Study Of Physical Systems Research Articles

Vector localized and periodic waves for the matrix Hirota equation with sign-alternating nonlinearity via the binary Darboux transformation

Dynamical properties of vector localized and periodic waves hold significant importance in the study of physical systems. In this work, we investigate the matrix Hirota equation with sign-alternating nonlinearity via the binary Darboux transformation. For the two interacting components, we construct the binary Darboux transformation formulas, vector localized, and periodic wave solutions. Via those solutions, different kinds of nonlinear waves can be achieved, including rogue waves, solitons, positons, and periodic waves. When the imaginary part of the spectral parameter is not zero, eye-shaped rogue waves appear in one component, and the twisted rogue wave pairs in the other component. As the spectral parameter is real, we derive distinct forms of vector localized and periodic waves on the non-zero background, such as the vector solitons, positons, periodic waves, breathers on the periodic wave background, and rational solitons. These results may be valuable in this investigation of nonlinear waves in physical systems.

Extending the Applicability of Cordero Type Iterative Method

Symmetries play a vital role in the study of physical systems. For example, microworld and quantum physics problems are modeled on the principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Most of these studies reduce to solving nonlinear equations in suitable abstract spaces iteratively. In particular, the convergence of a sixth-order Cordero type iterative method for solving nonlinear equations was studied using Taylor expansion and assumptions on the derivatives of order up to six. In this study, we obtained order of convergence six for Cordero type method using assumptions only on the first derivative. Moreover, we modified Cordero’s method and obtained an eighth-order iterative scheme. Further, we considered analogous iterative methods to solve an ill-posed problem in a Hilbert space setting.

Generative formalism of causality quantifiers for processes.

The concept of dynamical causal effect (DCE) is generalized and equipped with a formalism which allows one to formulate in a unified manner and interrelate a variety of causality quantifiers used in time series analysis. An elementary DCE from a subsystem Y to a subsystem X is defined within the stochastic dynamical systems framework as a response of a future X state to an appropriate variation of an initial (X,Y)-state distribution or a certain parameter of Y or of the coupling element Y→X; this response is quantified in a probabilistic sense via a certain distinction functional; elementary DCEs are assembled over a set of initial variations via an assemblage functional. To include all those aspects, a "triple brackets formula" for the general DCE is suggested and serves as a first principle to produce specific causality quantifiers as realizations of the general DCE. As an application, transfer entropy and Liang-Kleeman information flow are related surprisingly as opposite limit cases in a family of DCEs; it is shown that their "nats per time unit" may differ drastically. The suggested DCE viewpoint links any formal causality quantifier to "intervention-effect" experiments, i.e., future responses to initial variations, and so provides its dynamical interpretation, opening a way to its further physical interpretations in studies of physical systems.

Machine-learning iterative calculation of entropy for physical systems

Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding, and more. Current methods for entropy estimation suffer from a high computational cost, lack of generality, or inaccuracy and inability to treat complex, strongly interacting systems. In this paper, we present a method, termed machine-learning iterative calculation of entropy (MICE), for calculating the entropy by iteratively dividing the system into smaller subsystems and estimating the mutual information between each pair of halves. The estimation is performed with a recently proposed machine-learning algorithm which works with arbitrary network architectures that can be chosen to fit the structure and symmetries of the system at hand. We show that our method can calculate the entropy of various systems, both thermal and athermal, with state-of-the-art accuracy. Specifically, we study various classical spin systems and identify the jamming point of a bidisperse mixture of soft disks. Finally, we suggest that besides its role in estimating the entropy, the mutual information itself can provide an insightful diagnostic tool in the study of physical systems.

Chiral perturbation theory for nonzero chiral imbalance

We construct the most general low-energy effective lagrangian including local parity violating terms parametrized by an axial chemical potential or chiral imbalance μ5, up to mathcal{O}left({p}^4right) order in the chiral expansion for two light flavours. For that purpose, we work within the Chiral Perturbation Theory framework where only pseudo-NGB fields are included, following the external source method. The mathcal{O}left({p}^2right) lagrangian is only modified by constant terms, while the mathcal{O}left({p}^4right) one includes new terms proportional to {mu}_5^2 and new low-energy constants (LEC), which are renormalized and related to particular observables. In particular, we analyze the corrections to the pion dispersion relation and observables related to the vacuum energy density, namely the light quark condensate, the chiral and topological susceptibilities and the chiral charge density, providing numerical determinations of the new LEC when possible. In particular, we explore the dependence of the chiral restoration temperature Tc with μ5. An increasing Tc(μ5) is consistent with our fits to lattice data of the ChPT-based expressions. Although lattice uncertainties are still large and translate into the new LEC determination, a consistent physical description of those observables emerges from our present work, providing a theoretically robust model-independent framework for further study of physical systems where parity-breaking effects may be relevant, such as heavy-ion collisions.

