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H. Hernández-Saldaña

Publications and source records attributed to H. Hernández-Saldaña.

13 recordsLinked to original sources

The Locus of the apices of projectile trajectories under constant drag

We present an analytical solution for the projectile coplanar motion under constant drag parametrised by the velocity angle. We found the locus formed by the apices of the projectile trajectories. The range and time of flight are obtained numerically and we find that the optimal launching angle is smaller than in the free drag case. This is a good example of problems with constant dissipation of energy that includes curvature, and it is proper for intermediate courses of mechanics.

physics.gen-ph↗

Sociophysics in the mexican case (Sociofísica en el caso mexicano)

The availability of electoral data in electronic format allowed to physicist and mathematicians their own analysis. Beyond theoretical models for electoral processes, new regularities had been found in the data analysis of many countries and many elections. Here, we discuss some of the statistical regularities found for México, from power laws Daisy models linked in corporate vote. The methods used are those from standard statistics and statistical mechanics. As a particular application we discuss an entropic approach to the distribution of votes for the Partido Revolucionario Institucional and we demonstrate that this kind of method DOES NOT allow to discover a massive buy of vote. The argument is that such a distribution has been amazingly consistent in the last two decades elections. Other methods have been unsuccessful to discover signal of fraud. RESUMEN: Con la disponibilidad de datos electorales en formato electrónico los físicos y matemáticos iniciaron sus propios análisis de los datos. Más allá de los modelos teóricos desarrollados para los procesos electorales, nuevas regularidades empezaron a surgir de los datos en muchas elecciones y en muchos países. Aquí discutimos algunas de las regularidades estadísticas encontradas para México. En particular, la aparición de leyes de potencia y modelos Margarita (Daisy models) que se pueden asociar al voto corporativo. Los métodos utilizados son de estadística y física estadística estándar. Como una aplicación particular, discutimos una aproximación entrópica a la distribución de votos del Partido Revolucionario Institucional y demostramos que éste método NO permite diferenciar una compra masiva de votos pues su comportamiento ha sido sorprendentemente consistente. De igual forma otros métodos han resultado infructuosos en determinar signos de fraude.

physics.soc-ph↗

Results on Three predictions on July 2012 Federal Elections in Mexico based on past regularities

The Presidential Election in Mexico of July 2012 has been the third time that PREP, Previous Electoral Results Program works. PREP gives voting outcomes based in electoral certificates of each polling station that arrive to capture centers. In previous ones, some statistical regularities had been observed, three of them were selected to make predictions and were published in \texttt{arXiv:1207.0078 [physics.soc-ph]}. Using the database made public in July 2012, two of the predictions were completely fulfilled, while, the third one was measured and confirmed using the database obtained upon request to the electoral authorities. The first two predictions confirmed by actual measures are: (ii) The Partido Revolucionario Institucional, PRI, is a sprinter and has a better performance in polling stations arriving late to capture centers during the process. (iii) Distribution of vote of this party is well described by a smooth function named a Daisy model. A Gamma distribution, but compatible with a Daisy model, fits the distribution as well. The third prediction confirms that {\it errare humanum est}, since the error distributions of all the self-consistency variables appeared as a central power law with lateral lobes as in 2000 and 2006 electoral processes. The three measured regularities appeared no matter the political environment.

physics.soc-ph↗

Quantum and classical dissipation of charged particles

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. The Green's function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail.

quant-ph↗

Classical equivalents for quantum eigenfunctions in energy representation for simple hamiltonian systems

A calculation of the classical analogue for the quantum wave function and local denity of states, in energy representation, is presented for simple Hamiltonian systems. Sucha analogous were proposed by M. V. Berry and A. voros considering the intersection of energy shells of two systems as the only semiclassical object which can give support to eigenfunctions. One of them is the system unser study and the other is the "unperturbed system" used to express the wave functions, even in the case that both systems are not close. For simple systems and as for scalable ones analytical expressions are obtainable. In the present work we offer examples of both.

nlin.CD↗

Engineering a spin-fet: spin-orbit phenomena and spin transport induced by a gate electric field

In this work, we show that a gate electric field, applied in the base of the field-effect devices, leads to inducing spin-orbit interactions (Rashba and linear Dresselhauss) and confines the transport electrons in a two-dimensional electron gas. On the basis of these phenomena we solve analytically the Pauli equation when the Rashba strength and the linear Dresselhaus one are equal, for a tuning value of the gate electric field $\mathcal{E}_g^*$. Using the transfer matrix approach, we provide a joint description of the transport by varying the bias electric field, $\mathcal{E}_b$. We can flip the spin of the incident electrons, or block the spin-down completely. The robustness of this behavior is proved when $\mathcal{E}_g^*$ changes by $\mathcal{E}_g^* \pm δ\mathcal{E}_g$.

cond-mat.mes-hall↗

Three predictions on July 2012 Federal Elections in Mexico based on past regularities

