Conservation law ≈ Conservation law
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A new class of accurate, mesh-free hydrodynamic simulation methods Open
We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture a…
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Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws Open
We study the scrambling of local quantum information in chaotic many-body\nsystems in the presence of a locally conserved quantity like charge or energy\nthat moves diffusively. The interplay between conservation laws and scrambling\nsheds…
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Hamiltonian Neural Networks Open
Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models t…
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Hypocoercivity for linear kinetic equations conserving mass Open
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining …
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LIMITATIONS OF PHYSICS INFORMED MACHINE LEARNING FOR NONLINEAR TWO-PHASE TRANSPORT IN POROUS MEDIA Open
Deep learning techniques have recently been applied to a wide range of computational physics problems. In this paper, we focus on developing a physics-based approach that enables the neural network to learn the solution of a dynamic fluid-…
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Relativistic fluid dynamics with spin Open
Using the conservation laws for charge, energy, momentum, and angular\nmomentum, we derive hydrodynamic equations for the charge density, local\ntemperature, and fluid velocity, as well as for the spin tensor, starting from\nlocal equilibr…
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Nonequilibrium quantum dynamics and transport: from integrability to many-body localization Open
We review the non-equilibrium dynamics of many-body quantum systems after a\nquantum quench with spatial inhomogeneities, either in the Hamiltonian or in\nthe initial state. We focus on integrable and many-body localized systems that\nfail…
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The total energy--momentum tensor for electromagnetic fields in a dielectric Open
There are various formulations of energy--momentum tensors for an electromagnetic field in a linear dielectric. The total energy--momentum tensor, comprised of electromagnetic and material components, must be unique. We discuss the constru…
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Conserved charges of the extended Bondi-Metzner-Sachs algebra Open
Isolated objects in asymptotically flat spacetimes in general relativity are\ncharacterized by their conserved charges associated with the\nBondi-Metzner-Sachs (BMS) group. These charges include total energy, linear\nmomentum, intrinsic an…
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Momentum dissipation and effective theories of coherent and incoherent transport Open
We study heat transport in two systems without momentum conservation: a\nhydrodynamic system, and a holographic system with spatially dependent,\nmassless scalar fields. When momentum dissipates slowly, there is a\nwell-defined, coherent c…
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Hamiltonian Neural Networks Open
Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models t…
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Carrollian physics at the black hole horizon Open
We show that the geometry of a black hole horizon can be described as a\nCarrollian geometry emerging from an ultra-relativistic limit where the\nnear-horizon radial coordinate plays the role of a virtual velocity of light\ntending to zero…
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Optical solitons and conservation laws associated with Kudryashov�s sextic power-law nonlinearity of refractive index Open
We recover the cases of solutions in the shape of bright, dark and singular optical solitons for the self-phase modulation effect, which belongs to the type of N. A. Kudryashov's sextic power-law nonlinearity of refractive index.Three diff…
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A geometric viewpoint on generalized hydrodynamics Open
Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of\nmany-body integrable systems. It consists of an infinite set of conservation\nlaws for quasi-particles traveling with effective ("dressed") velocities that\ndepen…
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GEMPIC: geometric electromagnetic particle-in-cell methods Open
We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We derive a semi-discrete Poisson bracket, which retains the definin…
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Generalized Gibbs ensembles for quantum field theories Open
We consider the non-equilibrium dynamics in isolated systems, described by\nquantum field theories (QFTs). After being prepared in a density matrix that is\nnot an eigenstate of the Hamiltonian, such systems are expected to relax\nlocally …
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Collisions in Chiral Kinetic Theory Open
Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order O(ℏ), which includes collisions. We find a new contribution to the particle number current due to the side jumps required by the conservation of a…
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Multi-species simulation of porous sand and water mixtures Open
We present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys …
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Adiabatic hydrodynamics: the eightfold way to dissipation Open
Hydrodynamics is the low-energy effective field theory of any interacting quantum theory, capturing the long-wavelength fluctuations of an equilibrium Gibbs densitymatrix. Conventionally, one views the effective dynamics in terms of the co…
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An artificial neural network as a troubled-cell indicator Open
High-resolution schemes for conservation laws need to suitably limit the numerical solution near discontinuities, in order to avoid Gibbs oscillations. The solution quality and the computational cost of such schemes strongly depend on thei…
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Integrable Trotterization: Local Conservation Laws and Boundary Driving Open
We discuss a general procedure to construct an integrable real-time Trotterization of interacting lattice models. As an illustrative example, we consider a spin-1/2 chain, with continuous time dynamics described by the isotropic (XXX) Heis…
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Physics-informed dynamic mode decomposition Open
In this work, we demonstrate how physical principles—such as symmetries, invariances and conservation laws—can be integrated into the dynamic mode decomposition (DMD). DMD is a widely used data analysis technique that extracts low-rank mod…
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An efficient unstructured MUSCL scheme for solving the 2D shallow water equations Open
The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more …
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A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws Open
In this study, we consider the third order nonlinear Schrödinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numer…
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Optical Chirality Flux as a Useful Far-Field Probe of Chiral Near Fields Open
To optimize the interaction between chiral matter and highly twisted light, quantities that can help characterize chiral electromagnetic fields near nanostructures are needed. Here, by analogy with Poynting's theorem, we formulate the time…
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Rényi Generalization of the Accessible Entanglement Entropy Open
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, W…
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Machine Learning Conservation Laws from Trajectories Open
We present AI Poincaré, a machine learning algorithm for autodiscovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational three-body problem, and…
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Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case Open
In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic soluti…
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Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations Open
We analyze discontinuous Galerkin methods using upwind-biased numerical fluxes for time-dependent linear conservation laws. In one dimension, optimal a priori error estimates of order $k+1$ are obtained for the semidiscrete scheme when pie…
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Thermodynamic versus kinetic approach to polarization-vorticity coupling Open
We critically compare thermodynamic and kinetic approaches, that have been\nrecently used to study relations between the spin polarization and fluid\nvorticity in systems consisting of spin-one-half particles. The thermodynamic\napproach r…