5,190 research outputs found
Self-Similarity in Random Collision Processes
Kinetics of collision processes with linear mixing rules are investigated
analytically. The velocity distribution becomes self-similar in the long time
limit and the similarity functions have algebraic or stretched exponential
tails. The characteristic exponents are roots of transcendental equations and
vary continuously with the mixing parameters. In the presence of conservation
laws, the velocity distributions become universal.Comment: 4 pages, 4 figure
On the hereditary character of new strong variations of weyl type theorems
Berkani and Kachad [18], [19], and Sanabria et al. [32], introduced and studied
strong variations of Weyl type Theorems. In this paper, we study the behavior of these
strong variations of Weyl type theorems for an operator T on a proper closed and Tinvariant subspace W ⊆ X such that T
n
(X) ⊆ W for some n ≥ 1, where T ∈ L(X) and
X is an infinite-dimensional complex Banach space. The main purpose of this paper is to
prove that for these subspaces (which generalize the case T
n
(X) closed for some n ≥ 0),
these strong variations of Weyl type theorems are preserved from T to its restriction on W
and vice-versa. As consequence of our results, we give sufficient conditions for which these
strong variations of Weyl type Theorems are equivalent for two given operators. Also, some
applications to multiplication operators acting on the boundary variation space BV [0, 1]
are given
Thermodynamics of exponential Kolmogorov-Nagumo averages
This paper investigates generalized thermodynamic relationships in physical
systems where relevant macroscopic variables are determined by the exponential
Kolmogorov-Nagumo average. We show that while the thermodynamic entropy of such
systems is naturally described by R\'{e}nyi's entropy with parameter ,
their statistics under equilibrium thermodynamics are still described by an
ordinary Boltzmann distribution, which can be interpreted as a system with
inverse temperature quenched to another heat bath with inverse
temperature . For the non-equilibrium case, we show
how the dynamics of systems described by exponential Kolmogorov-Nagumo averages
still observe a second law of thermodynamics and H-theorem. We further discuss
the applications of stochastic thermodynamics in those systems - namely, the
validity of fluctuation theorems - and the connection with thermodynamic
length.Comment: 12 pages, 1 table. arXiv admin note: text overlap with
arXiv:2203.1367
A note on preservation of generalized fredholm spectra in berkani’s sense
In this paper, we study the relationships between the spectra derived from B-Fredholm theory
corresponding to two given bounded linear operators. The main goal of this paper is to obtain sufficient
conditions for which the spectra derived from B-Fredholm theory corresponding to two given operators
are respectively the same. Among other results, we prove that B-Fredholm type spectral properties for an
operator and its restriction are equivalent, as well as obtain conditions for which B-Fredholm type spectral
properties corresponding to two given operators are the same. As application of our results, we obtain
conditions for which the above mentioned spectra and the spectra derived from the classical Fredholm
theory are the same
Exactly Solvable Hydrogen-like Potentials and Factorization Method
A set of factorization energies is introduced, giving rise to a
generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for
the radial hydrogen-like Hamiltonian. An algebraic intertwining technique
involving such factorization energies leads to derive -parametric families
of potentials in general almost-isospectral to the hydrogen-like radial
Hamiltonians. The construction of SUSY partner Hamiltonians with ground state
energies greater than the corresponding ground state energy of the initial
Hamiltonian is also explicitly performed.Comment: LaTex file, 21 pages, 2 PostScript figures and some references added.
To be published in J. Phys. A: Math. Gen. (1998
Pulse Dynamics in a Chain of Granules With Friction
We study the dynamics of a pulse in a chain of granules with friction. We
present theories for chains of cylindrical granules (Hertz potential with
exponent ) and of granules with other geometries (). Our results are
supported via numerical simulations for cylindrical and for spherical granules
().Comment: Submitted to PR
Dynamical noise can enhance high-order statistical structure in complex systems
Recent research has provided a wealth of evidence highlighting the pivotal
role of high-order interdependencies in supporting the information-processing
capabilities of distributed complex systems. These findings may suggest that
high-order interdependencies constitute a powerful resource that is, however,
challenging to harness and can be readily disrupted. In this paper we contest
this perspective by demonstrating that high-order interdependencies can not
only exhibit robustness to stochastic perturbations, but can in fact be
enhanced by them. Using elementary cellular automata as a general testbed, our
results unveil the capacity of dynamical noise to enhance the statistical
regularities between agents and, intriguingly, even alter the prevailing
character of their interdependencies. Furthermore, our results show that these
effects are related to the high-order structure of the local rules, which
affect the system's susceptibility to noise and characteristic times-scales.
These results deepen our understanding of how high-order interdependencies may
spontaneously emerge within distributed systems interacting with stochastic
environments, thus providing an initial step towards elucidating their origin
and function in complex systems like the human brain.Comment: 8 pages, 4 figures, 2 table
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