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At least 1,045 records · Page 58

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗

TTEthernet for Integrated Spacecraft Networks

Aerospace projects have traditionally employed federated avionics architectures, in which each computer system is designed to perform one specific function (e.g. navigation). There are obvious downsides to this approach, including excessive weight (from so much computing hardware), and inefficient processor utilization (since modern processors are capable of performing multiple tasks). There has therefore been a push for integrated modular avionics (IMA), in which common computing platforms can be leveraged for different purposes. This consolidation of multiple vehicle functions to shared computing platforms can significantly reduce spacecraft cost, weight, and design complexity. However, the application of IMA principles introduces significant challenges, as the data network must accommodate traffic of mixed criticality and performance levels - potentially all related to the same shared computer hardware. Because individual network technologies are rarely so competent, the development of truly integrated network architectures often proves unreasonable. Several different types of networks are utilized - each suited to support a specific vehicle function. Critical functions are typically driven by precise timing loops, requiring networks with strict guarantees regarding message latency (i.e. determinism) and fault-tolerance. Alternatively, non-critical systems generally employ data networks prioritizing flexibility and high performance over reliable operation. Switched Ethernet has seen widespread success filling this role in terrestrial applications. Its high speed, flexibility, and the availability of inexpensive commercial off-the-shelf (COTS) components make it desirable for inclusion in spacecraft platforms. Basic Ethernet configurations have been incorporated into several preexisting aerospace projects, including both the Space Shuttle and International Space Station (ISS). However, classical switched Ethernet cannot provide the high level of network determinism required by real-time spacecraft applications. Even with modern advancements, the uncoordinated (i.e. event-driven) nature of Ethernet communication unavoidably leads to message contention within network switches. The arbitration process used to resolve such conflicts introduces variation in the time it takes for messages to be forwarded. TTEthernet1 introduces decentralized clock synchronization to switched Ethernet, enabling message transmission according to a time-triggered (TT) paradigm. A network planning tool is used to allocate each device a finite amount of time in which it may transmit a frame. Each time slot is repeated sequentially to form a periodic communication schedule that is then loaded onto each TTEthernet device (e.g. switches and end systems). Each network participant references the synchronized time in order to dispatch messages at predetermined instances. This schedule guarantees that no contention exists between time-triggered Ethernet frames in the network switches, therefore eliminating the need for arbitration (and the timing variation it causes). Besides time-triggered messaging, TTEthernet networks may provide two additional traffic classes to support communication of different criticality levels. In the rate-constrained (RC) traffic class, the frame payload size and rate of transmission along each communication channel are limited to predetermined maximums. The network switches can therefore be configured to accommodate the known worst-case traffic pattern, and buffer overflows can be eliminated. The best-effort (BE) traffic class behaves akin to classical Ethernet. No guarantees are provided regarding transmission latency or successful message delivery. TTEthernet coordinates transmission of all three traffic classes over the same physical connections, therefore accommodating the full spectrum of traffic criticality levels required in IMA architectures. Common computing platforms (e.g. LRUs) can share networking resources in such a way that failures in non-critical systems (using BE or RC communication modes) cannot impact flight-critical functions (using TT communication). Furthermore, TTEthernet hardware (e.g. switches, cabling) can be shared by both TTEthernet and classical Ethernet traffic.

Loveless, Andrew↗

Measurement-induced criticality in random quantum circuits

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical-mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the n th Rényi entropies for n ≥ 1 in this limit using relatively recent results for the conformal field theory describing the critical theory of two-dimensional (2D) percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. Here, we also comment on the relation to the entanglement transition in random tensor networks, studied previously in Vasseur et al. [Phys. Rev. B 100, 134203 (2019)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exploring interlayer coupling in the twisted bilayer PtTe 2

We have investigated interlayer interactions in the bilayer PtTe 2 system, which influence the electronic energy bands near the Fermi level. Our diffusion Monte Carlo (DMC) calculations for the high-symmetry bilayer stackings (AA, AB, AC) manifest distinct interlayer binding characteristics among the stacking modes by revealing significantly different interlayer separations depending on the stacking, which is critical to understanding the interlayer coupling of the twisted bilayers consisting of various local stacking arrangements. Furthermore, a comparison between the interlayer separations obtained from DMC and density functional theory (DFT) shows that meta-generalized gradient approximation (GGA)-based van der Waals–DFT results agree with DMC for different layer stackings, including twisted bilayers, but only the ground-state AA stacking matches well with GGA-based DFT predictions. This underscores the importance of accurate exchange-correlation potentials even for capturing the stacking-dependent interlayer binding properties. We further show that the variability in DFT-predicted interlayer separations is responsible for the large discrepancy of band structures in the 21 . 79 ∘ twisted bilayer PtTe 2 , affecting its classification as metallic or insulating. These results demonstrate the importance of obtaining a correct description of stacking-dependent interlayer coupling in modeling delicate bilayer systems at finite twists. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Yao, Tse-Min↗

Advanced development of the boundary element method for steady-state heat conduction

Considerable progress has been made in recent years toward advancing the state-of-the-art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general-purpose boundary element method (BEM) for steady-state heat conduction. In particular, the BEM implementation involves the use of higher-order conforming elements, self-adaptive integration and multi-region capability. Two- and three-dimensional, as well as axisymmetric analysis, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three-dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady-state heat conduction.