Topological theory of physical fields

We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid disk. If tearing or gluing get involved, i.e. the deformation is not continuous anymore, the initial topology will consequently change giving rise to a topologically distinct object, e.g., a torus. This simple concept in general topology may be employed in the study of physical systems described by fields. Instead of continuously deforming objects, we can take a continuously evolving field, with an appropriately defined topology, such that the topology remains unchanged in time unless the system undergoes an important physical change, e.g., a transition to a different energy state. For instance, a sudden change in the magnetic topology in an energetically relaxing plasma, a process called reconnection, strongly affects the dynamics, e.g., it is involved in launching solar flares and generating large scale magnetic fields in astrophysical objects. In this topological formalism, the magnetic topology in a plasma can spontaneously change due to the presence of dissipative terms in the induction equation which break its time symmetry. We define a topology for the vector field in the phase space . As for scalar fields represented by a perfect fluid, e.g., the inhomogeneous inflaton or Higgs fields, the fluid velocity defines the corresponding topology. The vector field topology in its corresponding phase space will be preserved in time if certain conditions including time reversal invariance are satisfied by the field and its governing differential equation. Otherwise, the field’s topology can suddenly change at some point, similar to a spontaneously broken symmetry, as time advances, e.g., corresponding to an energy transition.

Two-dimensional fractional algebraic internal solitary waves model and its solution

With the development of theory and advancement of scientific research, fractional calculus has begun to be considered as a method for the study of physical systems. In this work, based on the basic system of equations for internal solitary waves, we have derived two-dimensional Benjamin–Ono equation. Then, the integer-order two-dimensional Benjamin–Ono equation is transformed into the time-fractional Benjamin–Ono equation. To study the properties of the algebraic internal solitary waves, we discuss the conservation laws of the new model. Also, using the Hirota bilinear method, the derived new model is solved. Finally, we explore the characteristics of motion of the algebraic internal solitary waves with the help of the multi-soliton solutions.

Double crystallographic groups and their representations on the Bilbao Crystallographic Server

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPGandREPRESENTATIONS DSG). The toolDCOMPRELprovides compatibility relations between the irreducible representations of double space groups at differentkvectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The programDSITESYMimplements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the programBANDREPcalculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results ofBANDREPhave been extensively applied in the description of and the search for topological insulators.

SOME CRITICAL POINTS IN THE METHODS AND PHILOSPHY OF PHYSICAL SCIENCES

Nowadays, it seems that there are not enough studies on the philosophy and methods of physical sciences that would be attractive to the researchers in the field. However, many revolutionary inventions have come from the mechanism of the philosophical thought of the physical sciences. This is, of course, a vast and very interesting topic that must be investigated in detail by philosophers, scientists or philosopher-scientists such as physicists. In order to do justice to it one has to write a book. For example, you may think mainly of the historical aspect that is how methodology and philosophy of physical sciences developed in the last century and how it influenced the development in science. One may also think of the topic of methodology and philosophy in physics treated by a philosopher, a scientist or a physicist, which would mean from quite different points of view. Another important question of this topic that needs to be answered is the question of what can be done in methods and philosophy of physical sciences in the near future. The aim of the study: For a quarter of a century I have been interested in “ Philosophy of Sciences “ as a hobby and from time to time have given lectures on this subject to students of physics as an elective course, in which one of the main subjects of the course was “Philosophy and Methods of the Physical Sciences ,“ I would like to share my experience , knowledge and research results on these topics with distinguished science readers of public and to acquaint philosophical and methodological ideas that play an active role in the development process of physical sciences for those who want to do research to shed some light on this issue. In this direction, science of physics, relation between physics and philosophy-science, the philosophy and methods of classical physical sciences, philosophical comments of quantum theory, the methods and philosophy of modern physical sciences, Philosophy of Physics and the Methodology, how a scientist works to get a better understanding of the laws of nature, success through method, Einstein's methodology, impact of relativity, the conflicting views in the progress of modern physics, and the strategy adopted in the study of physical systems, have been examined.

