ALBERT

Description: 〈p〉Publication date: Available online 1 November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity〈/p〉 〈p〉Author(s): Robert J. Kunsch, Erich Novak, Daniel Rudolf〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a sample size based on a variance estimation, or – more generally – based on an estimation of a (central absolute) 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉p〈/mi〉〈/math〉-moment. That way one can guarantee a small absolute error with high probability, the problem is thus called solvable. The expected cost of the method depends on the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉p〈/mi〉〈/math〉-moment of the random variable, which can be arbitrarily large. In order to prove the optimality of our algorithm we also provide lower bounds. These bounds apply not only to methods based on i.i.d. samples but also to general randomized algorithms. They show that – up to constants – the cost of the algorithm is optimal in terms of accuracy, confidence level, and norm of the particular input random variable. Since the considered classes of random variables or integrands are very large, the worst case cost would be infinite. Nevertheless one can define adaptive stopping rules such that for each input the expected cost is finite. We contrast these positive results with examples of integration problems that are not solvable.〈/p〉〈/div〉

Description: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers in Industry, Volume 104〈/p〉 〈p〉Author(s): Jacques Bahi, Wiem Elghazel, Christophe Guyeux, Mourad Hakem, Kamal Medjaher, Noureddine Zerhouni〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Monitoring activities in industry may require the use of wireless sensor networks, for instance due to difficult access or hostile environment. But it is well known that this type of networks has various limitations like the amount of disposable energy. Indeed, once a sensor node exhausts its resources, it will be dropped from the network, stopping so to forward information about maybe relevant features towards the sink. This will result in broken links and data loss which impacts the diagnostic accuracy at the sink level. It is therefore important to keep the network's monitoring service as long as possible by preserving the energy held by the nodes. As packet transfer consumes the highest amount of energy comparing to other activities in the network, various topologies are usually implemented in wireless sensor networks to increase the network lifetime. In this paper, we emphasize that it is more difficult to perform a good diagnostic when data are gathered by a wireless sensor network instead of a wired one, due to broken links and data loss on the one hand, and deployed network topologies on the other hand. Three strategies are considered to reduce packet transfers: (1) sensor nodes send directly their data to the sink, (2) nodes are divided by clusters, and the cluster heads send the average of their clusters directly to the sink, and (3) averaged data are sent from cluster heads to cluster heads in a hop-by-hop mode, leading to an avalanche of averages. Their impact on the diagnostic accuracy is then evaluated. We show that the use of random forests is relevant for diagnostics when data are aggregated through the network and when sensors stop to transmit their values when their batteries are emptied. This relevance is discussed qualitatively and evaluated numerically by comparing the random forests performance to state-of-the-art PHM approaches, namely: basic bagging of decision trees, support vector machine, multinomial naive Bayes, AdaBoost, and Gradient Boosting. Finally, a way to couple the two best methods, namely the random forests and the gradient boosting, is proposed by finding the best hyperparameters of the former by using the latter.〈/p〉〈/div〉

Description: Public key encryption with disjunctive keyword search (PEDK) is a public key encryption scheme that allows disjunctive keyword search over encrypted data without decryption. This kind of scheme is crucial to cloud storage and has received a lot of attention in recent years. However, the efficiency of the previous scheme is limited due to the selection of a less efficient converting method which is used to change query and index keywords into a vector space model. To address this issue, we design a novel converting approach with better performance, and give two adaptively secure PEDK schemes based on this method. The first one is built on an efficient inner product encryption scheme with less searching time, and the second one is constructed over composite order bilinear groups with higher efficiency on index and trapdoor construction. The theoretical analysis and experiment results verify that our schemes are more efficient in time and space complexity as well as more suitable for the mobile cloud setting compared with the state-of-art schemes.

Description: Numerical investigations on flow and heat transfer characteristics in the heat exchanger tube with the V-wavy surface are presented. The finite volume method with the SIMPLE algorithm is selected to solve the present problem. The effects of flow attack angles (α = 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, and 60°) and flow directions (V-tip pointing downstream known as “V-Downstream” and V-tip pointing upstream known as “V-Upstream”) for the V-wavy surface on flow and heat transfer patterns are considered for both laminar and turbulent regions. The laminar regime is studied in the range Re = 100–1200, while the turbulent region is investigated in the range Re = 3000–10,000. The mechanisms on flow and heat transfer in the test section are reported. The numerical results reveal that the V-wavy surface changes the flow structure in the test section. The vortex flow is produced by the V-wavy surface. The vortex flow disturbs the thermal boundary layer on the heat transfer surface that is the reason for heat transfer and thermal performance enhancements. The optimum flow attack angles of the V-wavy surface for laminar and turbulent regimes are concluded.

Description: 〈p〉Publication date: 15 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 379〈/p〉 〈p〉Author(s): Takashi Shiroto, Naofumi Ohnishi, Yasuhiko Sentoku〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solved the first-principle equations of kinetic plasmas, such as the relativistic Vlasov–Maxwell system. This fatal problem is brought by the fact that both the Vlasov and Maxwell equations are indirectly associated with the conservation laws by means of some mathematical manipulations. Here we propose a quadratic conservative scheme, which can strictly maintain the conservation laws by discretizing the relativistic Vlasov–Maxwell system. A discrete product rule and summation-by-parts are the key players in the construction of the quadratic conservative scheme. Numerical experiments of the relativistic two-stream instability and relativistic Weibel instability prove the validity of our computational theory, and the proposed strategy will open the doors to the first-principle studies of mesoscopic and macroscopic plasma physics.〈/p〉〈/div〉

Description: Wu et al. (2014) showed that under the small set expansion hypothesis (SSEH) there is no polynomial time approximation algorithm with any constant approximation factor for several graph width parameters, including tree-width, path-width, and cut-width (Wu et al. 2014). In this paper, we extend this line of research by exploring other graph width parameters: We obtain similar approximation hardness results under the SSEH for rank-width and maximum induced matching-width, while at the same time we show the approximation hardness of carving-width, clique-width, NLC-width, and boolean-width. We also give a simpler proof of the approximation hardness of tree-width, path-width, and cut-widththan that of Wu et al.