Dargush, G. F.↗

Advances in reduction techniques for tire contact problems

Some recent developments in reduction techniques, as applied to predicting the tire contact response and evaluating the sensitivity coefficients of the different response quantities, are reviewed. The sensitivity coefficients measure the sensitivity of the contact response to variations in the geometric and material parameters of the tire. The tire is modeled using a two-dimensional laminated anisotropic shell theory with the effects of variation in geometric and material parameters, transverse shear deformation, and geometric nonlinearities included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The elemental arrays are obtained by using a modified two-field, mixed variational principle. For the application of reduction techniques, the tire finite element model is partitioned into two regions. The first region consists of the nodes that are likely to come in contact with the pavement, and the second region includes all the remaining nodes. The reduction technique is used to significantly reduce the degrees of freedom in the second region. The effectiveness of the computational procedure is demonstrated by a numerical example of the frictionless contact response of the space shuttle nose-gear tire, inflated and pressed against a rigid flat surface. Also, the research topics which have high potential for enhancing the effectiveness of reduction techniques are outlined.

Noor, Ahmed K.↗

A similarity hypothesis for the two-point correlation tensor in a temporally evolving plane wake

The analysis demonstrated that the governing equations for the two-point velocity correlation tensor in the temporally evolving wake admit similarity solutions, which include the similarity solutions for the single-point moment as a special case. The resulting equations for the similarity solutions include two constants, beta and Re(sub sigma), that are ratios of three characteristic time scales of processes in the flow: a viscous time scale, a time scale characteristic of the spread rate of the flow, and a characteristic time scale of the mean strain rate. The values of these ratios depend on the initial conditions of the flow and are most likely measures of the coherent structures in the initial conditions. The occurrences of these constants in the governing equations for the similarity solutions indicates that these solutions, in general, will only be the same for two flows if these two constants are equal (and hence the coherent structures in the flows are related). The comparisons between the predictions of the similarity hypothesis and the data presented here and elsewhere indicate that the similarity solutions for the two-point correlation tensors provide a good approximation of the measures of those motions that are not significantly affected by the boundary conditions caused by the finite extent of real flows. Thus, the two-point similarity hypothesis provides a useful tool for both numerical and physical experimentalist that can be used to examine how the finite extent of real flows affect the evolution of the different scales of motion in the flow.

Ewing, D. W.↗

Phase controlled metal–insulator transition in multi-leg quasiperiodic optical lattices

A tight-binding model of a multi-leg ladder network with a continuous quasiperiodic modulation in both the site potential and the inter-arm hopping integral is considered. The model mimics optical lattices where ultra-cold fermionic or bosonic atoms are trapped in double well potentials. It is observed that, the relative phase difference between the on-site potential and the inter-arm hopping integral, which can be controlled by the tuning of the interfering laser beams trapping the cold atoms, can result in a mixed spectrum of one or more absolutely continuous subband(s) and point like spectral measures. This opens up the possibility of a re-entrant metal–insulator transition. The subtle role played by the relative phase difference mentioned above is revealed, and we corroborate it numerically by working out the multi-channel electronic transmission for finite two-, and three-leg ladder networks. The extension of the calculation beyond the two-leg case is trivial, and is discussed in the work. - Graphical abstract: ▪ - Highlights: • Phase controlled metal–insulator transition is discussed. • An analytical prescription is given to understand MI transition. • Our work provides a way of designing experiments involving laser beams.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Low-Frequency Correlated Charge-Noise Measurements Across Multiple Energy Transitions in a Tantalum Transmon

Transmon qubits fabricated with tantalum metal have been shown to possess energy relaxation times greater than 400 𝜇⁢s and, as such, present an attractive platform for high precision, correlated noise studies across multiple higher-energy transitions. Tracking the multilevel fluctuating qudit frequencies with a precision enabled by the high coherence of the device allows us to extract the charge offset and quasiparticle dynamics. We observe qualitatively different charge-offset behavior in the tantalum device than those measured in previous low-frequency charge-noise studies. In particular, we find the charge-offset dynamics are dominated by rare, discrete jumps between a finite number of quasistationary charge configurations, a previously unobserved charge-noise process in superconducting qubits.

