Hasil untuk "Analytic mechanics"

J. Deutsch

The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy eigenstates behave in many ways like a statistical ensemble. A more detailed statement of this is named the eigenstate thermalization hypothesis (ETH). The reasons for why it works in so many cases are rooted in the early work of Wigner on random matrix theory and our understanding of quantum chaos. The ETH has now been studied extensively by both analytic and numerical means, and applied to a number of physical situations ranging from black hole physics to condensed matter systems. It has recently become the focus of a number of experiments in highly isolated systems. Current theoretical work also focuses on where the ETH breaks down leading to new interesting phenomena. This review of the ETH takes a somewhat intuitive approach as to why it works and how this informs our understanding of many body quantum states.

N. Goldenfeld

F. Dyson

K. Broberg

C. L. Siegel, J. Moser

M. K. Sparrow

L. Bertini, A. Sole, D. Gabrielli et al.

Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these states have been the subject of several theoretical investigations, both analytic and numerical. The macroscopic fluctuation theory, based on a formula for the probability of joint space-time fluctuations of thermodynamic variables and currents, provides a unified macroscopic treatment of such states for driven diffusive systems. We give a detailed review of this theory including its main predictions and most relevant applications.

D. Fedosov, B. Caswell, G. Karniadakis

Francesco Campaioli, F. A. Pollock, F. Binder et al.

Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when N batteries are charged collectively. We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian. We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive. For our main result, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted; i.e., at most k batteries are interacting. This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.

André Brock

A. Ushveridze

N. Kalita, A.J. Dutta

In this article, we study the spectrum, fine spectrum and boundedness property of second order quantum difference operator ∆2q (0 < q < 1) over the class of sequence lp (1 < p < ∞), the pth summable sequence space. The second order quantum difference operator ∆2q is a lower triangular triple band matrix ∆2q(1,−(1+ q),q). We also determine the approximate point spectrum, defect spectrum, compression spectrum, and Goldberg classification of the operator on the class of sequence. We obtained the results by solving an infinite system of linear equations and computing the inverse of a lower triangular infinite matrix. We also provide appropriate examples along with graphical representations where necessary.

B.E. Kanguzhin, M.O. Mustafina, O.A. Kaiyrbek

The Laplace-Beltrami operator is studied on a stratified set consisting of two punctured circles and an interval. A complete description of all well-posed boundary value problems for the Laplace-Beltrami operator on such a set is given. In the second part of the paper, a class of self-adjoint well-posed problems for the Laplace-Beltrami operator on the specified stratified set is identified. The obtained results can be considered as a generalization of known results on geometric graphs. In particular, the stratified set under consideration can be interpreted as graphs with loops. Studies on the spectral asymptotics of SturmLiouville operators on plane curves homotopic to a finite interval are also closely related to the present results paper. Since the punctured circle is diffeomorphic to a finite interval, the spectral methods applied to differential operators on a finite interval can be modified to study the spectral properties of differential operators on the punctured circle. The main results of this paper are obtained by modifications of methods that were previously used in the study of the asymptotic behavior of the eigenvalues of the Sturm-Liouville operator on a finite interval.

T. Chou, K. Mallick, R. Zia

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violates detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process. It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.

R. Aghababaei, D. Warner, J. Molinari

The adhesive wear process remains one of the least understood areas of mechanics. While it has long been established that adhesive wear is a direct result of contacting surface asperities, an agreed upon understanding of how contacting asperities lead to wear debris particle has remained elusive. This has restricted adhesive wear prediction to empirical models with limited transferability. Here we show that discrepant observations and predictions of two distinct adhesive wear mechanisms can be reconciled into a unified framework. Using atomistic simulations with model interatomic potentials, we reveal a transition in the asperity wear mechanism when contact junctions fall below a critical length scale. A simple analytic model is formulated to predict the transition in both the simulation results and experiments. This new understanding may help expand use of computer modelling to explore adhesive wear processes and to advance physics-based wear laws without empirical coefficients. Adhesive wear can proceed through qualitatively different mechanisms, with conflicting results in the literature. Here the authors observe a transition between two regimes in simulations using model interatomic potentials, allowing development of a simple analytical theory to describe past results.