The population dynamics of cancer incidence: The model of a second-order phase transition

This paper considers an approach to the description of the age-specific and time-dependent dynamics of cancer incidence. This approach is based on a model that describes the age-specific dynamics of cancer as a phase transition of the second order and is widely used in the study of physical systems. The proposed model of cancer development as the second-order phase transitions is quite consistent with the data of medical statistics, is well described using only two free parameters, easily verified by the statistical data, and is interpreted well. The applicability of the model of second-order phase transitions to the description of the processes in the nonphysical systems is likely to be determined by the versatile nature of the processes that occur during the phase transitions.

Hidden symmetries of dynamics in classical and quantum physics

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as non-relativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of non-trivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher dimensional black holes, the Dirac equation, supergravity with and without fluxes, providing a tool to probe the dynamics of non-linear systems.

Thermostatistical distribution of a trophic energy proxy with analytical consequences for evolutionary ecology, species coexistence and the maximum entropy formalism

Conventional thermodynamics and statistical mechanics deal with the study of physical systems under equilibrium conditions (EC). Internal EC at a temperature that differs from the environment temperature are sustained, in general, by some type of artificial boundaries imposed with research aims or with quotidian utility goals in many kind of domestic appliances; the typical example of academic lab is a closed system immersed in a thermal bath which keeps the temperature constant. However, the ecosystem is a far-from-EC open system. Therefore, conventional thermodynamics and statistical mechanics tend to be orthodoxly regarded as limited to explain the ecosystem functioning since, at the first glance; there seem to be several essential functional differences between it and the previously-mentioned kind of physical systems. This viewpoint averse to conventional physics is paradoxical in regard to the current ecological paradigm given the fully thermodynamic foundation of ecosystem ecology. However, additional evidence in favor of the usefulness of conventional physics to describe the ecosystem functioning have recently been published, pointing out to the possibility that the analytical approach to ecology based on our undergraduate knowledge of physics, unfortunately, could have been hastily neglected before producing its most valuable results. This paper, fully based on the above-mentioned evidence, performs an unavoidable additional step in order to complete such a proposal by showing that the Boltzmann distribution of molecular energy values can be simply and successfully adapted to model the distribution of values of a proxy for trophic energy across an increasing gradient of energy levels, in a very similar fashion to that of a standard trophic pyramid. Starting from this result and by using a balanced combination between plausible theoretical considerations and abundant empirical data, we analyze why this approach is in agreement with well-known ecological principles, at the same time that we explore the general empirical advantages and aftermaths derived from this suggestion. Finally, the article explores the usefulness of the thermo-statistical modeling of eco-kinetic energy per plot to understand those essential physical factors that: promote biological evolution, facilitate species coexistence, can explain the holes in the fossil record, and enhance our current viewpoint about the ecological meaning of entropy. In summary, this article provides simply understandable additional information that indicates, despite its far-from-EC nature, any natural ecosystem is not far away from the most orthodox principles of conventional physics.

Effects, Observables, States, and Symmetries in Physics

We show how effect algebras arise in physics and how they can be used to tie together the observables, states and symmetries employed in the study of physical systems. We introduce and study the unifying notion of an effect-observable-state-symmetry-system (EOSS-system) and give both classical and quantum-mechanical examples of EOSS-systems.

Modelling sequential circuits with cellular automata

Cellular automata are powerful computational models for the study of physical systems. In the recent past they have been used to solve VLSI and CAD problems such as synthesis and testing of integrated circuits. In this paper it is shown how cellular automata may be used to model the behaviour of sequential circuits. The nice property of the proposed approach is that it provides an homogeneous representation of all the components of the circuit under investigation : primary inputs, flip-flops, primary outputs and their related cones of combinational logic are modelled in the same way by means of cellular automaton cells. Clearly, it is necessary to differentiate cells representing the flip-flops, from cells modelling the primary outputs and the primary inputs ; in fact, for cells of the first type the evolution rules are fixed, and they are simply given by the boolean functions realized by the cones of logic feeding the flip-flops. A similar argument applies to cells of the second type, with the difference that the states of these cells do not influence the next state of any other cell of the automaton. For cells of the third type, on the other hand, the next state functions are boolean functions whose characteristics depend on the aspect of the external world the user would like to model. The choice of such functions is not trivial, and to be effective requires an accurate study of both the functional meaning of each primary input in the context of the circuit to be modelled, and the relationship, if any, between the primary input lines. This paper includes a discussion, supported by experimental data, on the criteria to be used for the choice of these functions.

