Classical Theory

In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs. *

Approximate critical conditions for a thermal explosion problem is developed for a two-step reactions based on theories of Semenov and Frank-Kamenetskii. The aim is to examine the contributions of the radical termination step and the temperature dependent pre-exponential factor on the critical parameters within the framework of classical stationary and non-stationary theories. In the non-stationary case, a more general expression for the critical Semenov parameter (cr) and critical temperature (θ cr) were obtained by asymptotic procedure. In the stationary case, numerical estimates for the critical Frank-Kamenetskii parameter (δ cr) and the critical temperature (θ cr) were obtained by variational method technique. It was observed that the Semenov and Frank-Kamenetskii parameters are greatly influenced by the termination step and the variable pre-exponential factor. Apart from elucidating hitherto unknown features in the theory of thermal explosion, the results are more general as some known results are easily recovered.

A dynamic object is an object whose properties change over time. A static object is an object whose properties do not change over time. Given such an idealization, the notion of 'static' lies at an extreme end of the spectrum of temporal relations between objects and properties. Indeed, modern physics tells us that no objects are truly static. Nevertheless, many of our physical, computational, and metaphysical theories turn a blind eye to the role of time, often for practical reasons. So, perhaps it is not surprising that in the philosophy of mind -where physical, computational, and metaphysical theories meet -there has been a consistent tendancy to articulate theories that consider function and time independently. As a result, contemporary theories in cognitive science consider time unsystematically (see the next section for specific examples). In this chapter, I suggest that the problem with this 'ad hocery' is that the systems we are trying to characterize are real-time systems, whose real-time performance demands principled explanation (a point on which many of these same contemporary theorists agree). After a discussion of the importance and roots of dynamics in cognitive theorizing, I describe the role of time in each of the three main approaches to cognitive science: symbolicism, connectionism and dynamicism. Subsequently, I outline a recently proposed method, the Neural Engineering Framework (NEF), that, unlike past approaches, permits a principled integration of dynamics into biologically realistic models of high-level cognition. After briefly presenting a model, BioSLIE, that demonstrates this integration using the NEF, I argue that this approach alone is in a position to properly integrate dynamics, biological realism, and high-level cognition.

Lattice structures can be developed for operating in high temperature environments. Ceramic-metal FGMs (Functionally graded materials) can be considered for manufacturing lattice plates. In the current study, an exact material modeling using Heaviside distribution functions is performed for lattice FGM plates. Using the classical theory, motion governing equations for lattice FGM plates under uniform temperature field has been derived. Free vibration problem of lattice FGM plates subjected to initial thermal loading and considering simply-supported boundary conditions has been solved using closed form Galerkin method. The analytical results are verified through comparison by those obtained from ABAQUS FEM (finite element method) commercial software. The solution presented here could be treated as a benchmark for future studies about FGM stiffened plates.

This paper applies Max Weber's proposition regarding the differences between the 'sciences' to the 'historicist controversy': the problems emerging from opposing approaches to understanding the past. The historiography in question is the development of the 'biomedical model' of health and disease, and the rise of 'medicine' in the course of 19 th century Europe and Britain. While Weber's theoretical framework does not answer the questions posed by present-day scholars about specific historical events, it enables a critique of the process through which history is 'constructed', and offers an alternative approach to the 'transformation' of 19 th century medicine.

Families of finite graphs of large girth were introduced in classical extremal graph theory. One important theoretical result here is the upper bound on the maximal size of the graph with girth 2d established in even circuit theorem by Erdös. We consider some results on such algebraic graphs over any field. The upper bound on the dimension of variety of edges for algebraic graphs of girth 2d is established. Getting the lower bound, we use the family of bipartite graphs D(n, K) with n 2 over a field K, whose partition sets are two copies of the vector space K n . We consider the problem of constructing homogeneous algebraic graphs with a prescribed girth and formulate some problems motivated by classical extremal graph theory. Finally, we present a very short survey on applications of finite homogeneous algebraic graphs to coding theory and cryptography.

Lattice plates have been extensively used as lightweight structures in many industries. In the present research, an exact material modeling using Heaviside distribution functions is presented for lattice composite plates. Using CLT (classical lamination theory), equilibrium equations for lattice composite plates under uniform temperature field are derived. The equations are solved by performing closed form Galerkin method. The thermal buckling modes are obtained by solving the eigenvalue problem. The general solution presented in this paper includes laminates with arbitrary stacking sequences. The accuracy of theoretical model is checked through comparisons with finite element results obtained by simulation in ABAQUS and good agreement is achieved.

In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.

