Dielectric properties of the hydrogen-bonded ferroelectric crystal KH_(2)PO_(4)(KDP)differ significantly from those of KD_(2)PO_(4)(DKDP).It is well established that deuteration affects the interplay of hydrogenbond s...
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Dielectric properties of the hydrogen-bonded ferroelectric crystal KH_(2)PO_(4)(KDP)differ significantly from those of KD_(2)PO_(4)(DKDP).It is well established that deuteration affects the interplay of hydrogenbond switches and heavy ion displacements that underlie the emergence of macroscopic polarization,but a detailed microscopic model is *** show that all-atompath integral molecular dynamics simulations can predict the isotope effects,revealing the microscopic mechanism that differentiates KDP and *** tunneling generates phosphate configurations that do not contribute to the *** low temperatures,these quantum dipolar defects are substantial in KDP but negligible in *** intrinsic defects explain why KDP has lower spontaneous polarization and transition entropy than *** prominent role of quantum fluctuations in KDP is related to the unusual strength of the hydrogen bonds and should be equally important in other crystals of the KDP family,which exhibit similar isotope effects.
In the basic vehicle routing problem (VRP), a vehicle must deliver goods from one centralized warehouse to multiple customers efficiently. Several VRP variants and constraints exist, including different product types,...
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Unsupervised methods for dimensionality reduction of neural activity and behavior have provided unprecedented insights into the underpinnings of neural information processing. One popular approach involves the recurre...
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We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force o...
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We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.
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
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.
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.
Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the se...
We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the...
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