Description: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 122〈/p〉 〈p〉Author(s): Hassan Talebi, Ute Mueller, Raimon Tolosana-Delgado〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Ore deposits usually consist of ore materials with different discrete (e.g. rock and alteration types) and continuous (e.g. geochemical and mineral composition) features. Financial feasibility studies are highly dependent on the modelling of these features and their associated joint uncertainties. Few geostatistical techniques have been developed for the joint modelling of high-dimensional mixed data (continuous and categorical) or constrained data, such as compositional data. The compositional nature of the mineral and geochemical data induces several challenges for multivariate geostatistical techniques, because such data carry relative information and are known for spurious statistical and spatial correlation effects. This paper investigates the application of the direct sampling algorithm for joint modelling of compositional and categorical data. In some mining projects the amount of available data may be enormous in some parts of the deposit and if the density of measurements is sufficient, multivariate geospatial patterns can be derived from that data and be simulated (without model inference) at other undersampled areas of the deposit with similar characteristics. In this context, the direct sampling multiple-point simulation method can be implemented for this reconstruction process. The compositional nature of the data is addressed via implementing an isometric log-ratio transformation. The approach is illustrated through two case studies, one synthetic and one real. The accuracy of the results is checked against a set of validation data, revealing the potential of the proposed methodology for joint modelling of compositional and categorical information. The direct sampling technique can be considered as a smart move to assess the future risk and uncertainty of a resource by making use of all the information hidden within the early data.〈/p〉〈/div〉 〈/div〉

Description: 〈p〉The small molecules thalidomide, lenalidomide, and pomalidomide induce the ubiquitination and proteasomal degradation of the transcription factors Ikaros (IKZF1) and Aiolos (IKZF3) by recruiting a Cys〈sub〉2〈/sub〉-His〈sub〉2〈/sub〉 (C2H2) zinc finger domain to Cereblon (CRBN), the substrate receptor of the CRL4〈sup〉CRBN〈/sup〉 E3 ubiquitin ligase. We screened the human C2H2 zinc finger proteome for degradation in the presence of thalidomide analogs, identifying 11 zinc finger degrons. Structural and functional characterization of the C2H2 zinc finger degrons demonstrates how diverse zinc finger domains bind the permissive drug-CRBN interface. Computational zinc finger docking and biochemical analysis predict that more than 150 zinc fingers bind the drug-CRBN complex in vitro, and we show that selective zinc finger degradation can be achieved through compound modifications. Our results provide a rationale for therapeutically targeting transcription factors that were previously considered undruggable.〈/p〉

Description: 〈p〉Speleothem oxygen isotope records have revolutionized our understanding of the paleo East Asian monsoon, yet there is fundamental disagreement on what they represent in terms of the hydroclimate changes. We report a multiproxy speleothem record of monsoon evolution during the last deglaciation from the middle Yangtze region, which indicates a wetter central eastern China during North Atlantic cooling episodes, despite the oxygen isotopic record suggesting a weaker monsoon. We show that this apparent contradiction can be resolved if the changes are interpreted as a lengthening of the Meiyu rains and shortened post-Meiyu stage, in accordance with a recent hypothesis. Model simulations support this interpretation and further reveal the role of the westerlies in communicating the North Atlantic influence to the East Asian climate.〈/p〉

Description: 〈p〉The pathologic accumulation and aggregation of α-synuclein (α-syn) underlies Parkinson’s disease (PD). The molecular mechanisms by which pathologic α-syn causes neurodegeneration in PD are not known. Here, we found that pathologic α-syn activates poly(adenosine 5'-diphosphate–ribose) (PAR) polymerase-1 (PARP-1), and PAR generation accelerates the formation of pathologic α-syn, resulting in cell death via parthanatos. PARP inhibitors or genetic deletion of PARP-1 prevented pathologic α-syn toxicity. In a feed-forward loop, PAR converted pathologic α-syn to a more toxic strain. PAR levels were increased in the cerebrospinal fluid and brains of patients with PD, suggesting that PARP activation plays a role in PD pathogenesis. Thus, strategies aimed at inhibiting PARP-1 activation could hold promise as a disease-modifying therapy to prevent the loss of dopamine neurons in PD.〈/p〉

Description: 〈p〉Broadly neutralizing antibodies against highly variable pathogens have stimulated the design of vaccines and therapeutics. We report the use of diverse camelid single-domain antibodies to influenza virus hemagglutinin to generate multidomain antibodies with impressive breadth and potency. Multidomain antibody MD3606 protects mice against influenza A and B infection when administered intravenously or expressed locally from a recombinant adeno-associated virus vector. Crystal and single-particle electron microscopy structures of these antibodies with hemagglutinins from influenza A and B viruses reveal binding to highly conserved epitopes. Collectively, our findings demonstrate that multidomain antibodies targeting multiple epitopes exhibit enhanced virus cross-reactivity and potency. In combination with adeno-associated virus–mediated gene delivery, they may provide an effective strategy to prevent infection with influenza virus and other highly variable pathogens.〈/p〉

Description: 〈p〉Gut microbes live in symbiosis with their hosts, but how mutualistic animal-microbe interactions emerge is not understood. By adaptively evolving the opportunistic fungal pathogen 〈i〉Candida albicans〈/i〉 in the mouse gastrointestinal tract, we selected strains that not only had lost their main virulence program but also protected their new hosts against a variety of systemic infections. This protection was independent of adaptive immunity, arose as early as a single day postpriming, was dependent on increased innate cytokine responses, and was thus reminiscent of "trained immunity." Because both the microbe and its new host gain some advantages from their interaction, this experimental system might allow direct study of the evolutionary forces that govern the emergence of mutualism between a mammal and a fungus.〈/p〉