3-dimensional systems↗

Time-evolution methods for matrix-product states

Highlights: • Introductory review of time-evolution methods for matrix-product states. • Detailed description of five state-of-the-art algorithms. • Extended comparison of numerical examples. • Extended error analysis of each algorithm. • Pseudo-code examples towards an implementation where necessary. - Abstract: Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W{sup I,II} method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter–Gummel scheme to non-Boltzmann (e.g. Fermi–Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An incompressible Navier-Stokes flow solver in three-dimensional curvilinear coordinate systems using primitive variables

An implicit, finite-difference computer code has been developed to solve the incompressible Navier-Stokes equations in a three-dimensional, curvilinear coordinate system. The pressure-field solution is based on the pseudo compressibility approach in which the time derivative pressure term is introduced into the mass conservation equation to form a set of hyperbolic equations. The solution procedure employs an implicit, approximate factorization scheme. The Reynolds stresses, that are uncoupled from the implicit scheme, are lagged by one time-step to facilitate implementing various levels of the turbulence model. Test problems for external and internal flows are computed, and the results are compared with existing experimental data. The application of this technique for general three-dimensional problems is then demonstrated.

Kwak, D.↗

Effect of liquid droplets on turbulence in a round gaseous jet

The main objective of this investigation is to develop a two-equation turbulence model for dilute vaporizing sprays or in general for dispersed two-phase flows including the effects of phase changes. The model that accounts for the interaction between the two phases is based on rigorously derived equations for turbulence kinetic energy (K) and its dissipation rate epsilon of the carrier phase using the momentum equation of that phase. Closure is achieved by modeling the turbulent correlations, up to third order, in the equations of the mean motion, concentration of the vapor in the carrier phase, and the kinetic energy of turbulence and its dissipation rate for the carrier phase. The governing equations are presented in both the exact and the modeled formes. The governing equations are solved numerically using a finite-difference procedure to test the presented model for the flow of a turbulent axisymmetric gaseous jet laden with either evaporating liquid droplets or solid particles. The predictions include the distribution of the mean velocity, volume fractions of the different phases, concentration of the evaporated material in the carrier phase, turbulence intensity and shear stress of the carrier phase, droplet diameter distribution, and the jet spreading rate. The predictions are in good agreement with the experimental data.

Mostafa, A. A.↗

A Numerical and Experimental Study of Compression-Loaded Composite Panels With Cutouts

Results from a numerical and experimental study on the effects of laminate orthotropy and circular cutout size on the response of compression-loaded composite curved panels are presented. Several 60-in-radius composite panels with four different laminate configurations were tested with cutout diameters that range from 10% to 60% of the panel width. Finite-element analyses were performed for each panel in order to identify the effects boundary conditions, measured initial geometric imperfections and thickness variations had on the nonlinear and buckling behavior of the panels. The compression-loaded panels considered herein exhibited two separate types of behavior depending on the laminate stacking sequence and cutout size. More specifically, some of the panels exhibited the classical snap-through type buckling response; however, some of the panels exhibited a monotonically increasing stable response and achieved compressive loads in excess of twice the predicted linear bifurcation buckling load. In general, the finite-element analyses were able to predict accurately the nonlinear response and buckling loads of the panels and the prebuckling and postbuckling out-of-plane deformations and strains.

Thornburgh, Robert P.↗

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier–Stokes–Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER–WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier–Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system. We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analysis of plasma-modes of a gated bilayer system in high electron mobility transistors

We present rigorous analytical and computational models to study the plasma-waves in a gated-bilayer system present in a double-channel high electron mobility transistor. By analytically deriving the dispersion relations, we have identified the optical and acoustic modes in such systems. We find that the presence of the metal gate selectively modifies the optical plasmons of an ungated-bilayer, while the acoustic plasmons remain largely unchanged. Analysis shows that these modified optical plasmons could be advantageous for resonant and non-resonant plasma-wave devices. The paper further serves to verify our analytical formulae using a full-wave hydrodynamic numerical solver, based on finite difference time domain algorithm. Using the solver, we examine these modes in the gated/ungated bilayers under a plane wave excitation. We observe that, most incident power couples to the optical mode for such an excitation. Nevertheless, acoustic modes can also be excited, if the discontinuity dimensions are optimized accordingly. These observations are also explained using 2D field-plots for the first time, thus providing intuitive understanding of the plasmon excitation in the bilayers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Low-frequency ionization-driven instability of a discrete auroral arc model

The low-frequency (time scales of tens of seconds) dynamics of the auroral ionosphere differs from that of the nonauroral ionosphere by the presence of strong, unstable space- and time-dependent ionospheric ionization produced by precipitating auroral electrons. If recombination is relatively unimportant (as at high ionospheric heights), it is shown that, in general, transport processes cannot remove this ionization as fast as it is created, and no equilibrium is possible. These nonequilibrium phenomena are investigated in the context of a nonlinear adiabatic auroral model, which has previously been studied in static situations. A linearized local perturbation analysis is given of what amounts to a current-driven E x B gradient-drift instability with an ionization source, as well as some exact nonlinear solutions valid in a finite but limited spatial region. These solutions show continuing motion of auroral potential and plasma density, as the aurora tries to shift its ionization problems from one place to another. The analysis gives clues to the possibility of generation of chaos and of fine-scale spatial structure.

Cornwall, John M.↗