This paper applies Max Weber's proposition regarding the differences between the 'sciences' to the 'historicist controversy': the problems emerging from opposing approaches to understanding the past. The historiography in question is the development of the 'biomedical model' of health and disease, and the rise of 'medicine' in the course of 19 th century Europe and Britain. While Weber's theoretical framework does not answer the questions posed by present-day scholars about specific historical events, it enables a critique of the process through which history is 'constructed', and offers an alternative approach to the 'transformation' of 19 th century medicine.

Résumé/Abstract As a critical concept, the public sphere has always been premised on two idealizing assumptions: in principle, public opinion should be normatively legitimate and politically efficacious. Yet these assumptions are hard to associate with the discursive ...

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Woelk and Strey recently criticized the temperature dependency of nucleation rates of the isothermal Classical Nucleation Theory, of water in its vapor, and showed that the apparent excellent agreement of the theory with experimental data, in a narrow temperature range, is in fact a "crossover" of the theory with experimental data. Similarly, Zanotto and Fokin criticized the isothermal Classical Nucleation Theory for nucleation (devitrification) in silicate glasses, claiming that "the theory fails to describe nucleation rates in glasses quantitatively." Finally, Schmelzer, Boltachev and Baidakov stated that: "…deviations between theoretical and experimental data for the steady-state nucleation rate may reach the order of 10 20-10 30 for condensation of one component vapors and even 10 100 or more for phase formation in glass-forming melts." This situation shows the need for new proposals to explain the phenomenon. We demonstrate that a simple Adiabatic Nucleation Theory predicts nucleation rates in "fragile" oxide glasses (T 00 /T g N 0.6, where T 00 is the Fulcher temperature and T g is the glass transition temperature) with an average deviation of only nine orders of magnitude (too high) and shows (within this uncertainty) correctly which glasses show devitrification and which ones do not, in experiments during "laboratory times." The theory could not yet be extended to "strong" glasses because of the very low Fulcher temperatures of these glasses (T 00 /T g b 0.6), in which the Stokes-Einstein relation loses its validity completely.

We investigate the dynamics of out-of-plane (OP) vortices, in a 2-dimensional (2D) classical Heisenberg magnet with a weak anisotropy in the coupling of z-components of spins (easy plane anisotropy), on square lattices, under the influence of a rotating in-plane (IP) magnetic field. Switching of the z-component of magnetization of the vortex is studied in computer simulations as a function of the magnetic field's amplitude and frequency. The effects of the size and the anisotropy of the system on the switching process are shown. An approximate dynamical equivalence of the system, in the bulk limit, to another system with both IP and OP static fields in the rotating reference frame is demonstrated, and qualitatively the same switching and critical behavior is obtained in computer simulations for both systems. We briefly discuss the interplay between finite size effects (image vortices) and the applied field in the dynamics of OP vortices. In the framework of a discrete reduced model of the vortex core we propose a mechanism for switching the vortex polarization, which can account qualitatively for all our results. A coupling between the IP movement (trajectories) of the vortex center and the OP core structure oscillations, due to the discreteness of the underlying lattice, is shown. A connection between this coupling and our reduced model is made clear, through an analogy with a generalized Thiele equation.

In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs. *

A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices with suitable Hermitian matrices.

We present the results of a detailed study of the influence of rotational angular momentum on vibrotational transfer in the system Li 2 *(V i ,j i ) + Ne f Li 2 *(V f ,j f ) + Ne, where V i,f and j i,f indicate initial and final vibrational and rotational levels, respectively, and Li 2 * is in its first electronically excited 1 Σ u + state. Level-to-level inelastic rate constants for j i up to 76 have been measured. The measurements span 4 orders of magnitude in size and include |∆V| e 5 and |∆j| e 50. The results extend the range of previous measurements in this system and further document the phenomenon of quasiresonant vibrotational transfer. This process, induced by high rotational angular momentum, results in large rate constants for vibrational transfer and a systematic correlation of ∆j and ∆V according to the rule ∆j ) -4∆V. At j i g 64, the total vibrationally inelastic rate constant is found to be larger than the total rotationally inelastic rate constant. A fully classical treatment of the dynamics on an ab initio potential surface results in rate constants that agree remarkably well with the data.

We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of Colombeau's simplified model. This generalizes the notion of G^∞-regularity introduced by M. Oberguggenberger. A key point is that these regularities can be characterized, for compactly supported generalized functions, by a property of their Fourier transform. This opens the door to microanalysis of singularities of generalized functions, with respect to these regularities. We present a complete study of this topic, including properties of the Fourier transform (exchange and regularity theorems) and relationship with classical theory, via suitable results of embeddings.