S. Liao

A.O. Basheyeva, S.M. Lutsak

The existence of a finite identity basis for any finite lattice was established by R. McKenzie in 1970, but the analogous statement for quasi-identities is incorrect. So, there is a finite lattice that does not have a finite quasi-identity basis and, V.A. Gorbunov and D.M. Smirnov asked which finite lattices have finite quasiidentity bases. In 1984 V.I. Tumanov conjectured that a proper quasivariety generated by a finite modular lattice is not finitely based. He also found two conditions for quasivarieties which provide this conjecture. We construct a finite modular lattice that does not satisfy Tumanov’s conditions but quasivariety generated by this lattice is not finitely based.

M.T. Kassymetova, N.M. Mussina

In this article, strongly minimal geometries of fragment hybrids are considered. In this article, a new concept was introduced as a family of Jonsson definable subsets of the semantic model of the Jonsson theory T, denoted by JDef(CT ). The classes of the Robinson spectrum and the geometry of hybrids of central types of a fixed RSp(A) are considered. Using the construction of a central type for theories from the Robinson spectrum, we formulate and prove results for hybrids of Jonsson theories. A criterion for the uncountable categoricity of a hereditary hybrid of Jonsson theories is proved in the language of central types. The results obtained can be useful for continuing research on various Jonsson theories, in particular, for hybrids of Jonsson theories.

Changchang Wang, Mindi Zhang

The physics and mechanism of sheet/cloud cavitation in a convergent–divergent channel are investigated using synchronized dynamic surface pressure measurement and high-speed imaging in a water tunnel to probe the cavity shedding mechanism. Experiments are conducted at a fixed Reynolds number of Re = 7.8 × 105 for different values of the cavitation number σ between 1.20 and 0.65, ranging from intermittent inception cavitation, sheet cavitation to quasi-periodic cloud cavitation. Two distinct cloud cavitation regimes, i.e. the re-entrant jet and shockwave shedding mechanism, are observed, accompanied by complex flow phenomenon and dynamics, and are examined in detail. An increase in pressure fluctuation intensity at the numbers 3 and 4 transducer locations are captured during the transition from re-entrant jet to shockwave shedding mechanism. The spectral content analysis shows that, in cloud cavitation, several frequency peaks are identified with the dominant frequency caused by the large-scale cavity shedding process and the secondary frequency related to re-entrant jet/shockwave dynamics. Statistical analysis based on defined grey level profiles reveals that, in cloud cavitation, the double-peak behaviours of the probability density functions with negative skewness values are found to be owing to the interactions of the re-entrant jet/shockwave with cavities in the region of 0.25 ~ 0.65 mean cavity length (Lc). In addition, multi-scale proper orthogonal decomposition analysis with an emphasis on the flow structures in the region of 0.25 ~ 0.65 Lc reveals that, under the shockwave shedding mechanism, both the re-entrant jet and shockwave are captured and their interactions are responsible for the dynamics and statistics of cloud shedding process.

Adrien Rouviere, Lucas Pascal, Fabien Méry et al.

Predicting the laminar to turbulent transition is an important aspect of computational fluid dynamics because of its impact on skin friction. Traditional transition prediction methods such as local stability theory or the parabolized stability equation method do not allow for the consideration of strongly non-parallel boundary layer flows, as in the presence of surface defects (bumps, steps, gaps, etc.). A neural network approach, based on an extensive database of two-dimensional incompressible boundary layer stability studies in the presence of gap-like surface defects, is used. These studies consist of linearized Navier–Stokes calculations and provide information on the effect of surface irregularity geometry and aerodynamic conditions on the transition to turbulence. The physical and geometrical parameters characterizing the defect and the flow are then provided to a neural network whose outputs inform about the effect of a given gap on the transition through the ${\rm \Delta} N$ method (where N represents the amplification of the boundary layer instabilities).