Role Of Conservation Laws Research Articles

Local Volume Conservation in Concentrated Electrolytes Is Governing Charge Transport in Electric Fields.

While ion transport processes in concentrated electrolytes, e.g., based on ionic liquids (IL), are a subject of intense research, the role of conservation laws and reference frames is still a matter of debate. Employing electrophoretic NMR, we show that momentum conservation, a typical prerequisite in molecular dynamics (MD) simulations, is not governing ion transport. Involving density measurements to determine molar volumes of distinct ion species, we propose that conservation of local molar species volumes is the governing constraint for ion transport. The experimentally quantified net volume flux is found to be zero, implying a nonzero local momentum flux, as tested in pure ILs and IL-based electrolytes for a broad variety of concentrations and chemical compositions. This constraint is consistent with incompressibility, but not with a local application of momentum conservation. The constraint affects the calculation of transference numbers as well as comparisons of MD results to experimental findings.

Role of Conservation Laws in the Development of Nonequilibrium and Emergence of Turbulence

It turns out that the equations of mathematical physics, which consist equations of the conservation laws for energy, linear momentum, angular momentum, and mass, possess additional, hidden, properties that enables one to describe not only a variation of physical quantities (such as energy, pressure, density) but also processes such as origination of waves, vortices, turbulent pulsations and other ones. It is caused by the conservation laws properties. In present paper the development of nonequilibrium in gasdynamic systems, which are described by the Euler and Navier-Stokes equations, will be investigated. Under studying the consistence of conservation laws equations, from the Euler and Navier-Stokes equations it can be obtained the evolutionary relation for entropy (as a state functional). The evolutionary relation possesses a certain peculiarity, namely, it turns out to be nonidentical. This fact points out to inconsistence of the conservation law equations and noncommutativity of conservation laws. Such a nonidentical relation discloses peculiarities of the solutions to the Navier-Stokes equations due to which the Euler and Navier-Stokes equations can describe the processes the development of nonequilibrium and emergence of vortices and turbulence. It has been shown that such processes can be described only with the help of two nonequivalent coordinate systems or by simultaneous using numerical and analytical methods.

On the role of conservation laws and input data in the generation of peaking modes in quasilinear multidimensional parabolic equations with nonlinear source and in their approximations

We study unbounded solutions of a broad class of initial–boundary value problems for multidimensional quasilinear parabolic equations with a nonlinear source. By using a conservation law, we obtain conditions imposed solely on the input data and ensuring that a solution of the problem blows up in finite time. The blow-up time of the solution is estimated from above. By approximating the source function with the use of Steklov averaging with weight function coordinated with the nonlinear coefficients of the elliptic operator, we construct finite-difference schemes satisfying a grid counterpart of the integral conservation law.

Forces in Aharonov–Bohm optical setting

The Aharonov–Bohm effect is usually associated with a path-dependent phase accumulated by a charged matter wave and determined by an effective vector potential. In a more general geometrical framework, such phase alterations have been the hallmark of a host of related phenomena in many different fields. However, besides phase changes, it was suggested that for finite wave-packets there is also an additional deflection leading to observable changes in the wave’s canonical momentum. In this paper, we create an optical scattering situation that permits observing nonconservative reaction forces, which result from the conservation of canonical momentum. We demonstrate experimentally, for the first time, the presence of such mechanical forces with the magnitude and direction determined by the phase dislocation of the vortex state. Our experimental results offer insights into essentially untested phenomena, where forces act on vortex fields, and allow examining the role of conservation laws and symmetries in complex interacting systems.

Comment on “Investigation of Hadron Multiplicity and Hadron Yield Ratios in Heavy-Ion Collisions”

Oliinychenko, Bugaev, and Sorin [arXiv:1204.0103 [hep-ph]] considered the role of conservation laws in discussing possible weaknesses of thermal models which are utilized in describing the hadron multiplicities measured in central nucleus-nucleus collisions. They argued to analyze the criteria for chemical freeze-out and to conclude that none of them was robust. Based on this, they suggested a new chemical freeze-out criterion. They assigned to the entropy per hadron the ad hoc value 7.18 and supposed to remain unchanged over the whole range of the baryo-chemical potentials. Due to the unawareness of the recent literature, the constant entropy per hadron has been discussed in Refs. [Fizika B 18, 141 (2009), Europhys. Lett. 75, 420 (2006), Phys. Rev. C 85, 014908 (2012) and nucl-ph/1306.3291]. Furthermore, it has been shown that the constant entropy per hadron is equivalent to the constant entropy normalized to the cubic temperature, an earlier criterion for the chemical freeze-out introduced in Refs. [Europhys. Lett. 75, 420 (2006), Nucl. Phys. A 764, 387 (2006)]. In this comment, we list out the ignored literature, compare between the entropy-number density ratio and two criteria of averaged energy per averaged particle number and constant entropy per cubic temperature. All these criteria are confronted to the experimental results. The physics of constant entropy per number density is elaborated. It is concluded that this ratio cannot remain constant, especially at large chemical potentials related to the AGS and SIS energies.

On the role of conservation laws in the problem on the occurrence of unstable solutions for quasilinear parabolic equations and their approximations

For a broad class of initial-boundary value problems for quasilinear parabolic equations with nonlinear source and their approximations, we show that if the initial energy is negative, then the solution always blows up in finite time. This is especially important for finding sufficiently simple and easy-to-verify conditions guaranteeing the presence of physical effects such as heat localization in peaking modes or thermal explosions and for deriving two-sided estimates of the solution lifespan. We construct the corresponding new classes of difference schemes for which grid analogs of integral conservation laws hold. We show that, to obtain efficient two-sided estimates for the blow-up time of the solution of the differential problem, in practice, one should use difference schemes with explicit as well as implicit approximation to the source.

