In recent work, Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of th...
We present a connection between the Killing fields that arise in the loop-group approach to integrable systems and conservation laws viewed as elements of the characteristic cohomology. We use the connection to generate the complete set of conservati...
We point out incorrect equations derived in a paper published in this journal Ref. [1] (E. O. Silva, Eur. Phys. J. Plus (2018) 133 : 530) for the Klein-Gordon equation with the Aharonov-Bohm and Coulomb potentials in a Gödel-type space-time. We deri...
We introduce a generalization of team semantics which provides a framework for manipulationist theories of causation based on structural equation models, such as Woodward's and Pearl's; our causal teams incorporate (partial or total) information abou...
A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality conditions of K...
A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise constraints. B...
Recent observations of neutron stars (NS) with radio, X-rays and gravitational waves have begun to constrain the equation of state (EoS) for nuclear matter beyond the nuclear saturation density. To one's surprise, there exist approximate universal re...
In this paper, we investigate conformal Killing's vectors (CKVs) admitted by some plane symmetric spacetimes. Ten conformal Killing's equations and their general forms of CKVs are derived along with their conformal factor. The existence of conformal...
This article reviews the use of differential forms and Lie derivatives to find symmetries of differential equations, as originally presented by Harrison and Estabrook, J. Math. Phys., 12 (1971), 653. An outline of the method is given, followed by e...
In this paper, we introduce a new extended version of the shallow water equations with surface tension which is skew-symmetric with respect to the L2 scalar product and allows for large gradients of fluid height. This result is a generalization of th...
Symplectic integrators offer vastly superior performance over traditional numerical techniques for conservative dynamical systems, but their application to \emph{dissipative} systems is inherently difficult due to dissipative systems' lack of symplec...
We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the success of usin...
Following on our previous work [S. Delong and B. E. Griffith and E. Vanden-Eijnden and A. Donev, Phys. Rev. E, 87(3):033302, 2013], we develop temporal integrators for solving Langevin stochastic differential equations that arise in fluctuating hydro...
A generalization of the kinetic equation is proposed for explaining observed shapes of wind wave spectra. The approach allows to fix a critical uncertainty in modeling wind wave spectra using a condition of equilibrium of nonlinear transfer and wave...
A skew meadow is a non-commutative ring with an inverse operator satisfying two special equations and in which the inverse of zero is zero. All skew fields and products of skew fields can be viewed as skew meadows. Conversely, we give an embedding...
A meadow is a zero totalised field (0^{-1}=0), and a cancellation meadow is a meadow without proper zero divisors. In this paper we consider differential meadows, i.e., meadows equipped with differentiation operators. We give an equational axiomati...
We study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $Π=\{x=(x_{h}, x_3)\ |\ |x_{h} |>1\}$, subject to the slip boundary condition. We construct unique global solutions for axisymm...
The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid equations...
I've been working on replacing standard O(n²) self-attention with something based on wave equation dynamics. Wanted to share the journey because the debugging process might be interesting to peop...
Wanted to share a PyTorch implementation of an alternative attention mechanism based on wave physics. How it works: 1. QKV projection (standard) 2. Bilinear scatter — deposit values onto a co...