We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyze the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyze and discuss the conditions under which the method has optimal performances. -92-06, SCCS 241, hep-lat/9205018

Using thermodynamic perturbation theory, we derive a simple formalism for treating intrinsic anharmonic effects in solids. In this formalism, the central quantity is the intrinsic anharmonicity parameter a, which can be derived from vibrational spectroscopy or computer simulation. Advantages of our approach include (1) correct low-and high-temperature behaviour, (2) analyticity of all the thermodynamic functions and (3) the possibility of systematic incorporation of higher-order anharmonic effects. This approach can be used in studying equations of state and thermodynamics of solids in a wide temperature range. A detailed comparison with other approaches is given.

This paper studies the destabilizing effects of dissipation on families of relative equilibria in Hamiltonian systems which are non-extremal constraint critical points in the energy-Casimir or the energy-momentum methods. The dissipation is allowed to destroy the conservation law associated with the symmetry group or Casimirs, as long as the family of relative equilibria stays on an invariant manifold. This approach complements earlier work in the literature, in which the dissipation did not affect the conservation law. First, Chetaev's instability theorem is extended to invariant manifolds and this extended theorem is used to prove instability of families of relative equilibria for several examples. Second, it is shown that families of non-extremal stationary solutions of the two-dimensional incompressible homogeneous Euler equations are unstable for the corresponding viscous perturbations of this system, that is, for the two-dimensional Navier-Stokes equations. Also, the instability of the sleeping top relative equilibria under friction can easily be proved in this way, even before the Hamiltonian sleeping top becomes linearly unstable. Finally, sufficient conditions are given for which friction destabilizes families of non-extremal relative equilibria in simple mechanical systems with abelian symmetry.

The pyrochlore antiferromagnet Tb 2 Ti 2 O 7 has proven to be an enigma to experimentalists and theorists working on frustrated magnetic systems. The experimentally determined energy level structure suggests a local 111 Ising antiferromagnet at low temperatures, T < ∼ 10K. An appropriate model then predicts a long-range ordered Q = 0 state below approximately 2K. However, muon spin resonance (µSR) experiments reveal a paramagnetic structure down to tens of milli-Kelvin. The importance of fluctuations out of the ground state effective Ising doublet has been recently understood, for the measured paramagnetic correlations can not be described without including the higher crystal field states. However, these fluctuations treated within the random phase approximation (RPA) fail to account for the lack of ordering in this system below 2K. In this work, we briefly review the experimental evidence for the collective paramagnetic state of Tb 2 Ti 2 O 7. The basic theoretical picture for this system is discussed, where results from classical spin models are used to motivate the investigation of quantum effects to lowest order via the RPA. Avenues for future experimental and theoretical work on Tb 2 Ti 2 O 7 are presented.

This paper studies the dynamics of a disequilibrium model of classical inspiration from a non-gravitational perspective. In each sector, capitalists decide on rates of accumulation that are revised if the desired rates are not feasible. The dynamics differ according to the hypotheses retained (cyclical growth interspersed by crises, convergence towards a stationary state or towards a regular but sluggish growth). These results are compared with those of the classical and Keynesian theories.

We investigate the physics of black holes in 1 + 1 dimensions. We demonstrate how an event horizon structure can arise in two dimensions given a variety of energy-momentum tensors, cataloguing the resultant particular solutions. We examine the motion of freely falling test particles in the vicinity of such horizons and demonstrate that they generically fall through in a finite amount of proper time and an infinite amount of coordinate time. The thermodynamic and quantum properties of these solutions are also examined, and give rise to a fundamental length scale in the theory whose origin is markedly different from that of the Planck mass in the higher-dimensional case. We show that 't Hooft's prescription for cutting off eigenmodes of particle wave functions in the vicinity of the horizon is source dependent and particle-mass dependent, unlike the four-dimensional case.

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Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of the discrete system. Excitation of internal mode causes orbital motion. This is confirmed by simulations. PACS. 75.10.Hk Classical spin models -75.30.Ds Spin waves -05.45.-a Nonlinear dynamics and nonlinear dynamical systems

We present the results of a detailed study of the influence of rotational angular momentum on vibrotational transfer in the system Li 2 *(V i ,j i ) + Ne f Li 2 *(V f ,j f ) + Ne, where V i,f and j i,f indicate initial and final vibrational and rotational levels, respectively, and Li 2 * is in its first electronically excited 1 Σ u + state. Level-to-level inelastic rate constants for j i up to 76 have been measured. The measurements span 4 orders of magnitude in size and include |∆V| e 5 and |∆j| e 50. The results extend the range of previous measurements in this system and further document the phenomenon of quasiresonant vibrotational transfer. This process, induced by high rotational angular momentum, results in large rate constants for vibrational transfer and a systematic correlation of ∆j and ∆V according to the rule ∆j ) -4∆V. At j i g 64, the total vibrationally inelastic rate constant is found to be larger than the total rotationally inelastic rate constant. A fully classical treatment of the dynamics on an ab initio potential surface results in rate constants that agree remarkably well with the data.