Description: 〈p〉The synthesis of ultrasmall supported bimetallic nanoparticles (between 1 and 3 nanometers in diameter) with well-defined stoichiometry and intimacy between constituent metals remains a substantial challenge. We synthesized 10 different supported bimetallic nanoparticles via surface inorganometallic chemistry by decomposing and reducing surface-adsorbed heterometallic double complex salts, which are readily obtained upon sequential adsorption of target cations and anions on a silica substrate. For example, adsorption of tetraamminepalladium(II) [Pd(NH〈sub〉3〈/sub〉)〈sub〉4〈/sub〉〈sup〉2+〈/sup〉] followed by adsorption of tetrachloroplatinate [PtCl〈sub〉4〈/sub〉〈sup〉2–〈/sup〉] was used to form palladium-platinum (Pd-Pt) nanoparticles. These supported bimetallic nanoparticles show enhanced catalytic performance in acetylene selective hydrogenation, which clearly demonstrates a synergistic effect between constituent metals.〈/p〉

Description: 〈p〉Gradient structures exist ubiquitously in nature and are increasingly being introduced in engineering. However, understanding structural gradient–related mechanical behaviors in all gradient structures, including those in engineering materials, has been challenging. We explored the mechanical performance of a gradient nanotwinned structure with highly tunable structural gradients in pure copper. A large structural gradient allows for superior work hardening and strength that can exceed those of the strongest component of the gradient structure. We found through systematic experiments and atomistic simulations that this unusual behavior is afforded by a unique patterning of ultrahigh densities of dislocations in the grain interiors. These observations not only shed light on gradient structures, but may also indicate a promising route for improving the mechanical properties of materials through gradient design.〈/p〉

Description: 〈p〉Publication date: Available online 14 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Mehdi Samiee, Mohsen Zayernouri, Mark M. Meerschaert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present the stability and error analysis of the unified Petrov–Galerkin spectral method, developed in [1], for linear fractional partial differential equations with two-sided derivatives and constant coefficients in any (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mn〉1〈/mn〉〈mo〉+〈/mo〉〈mi〉d〈/mi〉〈/math〉)-dimensional space-time hypercube, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉d〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mn〉3〈/mn〉〈mo〉,〈/mo〉〈mo〉⋯〈/mo〉〈/math〉, subject to homogeneous Dirichlet initial/boundary conditions. Specifically, we prove the existence and uniqueness of the weak form and perform the corresponding stability and error analysis of the proposed method. Finally, we perform several numerical simulations to compare the theoretical and computational rates of convergence.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Giovanni Soligo, Alessio Roccon, Alfredo Soldati〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we propose and test the validity of a modified Phase Field Method (PFM), which is specifically developed for large scale simulations of turbulent flows with large and deformable surfactant-laden droplets. The time evolution of the phase field, 〈em〉ϕ〈/em〉, and of the surfactant concentration field, 〈em〉ψ〈/em〉, are obtained from two Cahn–Hilliard-like equations together with a two-order-parameter Time-Dependent Ginzburg–Landau (TDGL) free energy functional. The modifications introduced circumvent existing limitations of current approaches based on PFM and improve the well-posedness of the model. The effect of surfactant on surface tension is modeled via an Equation Of State (EOS), further improving the flexibility of the approach. This method can efficiently handle topological changes, i.e. breakup and coalescence, and describe adsorption/desorption of surfactant. The capabilities of the proposed approach are tested in this paper against previous experimental results on the effects of surfactant on the deformation of a single droplet and on the interactions between two droplets. Finally, to appreciate the performances of the model on a large scale complex simulation, a qualitative analysis of the behavior of surfactant-laden droplets in a turbulent channel flow is presented and discussed.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Sergii V. Siryk〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We provide a careful Fourier analysis of the Guermond–Pasquetti mass lumping correction technique (Guermond and Pasquetti, 2013 [11]) applied to pure transport and convection–diffusion problems. In particular, it is found that increasing the number of corrections reduces the accuracy for problems with diffusion; however all the corrected schemes are more accurate than the consistent Galerkin formulation in this case. For the pure transport problems the situation is the opposite. We also investigate the differences between two numerical solutions – the consistent solution and the corrected ones, and show that increasing the number of corrections makes solutions of the corrected schemes closer to the consistent solution in all cases.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Adam S. Jermyn〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is actually set not by the rank but by the mutual information amongst the variables in question. Representations such as the tensor tree perform near-optimally when the tree decomposition is chosen to reflect the correlation structure in question, but making such a choice is non-trivial and good heuristics remain highly context-specific. In this work I present two new algorithms for choosing efficient tree decompositions, independent of the physical context of the tensor. The first is a brute-force algorithm which produces optimal decompositions up to truncation error but is generally impractical for high-rank tensors, as the number of possible choices grows exponentially in rank. The second is a greedy algorithm, and while it is not optimal it performs extremely well in numerical experiments while having runtime which makes it practical even for tensors of very high rank.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Lam H. Nguyen, Dominik Schillinger〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We describe a local iterative corrector scheme that significantly improves the accuracy of the multiscale finite element method (MsFEM). Our technique is based on the definition of a local corrector problem for each multiscale basis function that is driven by the residual of the previous multiscale solution. Each corrector problem results in a local corrector solution that improves the accuracy of the corresponding multiscale basis function at element interfaces. We cast the strategy of residual-driven correction in an iterative scheme that is straightforward to implement and, due to the locality of corrector problems, well-suited for parallel computing. We show that the iterative scheme converges to the best possible fine-mesh solution. Finally, we illustrate the effectiveness of our approach with multiscale benchmarks characterized by missing scale separation, including the microCT-based stress analysis of a vertebra with trabecular microstructure.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Brody Bassett, Brian Kiedrowski〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The meshless local Petrov–Galerkin (MLPG) method is applied to the steady-state and 〈em〉k〈/em〉-eigenvalue neutron transport equations, which are discretized in energy using the multigroup approximation and in angle using the discrete ordinates approximation. To prevent oscillations in the neutron flux, the MLPG transport equation is stabilized by the streamline upwind Petrov–Galerkin (SUPG) method. Global neutron conservation is enforced by using moving least squares basis and weight functions and appropriate SUPG parameters. The cross sections in the transport equation are approximated in accordance with global particle balance and without constraint on their spatial dependence or the location of the basis and weight functions. The equations for the strong-form meshless collocation approach are derived for comparison to the MLPG equations. The method of manufactured solutions is used to verify the resulting MLPG method in one, two and three dimensions. Results for realistic problems, including two-dimensional pincells, a reflected ellipsoid and a three-dimensional problem with voids, are verified by comparison to Monte Carlo simulations.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 28 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Frederic Gibou, David Hyde, Ron Fedkiw〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a review on numerical methods for simulating multiphase and free surface flows. We focus in particular on numerical methods that seek to preserve the discontinuous nature of the solutions across the interface between phases. We provide a discussion on the Ghost-Fluid and Voronoi Interface methods, on the treatment of surface tension forces that avoid stringent time step restrictions, on adaptive grid refinement techniques for improved efficiency and on parallel computing approaches. We present the results of some simulations obtained with these treatments in two and three spatial dimensions. We also provide a discussion of Machine Learning and Deep Learning techniques in the context of multiphase flows and propose several future potential research thrusts for using deep learning to enhance the study and simulation of multiphase flows.〈/p〉〈/div〉 〈h5〉Graphical abstract〈/h5〉 〈div〉〈p〉〈/p〉〈/div〉 〈figure〉〈img src="https://ars.els-cdn.com/content/image/1-s2.0-S0021999118303371-gr001.jpg" width="500" alt="Graphical abstract for this article" title=""〉〈/figure〉

