We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ ...
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We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency *** formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the ***,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of *** effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video *** results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.
We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 e V ...
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We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 e V to 1 ke V for comparative study. At the lowest excess energy, i.e., close to the double-ionization threshold, it is found that the projectile momentum is totally transferred to the recoil-ion while the residual energy is randomly partitioned among the three outgoing electrons, which are then most probably emitted with an equilateral triangle configuration. Our results agree well with experiments as compared with early quantum-mechanical calculation as well as classical simulation based on a two-dimensional Bohr's model. Furthermore, by mapping the final momentum vectors event by event into a Dalitz plot,we unambiguously demonstrate that the ergodicity has been reached and thus confirm a long-term scenario conceived by Wannier. The time scale for such few-body thermalization, from the initial nonequilibrium state to the final microcanonical distribution, is only about 100 attoseconds. Finally, we predict that, with the increase of the excess energy, the dominant emission configuration undergoes a transition from equilateral triangle to T-shape and finally to a co-linear mode. The associated signatures of such configuration transition in the electron–ion joint momentum spectrum and triple-electron angular distribution are also demonstrated.
Communication compression has been an important topic in Federated Learning (FL) for alleviating the communication overhead. However, communication compression brings forth new challenges in FL due to the interplay of...
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In this paper,we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac(KGD)*** from the derivation of the existing numerical methods given in literature where the nu...
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In this paper,we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac(KGD)*** from the derivation of the existing numerical methods given in literature where the numerical schemes are proposed by directly discretizing the KGD system,we translate the KGD equations into an equivalent system by introducing an auxiliary function,then derive a nonlinear Crank-Nicolson-type finite difference scheme for solving the equivalent *** scheme perfectly inherits the mass and energy conservative properties possessed by the KGD,while the energy preserved by the existing conservative numerical schemes expressed by two-level’s solution at each time *** using energy method together with the‘cut-off’function technique,we establish the optimal error estimate of the numerical solution,and the convergence rate is O(τ^(2)+h^(2))in l∞-norm with time stepτand mesh size *** experiments are carried out to support our theoretical conclusions.
In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem...
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In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.
The fabrication of supramolecular materials for biomedical applications such as drug delivery, bioimaging, wound-dressing, adhesion materials, photodynamic/photothermal therapy, infection control (as antibacterial), e...
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Many configurations in plasma physics are axisymmetric,it will be more convenient to depict them in cylindrical coordinates compared with Cartesian *** this paper,a gas-kinetic scheme for collisional Vlasov-Poisson eq...
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Many configurations in plasma physics are axisymmetric,it will be more convenient to depict them in cylindrical coordinates compared with Cartesian *** this paper,a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed,our algorithm is based on Strang *** equation is divided into two parts,one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme,and the other is the acceleration part solved by a Runge-Kutta *** asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch *** results show it can capture the process fromnon-equilibrium to equilibrium state by Coulomb collisions,and numerical accuracy is obtained.
Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctu...
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Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to ordinary liquids. The structure factor of disordered hyperuniform systems often obeys the scaling relation S(k)∼Bkα with B,α>0 in the limit k→0. Ground states of d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this paper, we systematically address these questions by deriving the analytical small-k behaviors (and, associated, α and B) of the total and spin-resolved structure factors of quasi-one-dimensional, two-dimensional, and three-dimensional electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our paper thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple
Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and...
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Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.
A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinfo...
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A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.
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