Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question &q...
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Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question "Can one hear the shape of a drum?" concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in d-dimensional Euclidean space Rd is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function g2(r). While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an n-particle basis (n ≥ 2). Here, we ask, What is nmin(d), the minimum value of n for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension d? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multi-particle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral 4-, 3- and 2-particle bases in one, two and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identical g2(r) up to infinite r. Based on our analyses, we conjecture that nmin(d) = 4, 3, 2 for d = 1, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with n = 3, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radia
We show with molecular dynamics simulations that spinodal decomposition is a probable initiation mechanism of spallation in impact-melted samples at extremely high strain rates. The formation of voids or bubbles is a ...
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We show with molecular dynamics simulations that spinodal decomposition is a probable initiation mechanism of spallation in impact-melted samples at extremely high strain rates. The formation of voids or bubbles is a secondary process following the spinodal amplification of density fluctuations. As a result, the spallation strength can be related to the inherent thermodynamic property of the liquid, i.e., the liquid-gas spinodal curve, which can be determined by independent equation-of-state studies in prior. This connection between high strain-rate spallation and spinodal decomposition may be further examined in future experiments.
The application of the standard quasi-steady-state approximation to the Michaelis–Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, d...
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Machine learning of microstructure–property relationships from data is an emerging approach in computational materials science. Most existing machine learning efforts focus on the development of task-specific models ...
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Non-diffusive, hydrodynamic-like transport of charge or heat has been observed in several materials, and recent, pioneering experiments have suggested the possible emergence of electron-phonon bifluids. Here we introd...
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The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limit...
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With the rise of artificial intelligence, many people nowadays use artificial intelligence to help solve some problems in life, and the medical field is also with the rise of artificial intelligence, many people are s...
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Constantine M. Dafermos has done extensive research at the interface of partial differential equations and continuum physics. He is a world leader in nonlinear hyperbolic conservation laws, where he introduced several...
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Constantine M. Dafermos has done extensive research at the interface of partial differential equations and continuum physics. He is a world leader in nonlinear hyperbolic conservation laws, where he introduced several fundamental methods in the subject including the methods of relative entropy, generalized characteristics, and wave-front tracking, as well as the entropy rate criterion for the selection of admissible wave fans. He has also made fundamental contributions on the mathematical theory of the equations of thermomechanics as it pertains in modeling and analysis of materials with memory, thermoelasticity, and thermoviscoelasticity. His work is distinctly characterized by an understanding of the fundamental issues of continuum physics and their role in developing new techniques of mathematical analysis.
This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singula...
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