Description: 〈p〉Publication date: Available online 26 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Xiaodong Liu, Jiguang Sun〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Inverse scattering has been an active research area for the past thirty years. While very successful in many cases, progress has lagged when only 〈em〉limited-aperture〈/em〉 measurement is available. In this paper, we perform some elementary study to recover data that can not be measured directly. In particular, we aim at recovering the 〈em〉full-aperture〈/em〉 far field data from 〈em〉limited-aperture〈/em〉 measurement. Due to the reciprocity relation, the multi-static response matrix (MSR) has a symmetric structure. Using the Green's formula and single layer potential, we propose two schemes to recover 〈em〉full-aperture〈/em〉 MSR. The recovered data is tested by a recently proposed direct sampling method and the factorization method. Numerical results show that it is possible to, at least, partially recover the missing data and consequently improve the reconstruction of the scatterer.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): D. Reiser, J. Romazanov, Ch. Linsmeier〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The problem of constructing Monte-Carlo solutions of drift-diffusion systems corresponding to Fokker–Planck equations with sources and sinks is revisited. Firstly, a compact formalism is introduced for the specific problem of stationary solutions. This leads to identification of the dwell time as the key quantity to characterize the system and to obtain a proper normalization for statistical analysis of numerical results. Secondly, the question of appropriate track length estimators for drift-diffusion systems is discussed for a 1D model system. It is found that a simple track length estimator can be given only for pure drift motion without diffusion. The stochastic nature of the diffusive part cannot be appropriately described by the path length of simulation particles. Further analysis of the usual situation with inhomogeneous drift and diffusion coefficients leads to an error estimate based on particle trajectories. The result for limits in grid cell size and time step used for the construction of Monte-Carlo trajectories resembles the Courant-Friedrichs-Lewy and von Neumann conditions for explicit methods.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Dinshaw S. Balsara, Roger Käppeli〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The time-dependent equations of computational electrodynamics (CED) are evolved consistent with the divergence constraints on the electric displacement and magnetic induction vector fields. Respecting these constraints has proved to be very useful in the classic finite-difference time-domain (FDTD) schemes. As a result, there has been a recent effort to design finite volume time domain (FVTD) and discontinuous Galerkin time domain (DGTD) schemes that satisfy the same constraints and, nevertheless, draw on recent advances in higher order Godunov methods. This paper catalogues the first step in the design of globally constraint-preserving DGTD schemes. The algorithms presented here are based on a novel DG-like method that is applied to a Yee-type staggering of the electromagnetic field variables in the faces of the mesh. The other two novel building blocks of the method include constraint-preserving reconstruction of the electromagnetic fields and multidimensional Riemann solvers; both of which have been developed in recent years by the first author.〈/p〉 〈p〉The resulting DGTD scheme is linear, at least when limiters are not applied to the DG scheme. As a result, it is possible to carry out a von Neumann stability analysis of the entire suite of DGTD schemes for CED at orders of accuracy ranging from second to fourth. The analysis requires some simplifications in order to make it analytically tractable, however, it proves to be extremely instructive. A von Neumann stability analysis is a necessary precursor to the design of a full DGTD scheme for CED. It gives us the maximal CFL numbers that can be sustained by the DGTD schemes presented here at all orders. It also enables us to understand the wave propagation characteristics of the schemes in various directions on a Cartesian mesh. We find that constraint-preserving DGTD schemes permit CFL numbers that are competitive with conventional DG schemes. However, like conventional DG schemes, the CFL of DGTD schemes decreases with increasing order. To counteract that, we also present constraint-preserving PNPM schemes for CED. We find that the third and fourth order constraint-preserving DGTD and P1PM schemes have some extremely attractive properties when it comes to low-dispersion, low-dissipation propagation of electromagnetic waves in multidimensions. Numerical accuracy tests are also provided to support the von Neumann stability analysis. We expect these methods to play a role in those problems of engineering CED where exceptional precision must be achieved at any cost.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Yinghe Qi, Jiacai Lu, Ruben Scardovelli, Stéphane Zaleski, Grétar Tryggvason〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface separating two immiscible fluids, given the volume fraction in the cell and the adjacent cells. Currently, the most accurate approach is to fit a curve (2D), or a surface (3D), matching the volume fractions and finding the curvature by differentiation. Here, a different approach is examined. A synthetic data set, relating curvature to volume fractions, is generated using well-defined shapes where the curvature and volume fractions are easily found and then machine learning is used to fit the data (training). The resulting function is used to find the curvature for shapes not used for the training and implemented into a code to track moving interfaces. The results suggest that using machine learning to generate the relationship is a viable approach that results in reasonably accurate predictions.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Mani Razi, Robert M. Kirby, Akil Narayan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we introduce a novel approach for the construction of multi-fidelity surrogate models with “discrete” fidelity levels. The notion of a discrete level of fidelity is in contrast to a mathematical model, for which the notion of refinement towards a high-fidelity model is relevant to sending a discretization parameter toward zero in a continuous way. Our notion of discrete fidelity levels encompasses cases for which there is no notion of convergence in terms of a fidelity parameter that can be sent to zero or infinity. The particular choice of how levels of fidelity are defined in this framework paves the way for using models that may have no apparent physical or mathematical relationship to the target high-fidelity model. However, our approach requires that models can produce results with a common set of parameters in the target model. Hence, fidelity level in this work is not directly representative of the degree of similarity of a low-fidelity model to a target high-fidelity model. In particular, we show that our approach is applicable to competitive ecological systems with different numbers of species, discrete-state Markov chains with a different number of states, polymer networks with a different number of connections, and nano-particle plasmonic arrays with a different number of scatterers. The results of this study demonstrate that our procedure boasts computational efficiency and accuracy for a wide variety of models and engineering systems.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Hasan Almanasreh〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work we will treat the spurious eigenvalues obstacle that appears in the computation of the radial Dirac eigenvalue problem using numerical methods. The treatment of the spurious solution is based on applying Petrov–Galerkin finite element method. The significance of this work is the employment of just continuous basis functions, thus the need of a continuous function which has a continuous first derivative as a basis, as in [2], [3], is no longer required. The Petrov–Galerkin finite element method for the Dirac eigenvalue problem strongly depends on a stability parameter, 〈em〉τ〈/em〉, that controls the size of the diffusion terms added to the finite element formulation for the problem. The mesh-dependent parameter 〈em〉τ〈/em〉 is derived based on the given problem with the particular basis functions.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): S.B. Adrian, F.P. Andriulli, T.F. Eibert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a Calderón preconditioner for the electric field integral equation (EFIE), which does not require a barycentric refinement of the mesh and which yields a Hermitian, positive definite (HPD) system matrix allowing for the usage of the conjugate gradient (CG) solver. The resulting discrete equation system is immune to the low-frequency and the dense-discretization breakdown and, in contrast to existing Calderón preconditioners, no second discretization of the EFIE operator with Buffa–Christiansen (BC) functions is necessary. This preconditioner is obtained by leveraging on spectral equivalences between (scalar) integral operators, namely the single layer and the hypersingular operator known from electrostatics, on the one hand, and the Laplace–Beltrami operator on the other hand. Since our approach incorporates Helmholtz projectors, there is no search for global loops necessary and thus our method remains stable on multiply connected geometries. The numerical results demonstrate the effectiveness of this approach for both canonical and realistic (multi-scale) problems.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 February 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Mehdi Samiee, Mohsen Zayernouri, Mark M. Meerschaert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We develop a unified Petrov–Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mmultiscripts〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈none〉〈/none〉〈none〉〈/none〉〈mrow〉〈mn〉2〈/mn〉〈mi〉τ〈/mi〉〈/mrow〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈none〉〈/none〉〈/mmultiscripts〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈msubsup〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msubsup〉〈mo stretchy="false"〉[〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉l〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉r〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo stretchy="false"〉]〈/mo〉〈mo〉+〈/mo〉〈mi〉γ〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉u〈/mi〉〈mo〉=〈/mo〉〈msubsup〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msubsup〉〈mo stretchy="false"〉[〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉κ〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉l〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉κ〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉r〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo stretchy="false"〉]〈/mo〉〈mo〉+〈/mo〉〈mi〉f〈/mi〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈mi〉τ〈/mi〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈mi〉τ〈/mi〉〈mo〉≠〈/mo〉〈mn〉1〈/mn〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, in a (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" overflow="scroll"〉〈mn〉1〈/mn〉〈mo〉+〈/mo〉〈mi〉d〈/mi〉〈/math〉)-dimensional 〈em〉space–time〈/em〉 hypercube, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.gif" overflow="scroll"〉〈mi〉d〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mn〉3〈/mn〉〈mo〉,〈/mo〉〈mo〉⋯〈/mo〉〈/math〉, subject to homogeneous Dirichlet initial/boundary conditions. We employ the eigenfunctions of the fractional Sturm–Liouville eigen-problems of the first kind in [1], called 〈em〉Jacobi poly-fractonomial〈/em〉s, as temporal bases, and the eigen-functions of the boundary-value problem of the second kind as temporal test functions. Next, we construct our spatial basis/test functions using Legendre polynomials, yielding mass matrices being independent of the spatial fractional orders (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉i〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉j〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mo〉⋯〈/mo〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈/math〉). Furthermore, we formulate a novel unified fast linear solver for the resulting high-dimensional linear system based on the solution of generalized eigen-problem of spatial mass matrices with respect to the corresponding stiffness matrices, hence, making the complexity of the problem optimal, i.e., 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.gif" overflow="scroll"〉〈mi mathvariant="script"〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈mo〉+〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉. We carry out several numerical test cases to examine the CPU time and convergence rate of the method. The corresponding stability and error analysis of the Petrov–Galerkin method are carried out in [2].〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Ruilian Du, Yubin Yan, Zongqi Liang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A new high-order finite difference scheme to approximate the Caputo fractional derivative 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/mfrac〉〈mo stretchy="true" maxsize="2.4ex" minsize="2.4ex"〉(〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mmultiscripts〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈/mrow〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈/mmultiscripts〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo〉+〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mmultiscripts〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈/mrow〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈/mmultiscripts〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="true" maxsize="2.4ex" minsize="2.4ex"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉k〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈mi〉N〈/mi〉〈/math〉, with the convergence order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si160.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈msup〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈mo〉−〈/mo〉〈mi〉α〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.gif" overflow="scroll"〉〈mi〉α〈/mi〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is obtained when 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si123.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈mrow〉〈mo〉‴〈/mo〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo〉=〈/mo〉〈mn〉0〈/mn〉〈/math〉, where Δ〈em〉t〈/em〉 denotes the time step size. Based on this scheme we introduce a finite difference method for solving fractional diffusion wave equation with the convergence order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈msup〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈mo〉−〈/mo〉〈mi〉α〈/mi〉〈/mrow〉〈/msup〉〈mo〉+〈/mo〉〈msup〉〈mrow〉〈mi〉h〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, where 〈em〉h〈/em〉 denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Jie Du, Yang Yang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Local discontinuous Galerkin (LDG) methods are popular for convection-diffusion equations. In LDG methods, we introduce an auxiliary variable 〈em〉p〈/em〉 to represent the derivative of the primary variable 〈em〉u〈/em〉, and solve them on the same mesh. It is well known that the maximum-principle-preserving (MPP) LDG method is only available up to second-order accuracy. Recently, we introduced a new algorithm, and solve 〈em〉u〈/em〉 and 〈em〉p〈/em〉 on different meshes, and obtained stability and optimal error estimates. In this paper, we will continue this approach and construct MPP third-order LDG methods for convection-diffusion equations on overlapping meshes. The new algorithm is more flexible and does not increase any computational cost. Numerical evidence will be given to demonstrate the accuracy and good performance of the third-order MPP LDG method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Yunchang Seol, Yu-Hau Tseng, Yongsam Kim, Ming-Chih Lai〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a two-dimensional immersed boundary method is developed to simulate the dynamics of Newtonian vesicle in viscoelastic Oldroyd-B fluid under shear flow. The viscoelasticity effect of extra stress is well incorporated into the immersed boundary formulation using the indicator function. Our numerical methodology is first validated in comparison with theoretical results in purely Newtonian fluid, and then a series of numerical experiments is conducted to study the effects of different dimensionless parameters on the vesicle motions. Although the tank-treading (TT) motion of Newtonian vesicle in Oldroyd-B fluid under shear flow can be observed just like in Newtonian fluid, it is surprising to find that the stationary inclination angle can be negative without the transition to tumbling (TB) motion. Moreover, the inertia effect plays a significant role that is able to turn the vesicle back to positive inclination angle through TT-TB-TT transition as the Reynolds number increases. To the best of our knowledge, this is the first numerical work for the detailed investigations of Newtonian vesicle dynamics suspended in viscoelastic Oldroyd-B fluid. We believe that our numerical results can be used to motivate further studies in theory and experiments for such coupling vesicle problems.〈/p〉〈/div〉

