Searcharxiv⌕ Search

arXiv subjects

S. Martinez

Publications and source records attributed to S. Martinez.

At least 19 recordsLinked to original sources
arXiv2009

The 3D velocity structure of the planetary nebula NGC 7009

In search for deviations from homologous expansion in planetary nebulae we present a 3D morphokinematical model of NGC 7009. The model has been constructed with {\em Shape} based on PV diagrams from the literature and HST images. We find that the data are consistent with a radial velocity field with increased gradient at high latitudes compared to the equatorial region (Model 1). In a second model we assume a linearly increasing radial velocity component with an added poloidal component of order 10 km/s at latitudes around $70^\circ$. The true velocity field is likely to be in between these two limiting cases. We also find that the expansion of the ansae is non-radial with reference to the central star. Their velocity field is focused near the apparent exit points from the main shell. We predict the proper motion pattern for the model with a non-zero poloidal velocity component.

astro-ph.SR↗
arXiv2006

Stationary processes whose filtrations are standard

We study the standard property of the natural filtration associated to a 0--1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.

math.PR↗
arXiv2005

Equivalence of the four versions of Tsallis statistics

In spite of its undeniable success, there are still open questions regarding Tsallis non-extensive statistical formalism, whose founding stone was laid in 1988 in JSTAT. Some of them are concerned with the so-called normalization problem of just how to evaluate expectation values. The Jaynes MaxEnt approach for deriving statistical mechanics is based on the adoption of (1) a specific entropic functional form S and (2) physically appropriate constraints. The literature on non-extensive thermostatistics has considered, in its historical evolution, four possible choices for the evaluation of expectation values: (i) 1988 Tsallis-original (TO), (ii) Curado-Tsallis (CT), (iii) Tsallis-Mendes- Plastino (TMP), and (iv) the same as (iii), but using centered operators as constraints (OLM). The 1988 was promptly abandoned and replaced, mostly with versions ii) and iii). We will here (a) show that the 1988 is as good as any of the others, (b) demonstrate that the four cases can be easily derived from just one (any) of them, i.e., the probability distribution function in each of these four instances may be evaluated with a unique formula, and (c) numerically analyze some consequences that emerge from these four choices.

cond-mat.stat-mech↗
arXiv2004

Thermodynamics' first law: what information theory tells us

Thermodynamics, and in particular its first law, is of fundamental importance to Science, and therefore of great general interest to all physicists. The first law, although undoubtedly true, and believed by everyone to be true because of its many verified consequences, rests on a rather weak experimental foundation as its path independent aspect has never been directly verified, and rests on a somewhat weak foundation apropos the need for invoking the so-called adiabatic theorem (AT) to prove it from first principles. We provide here a more direct and convincing theoretical demonstration, without the AT and some other usually employed axioms.

cond-mat.stat-mech↗
arXiv2003

q-Thermodynamics: First law for quasi-stationary states

We discuss peculiar aspects of the first law of thermodynamics for systems characterized by the presence of meta-equilibrium quasi-stationary states for which the pertinent phase/configuration spaces is generally inhomogeneous. As a consequence, the naive additivity requirement for thermodynamic quantities ceases to be satisfied.

cond-mat.stat-mech↗
arXiv2003

q-thermostatistics and the analytical treatment of the ideal Fermi gas

We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing statistics is derived. Special attention is paid to the mean occupation numbers of single-particle levels. Limiting instances of interest are discussed in some detail, namely, the thermodynamic limit, considering in particular both the high- and low-temperature regimes, and the approximate results pertaining to the case q \sim 1 (the conventional Fermi-Dirac statistics corresponds to q=1). We compare our findings with previous Tsallis' literature.

cond-mat.stat-mech↗
arXiv2002

Coverage control for mobile sensing networks

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

math.OC↗
arXiv2002

Entropic uncertainty relation for power-law wave packets

For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the Heisenberg-type formulation, since it involves only the finite quantities. It is found that the total amount of entropic uncertainty converges to its lower bound in the limit of a large value of the exponent.

quant-ph↗
arXiv2002

Skinner-Rusk approach to time-dependent mechanics

The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by R. Skinner and R. Rusk, is extended to the time-dependent framework.

math-ph↗
arXiv2002

Asymptotic of the Heat Kernel in General Benedicks Domains

Using a new inequality relating the heat kernel and the probability of survival, we prove asymptotic ratio limit theorems for the heat kernel (and survival probability) in general Benedicks domains. In particular, the dimension of the cone of positive harmonic measures with Dirichlet boundary condition can be derived from the rate of convergence to zero of the heat kernel (or the survival probability).

