4,740 research outputs found
Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling
The objective of this paper is to complete certain issues from our recent
contribution [J. Calatayud, J.-C. Cort\'es, M. Jornet, L. Villafuerte, Random
non-autonomous second order linear differential equations: mean square analytic
solutions and their statistical properties, Advances in Difference Equations,
2018:392, 1--29 (2018)]. We restate the main theorem therein that deals with
the homogeneous case, so that the hypotheses are clearer and also easier to
check in applications. Another novelty is that we tackle the non-homogeneous
equation with a theorem of existence of mean square analytic solution and a
numerical example. We also prove the uniqueness of mean square solution via an
habitual Lipschitz condition that extends the classical Picard Theorem to mean
square calculus. In this manner, the study on general random non-autonomous
second order linear differential equations with analytic data processes is
completely resolved. Finally, we relate our exposition based on random power
series with polynomial chaos expansions and the random differential transform
method, being the latter a reformulation of our random Fr\"obenius method.Comment: 15 pages, 0 figures, 2 table
Relativistic kinematics beyond Special Relativity
In the context of departures from Special Relativity written as a momentum
power expansion in the inverse of an ultraviolet energy scale M, we derive the
constraints that the relativity principle imposes between coefficients of a
deformed composition law, dispersion relation, and transformation laws, at
first order in the power expansion. In particular, we find that, at that order,
the consistency of a modification of the energy-momentum composition law fixes
the modification in the dispersion relation. We therefore obtain the most
generic modification of Special Relativity that preserves the relativity
principle at leading order in 1/M.Comment: Version with minor corrections, to appear in Phys. Rev.
Mechanical systems subjected to generalized nonholonomic constraints
We study mechanical systems subject to constraint functions that can be
dependent at some points and independent at the rest. Such systems are modelled
by means of generalized codistributions. We discuss how the constraint force
can transmit an impulse to the motion at the points of dependence and derive an
explicit formula to obtain the ``post-impact'' momentum in terms of the
``pre-impact'' momentum.Comment: 24 pages, no figure
Light-cone quantization of two dimensional field theory in the path integral approach
A quantization condition due to the boundary conditions and the
compatification of the light cone space-time coordinate is identified at
the level of the classical equations for the right-handed fermionic field in
two dimensions. A detailed analysis of the implications of the implementation
of this quantization condition at the quantum level is presented. In the case
of the Thirring model one has selection rules on the excitations as a function
of the coupling and in the case of the Schwinger model a double integer
structure of the vacuum is derived in the light-cone frame. Two different
quantized chiral Schwinger models are found, one of them without a
-vacuum structure. A generalization of the quantization condition to
theories with several fermionic fields and to higher dimensions is presented.Comment: revtex, 14 p
Dissipative vortex solitons in 2D-lattices
We report the existence of stable symmetric vortex-type solutions for
two-dimensional nonlinear discrete dissipative systems governed by a
cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of
vortex solitons with a topological charge S = 1. Surprisingly, the dynamical
evolution of unstable solutions of this family does not alter significantly
their profile, instead their phase distribution completely changes. They
transform into two-charges swirl-vortex solitons. We dynamically excite this
novel structure showing its experimental feasibility.Comment: 4 pages, 20 figure
Global controllability tests for geometric hybrid control systems
Hybrid systems are characterized by having an interaction between continuous
dynamics and discrete events. The contribution of this paper is to provide
hybrid systems with a novel geometric formulation so that controls can be
added. Using this framework we describe some new global controllability tests
for hybrid control systems exploiting the geometry and the topology of the set
of jump points, where the instantaneous change of dynamics take place.
Controllability is understood as the existence of a feasible trajectory for the
system joining any two given points. As a result we describe examples where
none of the continuous control systems are controllable, but the associated
hybrid system is controllable because of the characteristics of the jump set.Comment: 27 pages, 5 figure
Asymptotic approach to Special Relativity compatible with a relativistic principle
We propose a general framework to describe Planckian deviations from Special
Relativity (SR) compatible with a relativistic principle. They are introduced
as the leading corrections in an asymptotic approach to SR going beyond the
energy power expansion of effective field theories. We discuss the conditions
in which these Planckian effects might be experimentally observable in the near
future, together with the non-trivial limits of applicability of this
asymptotic approach that such a situation would produce, both at the very high
(ultraviolet) and the very low (infrared) energy regimes.Comment: 12 page
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