Description: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 122〈/p〉 〈p〉Author(s): Seth Goodman, Ariel BenYishay, Zhonghui Lv, Daniel Runfola〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Interdisciplinary use of geospatial data requires the integration of data from a breadth of sources, and frequently involves the harmonization of different methods of sampling, measurement, and technical data types. These integrative efforts are often inhibited by fundamental geocomputational challenges, including a lack of memory efficient or parallel processing approaches to traditional methods such as zonal statistics. GeoQuery (〈a href="http://geoquery.org/" target="_blank"〉geoquery.org〈/a〉) is a dynamic web application which utilizes a High Performance Computing cluster and novel parallel geospatial data processing methods to overcome these challenges. Through an online interface, GeoQuery users can request geospatial data - which spans categories including geophysical, environmental and social measurements - to be aggregated to user-selected units of analysis (e.g., subnational administrative boundaries). Once a request has been processed, users are provided with permanent links to access their customized data and documentation. Datasets made available through GeoQuery are reviewed, prepared, and provisioned by geospatial data specialists, with processing routines tailored for each dataset. The code used and steps taken while preparing datasets and processing user requests are publicly available, ensuring transparency and replicability of all data and processes. By mediating the complexities of working with geospatial data, GeoQuery reduces the barriers to entry and the related costs of incorporating geospatial data into research across disciplines. This paper presents the technology and methods used by GeoQuery to process and manage geospatial data and user requests.〈/p〉〈/div〉 〈/div〉