math.PR↗
arXiv2002

q-Thermostatistics and the black-body radiation problem

We give an exact information-theory treatment of the $n$-dimensional black-body radiation process in a non-extensive scenario. We develop a $q$ generalization of the laws of i) Stefan Boltzmann, ii) Planck, and iii) Wien, and show that conventional, canonical results are obtained at temperatures above $1 K$. Classical relationships between radiation, pressure, and internal energy are recovered (independently of the $q$-value). Analyzing the particles' density for $q\approx 1$ we see that the non-extensive parameter $q$ introduces a fictitious chemical potential. We apply our results to experimental data on the cosmic microwave background and reproduce it with acceptable accuracy for different temperatures (each one associated to a particular $q$ value

cond-mat.stat-mech↗
arXiv2001

Asymptotic behavior of a stationary silo with absorbing walls

We study the nearest neighbors one dimensional uniform q-model of force fluctuations in bead packs [Coppersmith et al (1996)], a stochastic model to simulate the stress of granular media in two dimensional silos. The vertical coordinate plays the role of time, and the horizontal coordinate the role of space. The process is a discrete time Markov process with state space $\R^{\{1,...,N\}}$. At each layer (time), the weight supported by each grain is a random variable of mean one (its own weight) plus the sum of random fractions of the weights supported by the nearest neighboring grains at the previous layer. The fraction of the weight given to the right neighbor of the successive layer is a uniform random variable in $[0,1]$ independent of everything. The remaining weight is given to the left neighbor. In the boundaries, a uniform fraction of the weight leans on the wall of the silo. This corresponds to \emph{absorbing boundary conditions}. For this model we show that there exists a unique invariant measure. The mean weight at site $i$ under the invariant measure is $i(N+1-i)$; we prove that its variance is $\frac12(i(N+1-i))^2 + O(N^3)$ and the covariances between grains $i\neq j$ are of order $O(N^3)$. Moreover, as $N\to\infty$, the law under the invariant measure of the weights divided by $N^2$ around site (integer part of) $rN$, $r\in (0,1)$, converges to a product of gamma distributions with parameters 2 and $2(r(1-r))^{-1}$ (sum of two exponentials of mean $r(1-r)/2$). Liu {\it et al} (1995) proved that for a silo with infinitely many weightless grains, any product of gamma distributions with parameters 2 and $2/ρ$ with $ρ\in [0,\infty)$ are invariant. Our result shows that as the silo grows, the model selects exactly one of these Gamma's at each macroscopic place.

math.PR↗
arXiv2001

Thermodynamical Test of Non Extensive Thermostatistics

An ideal mixture of parahydrogen (with nuclear spin K=0) and orthohydrogen (with K=1), in statistical weights 1/4 and 3/4, respectively, is used as a test ground for the existence of non-extensivity in chemical physics. We report on a new bound on the non extensivity parameter q - 1 that characterizes generalized thermostatistics a la Tsallis. This bound is obtained on the basis of laboratory measurements of the specific heat of hydrogen. Suggestions are advanced for the performance of improved measurements.

cond-mat.stat-mech↗
arXiv2001

Nonextensive thermodynamic relations

The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic relations for nonextensive systems. Here, taking the first law of thermodynamics and the Legendre transform structure as the basic premises, it is found that Clausius definition of the thermodynamic entropy has to be appropriately modified, and accordingly the thermodynamic relations proposed by Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be rectified. It is shown that the definition of specific heat and the equation of state remain form invariant. As an application, the classical gas model is reexamined and, in marked contrast with the previous result obtained by Abe [Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical temperature and the unphysical pressure, the specific heat and the equation of state are found to be similar to those in ordinary extensive thermodynamics.

cond-mat.stat-mech↗
arXiv2000

Tsallis' entropy maximization procedure revisited

The proper way of averaging is an important question with regards to Tsallis' Thermostatistics. Three different procedures have been thus far employed in the pertinent literature. The third one, i.e., the Tsallis-Mendes-Plastino (TMP) normalization procedure, exhibits clear advantages with respect to earlier ones. In this work, we advance a distinct (from the TMP-one) way of handling the Lagrange multipliers involved in the extremization process that leads to Tsallis' statistical operator. It is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the Tsallis-Mendes-Plastino formalism.

physics.data-an↗
arXiv2000

Blackbody radiation in a nonextensive scenario

An exact analysis of the N-dimensional blackbody radiation process in a nonextensive à la Tsallis scenario is performed for values of the nonextensive's index in the range ($0<q<1$). The recently advanced ``Optimal Lagrange Multipliers" (OLM) technique has been employed. The results are consistent with those of the extensive, $q=1$ case. The generalization of the celebrated laws of Planck, Stefan-Boltzmann, and Wien are investigated. PACS: 05.30.-d, 95.35.+d, 05.70.Ce, 75.10.-b Keywords: Tsallis Thermostatistics, Blackbody radiation.

cond-mat.stat-mech↗
arXiv2000

Thermodynamics' 0-th-Law in a nonextensive scenario

Tsallis' thermostatistics is by now recognized as a new paradigm for statistical mechanical considerations. However, it is still affected by a serious hindrance: the generalization of thermodynamics' zero-th law to a nonextensive scenario is plagued by difficulties. Here we show how to overcome this problem.

cond-mat.stat-mech↗