On a rational approximation problem in the real Hardy space H 2

1. Introduction The problem of finding a rational approximation to a holomorphic function in a domain 52 often arises in practice. Let us give an example from system theory which has first motivated our work [l]. System theory is concerned with the study of physical systems that can be described by a relation between inputs and outputs. When considering discrete time systems, it is a convention to denote by u(z)=Cksko ukzmk, UkER,

An algorithm to study tunnelling in a wide class of one-dimensional multiwell potentials. I

The author proves a theorem which gives an algorithmic solution to the problem of finding the logarithmic derivative of the ground-state wavefunction of one-dimensional systems. By means of this quantity, as is well known, one can determine the lowest part of the spectrum of the Hamiltonian by probabilistic methods. The author shows that, in some natural classes of potentials, the complexity of the algorithm is less than N3, where N is the number of the absolute minima of the potential. The author's approach allows a systematic treatment of cases of much greater complexity than those analysed so far in the literature and it can be useful in the study of physical systems like, for example, long molecular chains or superlattice structures.

Randomly Exact Methods

Important advances in the understanding of "random" processes have produced a variety of stochastic algorithms that offer unprecedented scope and utility in the study of physical systems. These algorithms represent a departure from the usual philosophy inherent in the study of many-body problems and have a number of significant features. Chief among these features are simplicity, weak dependence on dimensionality, and ease of transition between classical and quantum-mechanical descriptions. These methods are also readily adapted for use on massively paraliel computer architectures. These new stochastic methods represent a valuable addition to the tools available for the analysis of both equilibrium and time-dependent many-body problems.

Path integral quantisation and coherent states

Generalised coherent states are used in the quantum mechanical study of physical systems with homogeneous phase spaces, for which there is a group theoretical approach to quantisation. New sets of coherent states are introduced based on dynamical subalgebras and also with fiducial vectors in the rigged Hilbert space. The path integral expression for coherent state transition amplitudes is examined from a group theoretical point of view.

Does cross-impact analysis have a future?

where event 3 is the incidence of grave social troubles in Spain in 1974 and event 6 is the end of net emigration of Spanish worker in 1975. Thus we are forced to the conclusion that when the grave social troubles of 1974 have been taken into consideration the workers of Spain are more likely than they would otherwise have been to stay in Spain. Presumably for the riots. Again, various contentions are arguable and it is fair to say that the Battelle exercise must properly be assessed in terms of all the events considered. The fact remains that such procedures are being used to endow a quite spurious mathematical respectability to the consideration of events which are grossly aggregated for simplicity and are causally related to each other in varying degrees which, because of the absence of any coherent theory of the mechanics of social systems, are not even quantifiable in relative terms. Cross-impact analysis was born of conditional probability theory which in turn was derived from the study of physical systems containing random elements. When applied to social systems it is at best a game as it must be if the events considered are sufficiently precise to allow accurate assessment of probabilities, for any such set of events fully describing even the simplest of social developments must be exceedingly numerous; at worst cross-impact analysis is an ineffective tool tempting its users to the delusion that it allows the accurate assessment of the probability of future events and scenarios. The application of inappropriate scientific techniques to the analysis of social systems has happened before and will again; it is time that this particular bag of chicken bones was laid to rest.

A generalized sensitivity approach to feedback systems in Hilbert space

A generalized sensitivity study of physical systems in Hilbert space, which involve any feedback law, is presented. Some of the results previously obtained for the class of physical systems which are described by ordinary differential equations appear as special cases. Situations where the systems involve time delays or time lags or distributed-parameters, etc., can be treated by the present theory. The results are based on a general model of physical systems consisting of a left-hand side linear (or non-linear) operator acting on the systems state and of a right-hand aide nonlinear operator acting on the state, the control input, and a set of unknown parameters. A computational method for solving the resulting equations is suggested which possesses second-order convergence and proved to be successful in a wide range of applications.