Description: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 123〈/p〉 〈p〉Author(s): Pouyan Pirnia, François Duhaime, Yannic Ethier, Jean-Sébastien Dubé〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The thermal, mechanical and hydrodynamic behaviour of porous media in geoscience applications is usually modelled through the finite-element (FEM) or finite-difference methods. These continuum models tend to perform poorly when modelling phenomena that are essentially dependent on behaviour at the particle scale or phenomena that are not accurately described by partial differential equations (PDE), such as internal erosion and filtration. The discrete nature of granular materials can be modelled through the discrete-element method (DEM). However, in some instances, DEM models would benefit from an interface with continuum models to solve coupled PDEs or to model phenomena that occur at a different scale. This paper introduces ICY, an interface between COMSOL Multiphysics, a commercial finite-element engine, and YADE, an open-source discrete-element code. The interface is centred on a JAVA class. It was verified using the simple example of a sphere falling in water according to Stokes’ law. For this example, the drag force was calculated in COMSOL and body forces (gravity, buoyancy and drag) on the sphere were summed in YADE. The paper also presents an application example for the interface based on the modelling of internal erosion tests.〈/p〉〈/div〉 〈/div〉 〈h5〉Graphical abstract〈/h5〉 〈div〉〈p〉〈figure〉〈img src="https://ars.els-cdn.com/content/image/1-s2.0-S0098300417313213-fx1.jpg" width="334" alt="Image 1" title="Image 1"〉〈/figure〉〈/p〉〈/div〉