Investigation of Hadron Multiplicities and Hadron Yield Ratios in Heavy Ion Collisions

We thoroughly discuss some weak points of the thermal model, which is traditionally used to describe the hadron multiplicities measured in the central nucleus-nucleus collisions. In particularly, the role of conservation laws and the values of hard-core radii along with the effects of the Lorentz contraction of hadron eigenvolumes and the hadronic surface tension are systematically studied. It is shown that, for the adequate description of hadron multiplicities, the conservation laws should be modified, whereas the conservation laws are not necessary at all for the description of hadron yield ratios. We analyzed the usual criteria for the chemical freeze-out and found that none of them is robust. A new chemical freeze-out criterion of constant entropy per hadron equals to 7.18 is suggested, and a novel effect of adiabatic chemical hadron production is discussed. Additionally, we found that the data for the center-of-mass energies above 10 GeV lead to the temperature of the nil hadronic surface tension coefficient of about T0 = 147 ± 7 MeV. This is a very intriguing result, since a very close estimate for such a temperature was obtained recently within an entirely different approach. We argue that these two independently obtained results evidence that the (tri)critical temperature of a QCD phase diagram is between 140 and 154 MeV. In addition, we suggest to consider the pion and kaon hardcore radii as new fitting parameters. Such an approach allows us, for the first time, to simultaneously describe the hadron multiplicities and the Strangeness Horn and to get a high-quality fit of the available experimental data.

Modeling segmental patterning in Drosophila: Maternal and gap genes

We propose a new mathematical model describing the establishment of maternal and gap proteins segmental patterning along the antero-posterior axis of the Drosophila early embryo. This model is based on experimental data and, without recurring to pre-defined activation thresholds, predicts qualitatively and quantitatively the expression patterns of the maternal and gap proteins, as well as the expression patterns of proteins resulting from mRNA ectopic expression and from some loss-of-function mutations. We conclude that the gap genes segmental patterning and consequent spatial organization of the embryo is determined by three main factors: (1) the initial positioning of the maternal bicoid and torso mRNA inside the egg, and subsequent diffusion of the corresponding proteins; (2) the structure of the genetic regulatory network; (3) the role of conservation laws in the establishment of steady and non-uniform spatial distributions of non-diffusing proteins.

Combined development of middle school children's conceptual understanding in momentum conservation, procedural skills and epistemological awareness in a constructionist learning environment

1D collisions are part of the curriculum for 15–16 year olds in the educational system of Cyprus. The curriculum activities in this domain commonly rely on a mathematical approach and are constrained by prerequisite algebraic skills. Conservation laws have the broadest possible application of all laws in physics and are thus considered by many scientists to be the most fundamental laws in our representations of nature. However, they are currently presented in the educational system in a very didactic manner with the result that students identify them as meaningless algorithms to be implemented in working out a solution as to the outcome of a collision. In this paper, we focus on the design of inquiry based curriculum that aims to help 13 and 14 year olds to foster conceptual understanding and modelling skills in an integrated manner in the domain of 1D collisions. Through the model-based curriculum students are also expected to appreciate the important role of conservation laws in science as a fundamental principle in analysing process end states. We will also present some preliminary pre-test results related to our threefold objective.

Role of conservation laws in small Reynolds number closures: Application to large-scale dynamics of compressible flows

We emphasize the role played by conserved integral quantities in the construction of multiple-scale solutions of hydrodynamic equations, for flows stirred by a prescribed body force. We illustrate the point by comparing the multidimensional Burgers' equation with the case of a polytropic gas for which momentum conservation ensures the possibility of scale separation at low Reynolds number. Our analysis does not support the possibility of an alpha dynamo type instability in low Reynolds number isotropic non-magnetic compressible flows.

Time-dependent variational principles and conservation laws in wavepacket dynamics

A criterion for the equivalence of time-dependent variational principles in current use in chemistry and physics is demonstrated. Conservation laws are considered and it is shown that under certain conditions quantal conservation laws also hold for the time evolution derived from the variational principle. The formalism is applied to an N-dimensional spherical Gaussian wavepacket. A numerical example for the three-dimensional spherical Gaussian potential well is worked out to illustrate the dynamics and the role of conservation laws.

Role of Conservation Laws in the Callan-Rubakov Processes with Arbitrary Number of Generations of Fermions

Role of Conservation Laws in the Callan-Rubakov Processes with Arbitrary Number of Generations of Fermions

Analysis of the Quantum Mechanical Measurement Process

The quantum mechanical measurement process is analysed in detail, especially from the group theoretical point of view. The first three chapters review the results obtained before briefly. In §1, the classical theory of measurement, originated by von Neumann, is birefly described. The importance of considering more general schemes of measurements than the original one is, however, emphasized In §2, the role of conservation laws, in imposing limitations on the possibility of measurements, is discussed. Accurately measurable quantities are defined in this context. In §3, the role of conservation laws is further analysed. It is shown that the conserved quantity of the apparatus cannot be used for a “pointer reading.” The following two chapters discuss the nature of the exactly measurable quantities. In §4, exactly measurable quantities are explicitly determined. It is shown that the measurement of projection operators in the Hilbert space of the object which commute with the operators of the restricted Poincare group give all the information on the states of the object that can be obtained by accurate measurements. In §5, the measurement on objects which are composed of more than one particle is discussed.