The Benjamin-Ono equation is shown to admit a two-parameter family of Miura transformations, leading to a proof that the equation has an infinite number of conserved densities. Linearized equations are derived from a ...
The Benjamin-Ono equation is shown to admit a two-parameter family of Miura transformations, leading to a proof that the equation has an infinite number of conserved densities. Linearized equations are derived from a special case of the transformation.
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then...
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then the curve L obtained from a rotation of L about its center by an arbitrary angle is also a solution with the same velocity U. Similar results hold for the case with surface tension if and only if the Schwarz function of the curve L is regular in the fluid region and at most a linear function at infinity. Several examples in which this principle is used to generate new solutions to the problem are also discussed.
A class of Hamiltonian systems derived from nonstandard Poisson brackets are investigated. For each system a conserved quantity is constructed that depends only upon the definition of the Poisson bracket. The quantum ...
A class of Hamiltonian systems derived from nonstandard Poisson brackets are investigated. For each system a conserved quantity is constructed that depends only upon the definition of the Poisson bracket. The quantum theory for these systems is sketched and classical and quantum ''blowup'' phenomena are compared.
Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ...
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Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ̃V(k), which can be obtained experimentally from scattering data, enables accurate determination of various transport and wave propagation characteristics, including the time-dependent diffusion spreadability S(t) and effective dynamic dielectric constant εe for electromagnetic wave propagation. Moreover, χ̃V(k) determines rigorous upper bounds on the fluid permeability K. Given the importance of χ̃V(k), we present here an efficient Fourier-space based computational framework to construct three-dimensional (3D) statistically isotropic two-phase heterogeneous materials corresponding to targeted spectral density functions. In particular, we employ a variety of analytical functional forms for χ̃V(k) that satisfy all known necessary conditions to construct disordered stealthy hyperuniform, standard hyperuniform, nonhyperuniform, and antihyperuniform two-phase heterogeneous material systems at varying phase volume fractions. We show that by tuning the correlations in the system across length scales via the targeted functions, one can generate a rich spectrum of distinct structures within each of the above classes of materials. Importantly, we present the first realization of antihyperuniform two-phase heterogeneous materials in 3D, which are characterized by autocovariance function χV(r) with a power-law tail, resulting in microstructures that contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability S(t) and estimate the fluid permeability K associated with all of the constructed materials directly from the corresponding spectral densities. Although it is well established that the long-time asymptotic scaling behavior of S(t) only depends on the functional form of χ̃V(k), with the stealthy hyperuniform a
The Estabrook-Wahlquist method for establishing the integrability of partial differential equations is extended to semidiscrete (lattice) systems. If successful, the method constructs the linear eigenvalue problem ass...
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The Estabrook-Wahlquist method for establishing the integrability of partial differential equations is extended to semidiscrete (lattice) systems. If successful, the method constructs the linear eigenvalue problem associated with the equation.
Until now multiscale quantum problems have appeared to be out of reach at the many-body level relevant to strongly correlated materials and current quantum information devices. In fact, they can be modeled with q-th o...
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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 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.
Background: Several studies show that large language models (LLMs) struggle with phenotype-driven gene prioritization for rare diseases. These studies typically use Human Phenotype Ontology (HPO) terms to prompt found...
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The design of most consumer products can play a key role in their commercial success, and, therefore, the ability to protect new and innovative designs is an important part of a modern competitive marketplace. Since 1...
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The design of most consumer products can play a key role in their commercial success, and, therefore, the ability to protect new and innovative designs is an important part of a modern competitive marketplace. Since 1 April 2003, it has been possible to obtain European Union (EU)-wide design protection by means of a single registration made under the Community Design regulation (Council Regulation 6/2002 of 12 December 2001), usually referred to as a Registered Community Design (RCD). Before the advent of the RCD, a designer seeking protection across the EU was restricted to seeking registration at a national level. Now, with 28 member states in the EU, the ability to register a design with just a single filing is a major step forward in terms of protection of intellectual property rights in the EU.
We compute the domain of existence of two-dimensional invariant tori with fixed frequency vectors for a four-dimensional, complex, symplectic map. The map is a generalization of the semi-standard map studied by Greene...
We compute the domain of existence of two-dimensional invariant tori with fixed frequency vectors for a four-dimensional, complex, symplectic map. The map is a generalization of the semi-standard map studied by Greene and Percival; it has three parameters, a 1 and a 2 representing the strength of the kicks in each degree of freedom, and ϵ, the coupling. The domain of existence of a torus in ( a 1 , a 2 ) is shown to be complete and log-convex for fixed k = ϵ / a 1 a 2 . Explicit bounds on the domain for fixed k are obtained. Numerical results show that quadratic irrationals can be more robust than the cubic irrational, “the spiral mean”.
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