Description: 〈p〉The bulk of Earth’s biological materials consist of few base substances—essentially proteins, polysaccharides, and minerals—that assemble into large varieties of structures. Multifunctionality arises naturally from this structural complexity: An example is the combination of rigidity and flexibility in protein-based teeth of the squid sucker ring. Other examples are time-delayed actuation in plant seed pods triggered by environmental signals, such as fire and water, and surface nanostructures that combine light manipulation with mechanical protection or water repellency. Bioinspired engineering transfers some of these structural principles into technically more relevant base materials to obtain new, often unexpected combinations of material properties. Less appreciated is the huge potential of using bioinspired structural complexity to avoid unnecessary chemical diversity, enabling easier recycling and, thus, a more sustainable materials economy.〈/p〉

Description: 〈p〉Composite materials with carbon nanotube and graphene additives have long been considered as exciting prospects among nanotechnology applications. However, after nearly two decades of work in the area, questions remain about the practical impact of nanotube and graphene composites. This uncertainty stems from factors that include poor load transfer, interfacial engineering, dispersion, and viscosity-related issues that lead to processing challenges in such nanocomposites. Moreover, there has been little effort to identify selection rules for the use of nanotubes or graphene in composite matrices for specific applications. This review is a critical look at the status of composites for developing high-strength, low-density, high-conductivity materials with nanotubes or graphene. An outlook of the different approaches that can lead to practically useful nanotube and graphene composites is presented, pointing out the challenges and opportunities that exist in the field.〈/p〉

Description: 〈p〉Exploration of intermediates that enable chemoselective cycloaddition reactions and expeditious construction of fused- or bridged-ring systems is a continuous challenge for organic synthesis. As an intermediate of interest, the oxyallyl cation has been harnessed to synthesize architectures containing seven-membered rings via (4+3) cycloaddition. However, its potential to access five-membered skeletons is underdeveloped, largely due to the thermally forbidden (3+2) pathway. Here, the combination of a tailored precursor and a Pd(0) catalyst generates a Pd-oxyallyl intermediate that cyclizes with conjugated dienes to produce a diverse array of tetrahydrofuran skeletons. The cycloaddition overrides conventional (4+3) selectivity by proceeding through a stepwise pathway involving a Pd-allyl transfer and ring closure sequence. Subsequent treatment of the (3+2) adducts with a palladium catalyst converts the heterocycles to the carbocyclic cyclopentanones.〈/p〉

Description: This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise variance and noise model, a bias correction term is added into the least squares estimate, and the system parameters and states are computed interactively. The proposed algorithm can generate the unbiased parameter estimate. Two illustrative examples are given to show the effectiveness of the proposed algorithm.

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 378〈/p〉 〈p〉Author(s): Oscar P. Bruno, Martín Maas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate and efficient for challenging configurations including randomly rough surfaces, deep corrugations, large periods, near grazing incidences, and, importantly, Wood-anomaly resonant frequencies. The proposed approach is based on use of certain “shifted equivalent sources” which enable FFT acceleration of a Wood-anomaly-capable quasi-periodic Green function introduced recently (Bruno and Delourme (2014) [4]). The Green-function strategy additionally incorporates an exponentially convergent shifted version of the classical 〈em〉spectral〈/em〉 series for the Green function. While the computing-cost asymptotics depend on the asymptotic configuration assumed, the computing costs rise at most linearly with the size of the problem for a number of important rough-surface cases we consider. In practice, single-core runs in computing times ranging from a fraction of a second to a few seconds suffice for the proposed algorithm to produce highly-accurate solutions in some of the most challenging contexts arising in applications.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 379〈/p〉 〈p〉Author(s): Denis S. Grebenkov, Sergey D. Traytak〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The generalized method of separation of variables (GMSV) is applied to solve boundary value problems for the Laplace operator in three-dimensional domains with disconnected spherical boundaries (e.g., an arbitrary configuration of non-overlapping partially reactive spherical sinks or obstacles). We consider both exterior and interior problems and all most common boundary conditions: Dirichlet, Neumann, Robin, and conjugate one. Using the translational addition theorems for solid harmonics to switch between the local spherical coordinates, we obtain a semi-analytical expression of the Green function as a linear combination of partial solutions whose coefficients are fixed by boundary conditions. Although the numerical computation of the coefficients involves series truncation and solution of a system of linear algebraic equations, the use of the solid harmonics as basis functions naturally adapted to the intrinsic symmetries of the problem makes the GMSV particularly efficient, especially for exterior problems. The obtained Green function is the key ingredient to solve boundary value problems and to determine various characteristics of stationary diffusion such as reaction rate, escape probability, harmonic measure, residence time, and mean first passage time, to name but a few. The relevant aspects of the numerical implementation and potential applications in chemical physics, heat transfer, electrostatics, and hydrodynamics are discussed.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Samar Chehade, Audrey Kamta Djakou, Michel Darmon, Gilles Lebeau〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Non Destructive Examination (NDE) of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, backwall …) of inspected blocks. For that purpose, the study of plane wave diffraction by a wedge is of great interest. The work presented here is preliminary research to model the case of an elastic wave diffracted by a wedge in the future, for which there exist various modeling approaches but the numerical aspects have only been developed for wedge angles lower than 〈em〉π〈/em〉. The spectral functions method has previously been introduced to solve the 2D diffraction problem of an immersed elastic wedge for angles lower than 〈em〉π〈/em〉. As a first step, the spectral functions method has been developed here for the diffraction on an acoustic wave by a stress-free wedge, in 2D and for any wedge angle, before studying the elastic wave diffraction from a wedge. In this method, the solution to the diffraction problem is expressed in terms of two unknown functions called the spectral functions. These functions are computed semi-analytically, meaning that they are the sum of two terms. One of them is determined exactly and the other is approached numerically, using a collocation method. A successful numerical validation of the method for all wedge angles is proposed, by comparison with the GTD (Geometrical Theory of Diffraction) solution derived from the exact Sommerfeld integral.〈/p〉〈/div〉

Description: The Recurrent Neural Network (RNN) utilizes dynamically changing time information through time cycles, so it is very suitable for tasks with time sequence characteristics. However, with the increase of the number of layers, the vanishing gradient occurs in the RNN. The Grid Long Short-Term Memory (GridLSTM) recurrent neural network can alleviate this problem in two dimensions by taking advantage of the two dimensions calculated in time and depth. In addition, the time sequence task is related to the information of the current moment before and after. In this paper, we propose a method that takes into account context-sensitivity and gradient problems, namely the Bidirectional Grid Long Short-Term Memory (BiGridLSTM) recurrent neural network. This model not only takes advantage of the grid architecture, but it also captures information around the current moment. A large number of experiments on the dataset LibriSpeech show that BiGridLSTM is superior to other deep LSTM models and unidirectional LSTM models, and, when compared with GridLSTM, it gets about 26 percent gain improvement.