Electoral systems are subject of study for physicist and mathematicians in last years given place to a new area: sociophysics. Based on previous works of the author on the Mexican electoral processes in the new millennium, he found three characteristics appearing along the 2000 and 2006 preliminary dataset offered by the electoral authorities, named PREP: I) Error distributions are not Gaussian or Lorentzian, they are characterized for power laws at the center and asymmetric lobes at each side. II) The Partido Revolucionario Institucional (PRI) presented a change in the slope of the percentage of votes obtained when it go beyond the 70% of processed certificates; hence it have an improvement at the end of the electoral computation. III) The distribution of votes for the PRI is a smooth function well described by Daisy model distributions of rank $r$ in all the analyzed cases, presidential and congressional elections in 2000, 2003 and 2006. If all these characteristics are proper of the Mexican reality they should appear in the July 2012 process. Here I discuss some arguments on why such a behaviors could appear in the present process

physics.soc-ph↗

On the reliability of voting processes: the Mexican case

Analysis of vote distributions using current tools from statistical physics is of increasing interest. While data considered for physics studies are subject to a careful understanding of error sources, such analysis are almost absent in studies of voting process. As a way to test reliability in electoral processes we choose to investigate the July 2006 presidential election in Mexico. We use records which appeared in the Programa de Resultados Preliminares, PREP, the program which offers electoral results as soon as they are captured. In order to contrast the results we used the congressional election data-set and the July 2000 presidential record. We demonstrate the existence of correlations in the percentage of votes and, we offer evidence of the strong influence of the PRI in the curious results in the presidential case. Distributions of errors in the data-sets are analyzed for all the elections and no large deviations were found. That is, even when the sum of errors is around 45% in all cases, their global behavior is similar. This result gives support to the thesis of no large fraud for the July 2006 presidential election. Distribution of votes in all cases is obtained for all the parties. Parties and candidates with few votes, annulled votes and non-registered candidates follow a power law distribution, and the corporate party follows a daisy model distribution. Parties and candidates with many votes show a mixed behavior.

physics.soc-ph↗

Statistical distributions of quasi-optimal paths in the traveling salesman problem: the role of the initial distribution of cities

Solutions to Traveling salesman problem have been obtained with several algorithms. However, few of them has discussed about the statistical distribution of lengths for the quasi-optimal path obtained. For a random set of cities such a distribution follows a rank 2 daisy model but our analysis on actual distribution of cities does not show the characteristic quadratic growth of the daisy model. The role played by the initial city distribution is explored in this work. The importance of understanding such a behavior in the context of electoral processes is discussed.

cond-mat.stat-mech↗

On the locus formed by the maximum heights of projectile motion with air resistance

We present an analysis on the geometrical place formed by the set of maxima of the trajectories of a projectile launched in a media with linear drag. Such a place, the locus of apexes, is written in term of the Lambert $W$ function in polar coordinates, confirming the special role played by this function in the problem. In order to characterize the locus, a study of its curvature is presented in two parameterizations, in terms of the launch angle and in the polar one. The angles of maximum curvature are compared with other important angles in the projectile problem. As an addendum, we find that the synchronous curve in this problem is a circle as in the drag-free case.

physics.class-ph↗

On the Corporate Votes and their relation with Daisy Models

The distribution of votes of one of the corporate parties in Mexico during elections of 2000, 2003 and 2006 is analyzed. After proper normalization and unfolding the agreement of the votes distributions with those of daisy models of several ranks is good. These models are generated by retaining each $r+1$ level in a sequence which follows a Poisson distribution.Beyond the fact that rank 2 daisy model resembles the distribution of the quasi-optimal distances for the Traveling Salesman Problem no clear explanation exists for this behavior, but the agreement is not fortuitous and the possibility of a universal phenomena for corporate vote is discussed.

physics.soc-ph↗

Nearest neighbour spacing distribution of basis in some intron-less and intron-containing DNA sequences

We show that the nearest neighbour distribution of distances between basis pairs of some intron-less and intron-containing coding regions are the same when a procedure, called {\em unfolding}, is applied. Such a procedure consists in separating the secular variations from the oscillatory terms. The form of the distribution obtained is quite similar to that of a random, i.e. Poissonian, sequence. This is done for the HUMBMYH7CD, DROMYONMA, HUMBMYH7 and DROMHC sequences. The first two correspond to highly coding regions while the last two correspond to non-coding regions. We also show that the distributions before the unfolding procedure depend on the secular part but, after the unfolding procedure we obtain an striking result: all distributions are similar to each other. The result becomes independent of the content of introns or the species we have chosen. This is in contradiction with the results obtained with the detrended fluctuation analysis in which the correlations yield different results for intron-less and intron-containing regions.

q-bio.QM↗

Fluctuating dynamics at the quasiperiodic onset of chaos, Tsallis q-statistics and Mori's q-phase thermodynamics

We analyze the fluctuating dynamics at the golden-mean transition to chaos in the critical circle map and find that trajectories within the critical attractor consist of infinite sets of power laws mixed together. We elucidate this structure assisted by known renormalization group (RG) results. Next we proceed to weigh the new findings against Tsallis' entropic and Mori's thermodynamic theoretical schemes and observe behavior to a large extent richer than previously reported. We find that the sensitivity to initial conditions has the form of families of intertwined q-exponentials, of which we determine the q-indexes and the generalized Lyapunov coefficient spectra. Further, the dynamics within the critical attractor is found to consist of not one but a collection of Mori's q-phase transitions with a hierarchical structure. The value of Mori's `thermodynamic field' variable q at each transition corresponds to the same special value for the entropic index q. We discuss the relationship between the two formalisms and indicate the usefulness of the methods involved to determine the universal trajectory scaling function and/or the ocurrence and characterization of dynamical phase transitions.

cond-mat.stat-mech↗