133,052 research outputs found
The Maslov dequantization, idempotent and tropical mathematics: a very brief introduction
This paper is a very brief introduction to idempotent mathematics and related
topics.Comment: 24 pages, 2 figures. An introductory paper to the volume "Idempotent
Mathematics and Mathematical Physics" (G.L. Ltvinov, V.P. Maslov, eds.; AMS
Contemporary Mathematics, 2005). More misprints correcte
Optimal equilibrium for a reformulated Samuelson economical model
This paper studies the equilibrium of an extended case of the classical
Samuelson's multiplier-accelerator model for national economy. This case has
incorporated some kind of memory into the system. We assume that total
consumption and private investment depend upon the national income values.
Then, delayed difference equations of third order are employed to describe the
model, while the respective solutions of third order polynomial, correspond to
the typical observed business cycles of real economy. We focus on the case that
the equilibrium is not unique and provide a method to obtain the optimal
equilibrium
The Samuelson's model as a singular discrete time system
In this paper we revisit the famous classical Samuelson's
multiplier-accelerator model for national economy. We reform this model into a
singular discrete time system and study its solutions. The advantage of this
study gives a better understanding of the structure of the model and more deep
and elegant results
Homogeneous linear matrix difference equations of higher order: Singular case
In this article, we study the singular case of an homogeneous generalized
discrete time system with given initial conditions. We consider the matrix
pencil singular and provide necessary and sufficient conditions for existence
and uniqueness of solutions of the initial value problem.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0566
Variational integrators for stochastic dissipative Hamiltonian systems
Variational integrators are derived for structure-preserving simulation of
stochastic forced Hamiltonian systems. The derivation is based on a stochastic
discrete Hamiltonian which approximates a type-II stochastic generating
function for the stochastic flow of the Hamiltonian system. The generating
function is obtained by introducing an appropriate stochastic action functional
and considering a stochastic generalization of the deterministic
Lagrange-d'Alembert principle. Our approach presents a general methodology to
derive new structure-preserving numerical schemes. The resulting integrators
satisfy a discrete version of the stochastic Lagrange-d'Alembert principle, and
in the presence of symmetries, they also satisfy a discrete counterpart of
Noether's theorem. Furthermore, mean-square and weak Lagrange-d'Alembert
Runge-Kutta methods are proposed and tested numerically to demonstrate their
superior long-time numerical stability and energy behavior compared to
non-geometric methods. The Vlasov-Fokker-Planck equation is considered as one
of the numerical test cases, and a new geometric approach to collisional
kinetic plasmas is presented.Comment: 54 pages, 11 figures. arXiv admin note: text overlap with
arXiv:1609.0046
Spectral semi-implicit and space-time discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered Cartesian grids
In this paper two new families of arbitrary high order accurate spectral DG
finite element methods are derived on staggered Cartesian grids for the
solution of the inc.NS equations in two and three space dimensions. Pressure
and velocity are expressed in the form of piecewise polynomials along different
meshes. While the pressure is defined on the control volumes of the main grid,
the velocity components are defined on a spatially staggered mesh. In the first
family, h.o. of accuracy is achieved only in space, while a simple
semi-implicit time discretization is derived for the pressure gradient in the
momentum equation. The resulting linear system for the pressure is symmetric
and positive definite and either block 5-diagonal (2D) or block 7-diagonal (3D)
and can be solved very efficiently by means of a classical matrix-free
conjugate gradient method. The use of a preconditioner was not necessary. This
is a rather unique feature among existing implicit DG schemes for the NS
equations. In order to avoid a stability restriction due to the viscous terms,
the latter are discretized implicitly. The second family of staggered DG
schemes achieves h.o. of accuracy also in time by expressing the numerical
solution in terms of piecewise space-time polynomials. In order to circumvent
the low order of accuracy of the adopted fractional stepping, a simple
iterative Picard procedure is introduced. In this manner, the symmetry and
positive definiteness of the pressure system are not compromised. The resulting
algorithm is stable, computationally very efficient, and at the same time
arbitrary h.o. accurate in both space and time. The new numerical method has
been thoroughly validated for approximation polynomials of degree up to N=11,
using a large set of non-trivial test problems in two and three space
dimensions, for which either analytical, numerical or experimental reference
solutions exist.Comment: 46 pages, 15 figures, 4 table
A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations
In this work we present a mimetic spectral element discretization for the 2D
incompressible Navier-Stokes equations that in the limit of vanishing
dissipation exactly preserves mass, kinetic energy, enstrophy and total
vorticity on unstructured grids. The essential ingredients to achieve this are:
(i) a velocity-vorticity formulation in rotational form, (ii) a sequence of
function spaces capable of exactly satisfying the divergence free nature of the
velocity field, and (iii) a conserving time integrator. Proofs for the exact
discrete conservation properties are presented together with numerical test
cases on highly irregular grids
Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
In this paper we present a novel arbitrary high order accurate discontinuous
Galerkin (DG) finite element method on space-time adaptive Cartesian meshes
(AMR) for hyperbolic conservation laws in multiple space dimensions, using a
high order \aposteriori sub-cell ADER-WENO finite volume \emph{limiter}.
Notoriously, the original DG method produces strong oscillations in the
presence of discontinuous solutions and several types of limiters have been
introduced over the years to cope with this problem. Following the innovative
idea recently proposed in \cite{Dumbser2014}, the discrete solution within the
troubled cells is \textit{recomputed} by scattering the DG polynomial at the
previous time step onto a suitable number of sub-cells along each direction.
Relying on the robustness of classical finite volume WENO schemes, the sub-cell
averages are recomputed and then gathered back into the DG polynomials over the
main grid. In this paper this approach is implemented for the first time within
a space-time adaptive AMR framework in two and three space dimensions, after
assuring the proper averaging and projection between sub-cells that belong to
different levels of refinement. The combination of the sub-cell resolution with
the advantages of AMR allows for an unprecedented ability in resolving even the
finest details in the dynamics of the fluid. The spectacular resolution
properties of the new scheme have been shown through a wide number of test
cases performed in two and in three space dimensions, both for the Euler
equations of compressible gas dynamics and for the magnetohydrodynamics (MHD)
equations.Comment: Computers and Fluids 118 (2015) 204-22
Alliances and related parameters in graphs
In this paper, we show that several graph parameters are known in different
areas under completely different names. More specifically, our observations
connect signed domination, monopolies, -domination,
-independence, positive influence domination, and a parameter
associated to fast information propagation in networks to parameters related to
various notions of global -alliances in graphs. We also propose a new
framework, called (global) -alliances, not only in order to characterize
various known variants of alliance and domination parameters, but also to
suggest a unifying framework for the study of alliances and domination.
Finally, we also give a survey on the mentioned graph parameters, indicating
how results transfer due to our observations
A note on the relation between a singular linear discrete time system and a singular linear system of fractional nabla difference equations
In this article we focus our attention on the relation between a singular
linear discrete time system and a singular linear system of fractional nabla
difference equations whose coefficients are square constant matrices. By using
matrix pencil theory, first we give necessary and sufficient condition to
obtain a unique solution for the continuous time model. After by assuming that
the input vector changes only at equally space sampling instants, we shall
derive the corresponding discrete time state equation which yield the values of
the solutions of the continuous time model which will connect the initial
system to the singular linear system of fractional nabla difference equations.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1406.6669 by
other author
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