Description: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 123〈/p〉 〈p〉Author(s): Timothy J. Naegeli, Jason Laura〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we present an extension to the Large Crater Clustering (LCC) tool set which places a cone of uncertainty around the trajectories of secondary impact craters to determine potential locations of source craters. The LCC tool set was a first step in the spatial quantification of primary and secondary cratering processes, which allows planetary geologists to accurately estimate the geologic age of a celestial surface. This work builds on the LCC tool set by accounting for the ambiguity of flight path trajectories through a Python script that leverages ArcGIS's ArcPy library. We chronicle the mechanics of the script, which creates geodetically correct cones then counts them within equally sized cells of a vector grid. We describe the process that was used to derive the shape of the cone and provide parameters for the sizes of the cones and the grid. We demonstrate that the cone of uncertainty has the ability to compensate for error in secondary crater trajectories by introducing deviation in the trajectory bearing and comparing the predicted primary crater location. We use two study areas on Mars as well as the entire lunar surface to illustrate the usefulness of the extension as an aid to human interpretation of back-projections.〈/p〉〈/div〉 〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Hong Fang, Yikun Hu, Caihui Yu, Ming Tie, Jie Liu, Chunye Gong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The mesh deformation method based on radial basis functions (RBF) has many advantages and is widely used. RBF based mesh deformation method mainly has two steps: data reduction and displacement interpolation. The data reduction step includes solving interpolation weight coefficients and searching for the node with the maximum interpolation error. The data reduction schemes based on greedy algorithm is used to select an optimum reduced set of surface mesh nodes. In this paper, a parallel mesh deformation method based on parallel data reduction and displacement interpolation is proposed. The proposed recurrence Choleskey decomposition method (RCDM) can decrease the computational cost of solving interpolation weight coefficients from 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mrow〉〈mo stretchy="true"〉(〈/mo〉〈msubsup〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈/mrow〉〈/msubsup〉〈mo stretchy="true"〉)〈/mo〉〈/mrow〉〈/math〉 to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mrow〉〈mo stretchy="true"〉(〈/mo〉〈msubsup〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msubsup〉〈mo stretchy="true"〉)〈/mo〉〈/mrow〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈/msub〉〈/math〉 denotes the number of support nodes. The technology of parallel computing is used to accelerate the searching for the node with the maximum interpolation error and displacement interpolation. The combination of parallel data reduction and parallel interpolation can greatly improve the efficiency of mesh deformation. Two typical deformation problems of the ONERA M6 and DLR-F6 wing-body-Nacelle-Pylon configuration are taken as the test cases to validate the proposed approach and can get up to 19.57 times performance improvement with the proposed approach. Finally, the aeroelastic response of HIRENASD wing-body configuration is used to verify the efficiency and robustness of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Daniil Bochkov, Frederic Gibou〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present two finite volume schemes to solve a class of Poisson-type equations subject to Robin boundary conditions in irregular domains with 〈em〉piecewise smooth〈/em〉 boundaries. The first scheme results in a symmetric linear system and produces second-order accurate numerical solutions with first-order accurate gradients in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msup〉〈/math〉-norm (for solutions with two bounded derivatives). The second scheme is nonsymmetric but produces second-order accurate numerical solutions as well as second-order accurate gradients in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msup〉〈/math〉-norm (for solutions with three bounded derivatives). Numerical examples are given in two and three spatial dimensions.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 19 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Mandeep Deka, Shuvayan Brahmachary, Ramakrishnan Thirumalaisamy, Amaresh Dalal, Ganesh Natarajan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We describe a new and simple strategy based on the Gauss divergence theorem for obtaining centroidal gradients on unstructured meshes. Unlike the standard Green–Gauss (SGG) reconstruction which requires face values of quantities whose gradients are sought, the proposed approach reconstructs the gradients using the normal derivative(s) at the faces. The new strategy, referred to as the Modified Green–Gauss (MGG) reconstruction results in consistent gradients which are at least first-order accurate on arbitrary polygonal meshes. We show that the MGG reconstruction is linearity preserving independent of the mesh topology and retains the consistent behaviour of gradients even on meshes with large curvature and high aspect ratios. The gradient accuracy in MGG reconstruction depends on the accuracy of discretisation of the normal derivatives at faces and this necessitates an iterative approach for gradient computation on non-orthogonal meshes. Numerical studies on different mesh topologies demonstrate that MGG reconstruction gives accurate and consistent gradients on non-orthogonal meshes, with the number of iterations proportional to the extent of non-orthogonality. The MGG reconstruction is found to be consistent even on meshes with large aspect ratio and curvature with the errors being lesser than those from linear least-squares reconstruction. A non-iterative strategy in conjunction with MGG reconstruction is proposed for gradient computations in finite volume simulations that achieves the accuracy and robustness of MGG reconstruction at a cost equivalent to that of SGG reconstruction. The efficacy of this strategy for fluid flow problems is demonstrated through numerical investigations in both incompressible and compressible regimes. The MGG reconstruction may, therefore, be viewed as a novel and promising blend of least-squares and Green–Gauss based approaches which can be implemented with little effort in open-source finite-volume solvers and legacy codes.〈/p〉〈/div〉