by a hoping selective renormalization model for a spin/orbital correlated state that may naturally explain both the evolution of the band structure with temperature and nematicity.

Description: A comprehensive study of superconductor-constriction-superconductor contacts, obtained using the “break junction” technique in layered superconductors. Depending on the constriction transparency, tunneling and SnS-Andreev spectroscopies could be used to directly determine the values of the superconducting gaps, characteristic BCS ratios and temperature dependences of the gaps in cuprates, magnesium diboride and iron pnictides and chalcogenides. Based on these results we can estimate the gap anisotropy and the electron-boson coupling constants. The advantages and drawbacks of “break junction” technique are discussed, and we demonstrate that this method is powerful enough for the study of optical phonon modes in high-temperature superconducting cuprates and for creating contacts with selective transparency in Mg 1- x Al x B 2 compounds.

Description: Results are presented from a theoretical study of the possibility of hole carrier localization and metal-insulator transitions which show up in the temperature dependences of the magnetic susceptibility χ( T ) of doped copper-oxide (cuprate) compounds. The criteria for metal-insulator transitions owing to strong hole-lattice interactions and the formation of very narrow polaron bands in these materials with reduced doping level x are analyzed. It is shown that these kinds of metal-insulator transitions occur in underdoped La 2- x Sr x CuO 4 and YBa 2 Cu 3 O 6+ x cuprates (i.e., for x ranging from 0.04 to 0.12). The characteristic temperature dependences χ( T ) of the HTSC cuprates are found for different doping levels. These results are in good agreement with experimental data on metal-insulator transitions and the magnetic susceptibility of the HTSC cuprates.

Description: The possibility of an anomalous structure in the differential conductivity of tunnel junctions based on high-temperature superconductors as a result of degradation of their surface layer is analyzed. This feature is in the form of two peaks near an energy gap separated by a region of suppressed conductivity. One peak is usually high and sharp, while the other is much more spread out. Differential conductivity and shot noise spectra in contacts of a normal injector with s - and d -type superconductors are calculated and compared. It is shown that combined measurements of these two characteristics can provide new information on the kinetics of transport processes in these structures.

Description: During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.