We investigate spin excitations in classical continuum Heisenberg antiferromagnetic spin systems in both low (one) and higher (two and three) dimensions at different levels of continuum approximation. The spin excitations in one-dimensional anisotropic chains, when the adjacent spins are locked antiparallel, are found during evolution to reduce under appropriate limits to that of isotropic chains reported earlier. For isotropic systems, we unlock the adjacent spins and stereographically project the unit spheres of spins onto complex planes and investigate the underlying spin excitations in the new variable. Both in the case of one-dimensional chains and in higher dimensional antiferromagnets we obtain a class of static planar configurations. 0375-9601/94/$07.00

First, we reflect on computing sets and functions using measurements from experiments with a class of physical systems. We call this experimental computation. We outline a programme to analyse theoretically experimental computation in which a central problem is: Given a physical theory T , explore and classify the computational models that can be embedded in, and abstracted from, the physical systems specified by the physical theory T . We consider the embedding arbitrary sets, functions, programs, and computers into designs for systems that can be specified in subtheories or fragments T of Newtonian kinematics in order to explore some of the physical assumptions of T that allowed its systems to qualify as hyper-computers, i.e., physical models that compute sets and functions that cannot be computed in classical computability theory. In designing systems we work strictly within the chosen theory T and do not concern ourself with whether or not T is valid of the world today. We are interested in exploring the subtheory from a computational point of view and especially in restrictions on the assumptions of T that allow us to return from hyper-computation to classical computation.

Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say S n = g X 1 + • • • + g X n , where E g X 1 = 0 and E g X 1 2 < ∞. The conditions imposed restrict the moments of g and the growth of the conditional means E S n X 1. No other restrictions on the dependence structure of the chain are required. When specialized to shift processes, the conditions are implied by simple integral tests involving g.

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The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the Schrödinger equation separates into one-dimensional equations belonging to the class of generalized Lamé differential equations.

We review an scenario for the non-equilibrium dynamics of glassy systems that has been motivated by the exact solution of simple models. This approach allows one to set on firmer grounds well-known phenomenological theories. The old ideas of entropy crisis, fictive temperatures, free-volume... have clear definitions within these models. Aging effects in the glass phase are also captured. One of the salient features of the analytic solution, the breakdown of the fluctuation-dissipation relations, provides a definition of a bonafide effective temperature that is measurable by a thermometer, controls heat flows, partial equilibrations, and the reaction to the external injection of heat. The effective temperature is an extremely robust concept that appears in non-equilibrium systems in the limit of small entropy production as, for instance, sheared fluids, glasses at low temperatures when quantum fluctuations are relevant, tapped or vibrated granular matter, etc. The emerging scenario is one of partial equilibrations, in which glassy systems arrange their internal degrees of freedom so that the slow ones select their own effective temperatures. It has been proven to be consistent within any perturbative resummation scheme (mode coupling, etc) and it can be challenged by experimental and numerical tests, some of which it has already passed.

The dynamics of a non-planar vortex in a two-dimensional easy-plane ferromagnet of finite size is studied. Spin dynamics simulations show small cycloidal oscillations of the vortex around its mean path. In contrast to an earlier phenomenological theory we give a physical explanation: The oscillations occur due to the interaction of the vortex with coherent spin waves which are excited by this vortex at the moment when it starts to move, in order to conserve the total energy and angular momentum. The calculation of these quantities yields the frequencies and amplitudes of the cycloidal oscillations in good agreement with the simulation data.

The results of decomposition of texture function into Gauss-shaped components are presented. Such the decomposition is useful in many applications, especially if one is directly interested in participation of different texture components, corresponding to given crystal orientations (ideal orientations). Texture presentation by Gauss-shaped components enables also in many cases the simplification of data treatment and important reduction of computer time and memory. Two methods of decomposition are presented: the classical one (deterministic) and that based on genetic algorithm method. The quality of both methods is compared. The source code of computer program for classical texture decomposition is available from the authors.

Approximate critical conditions for a thermal explosion problem is developed for a two-step reactions based on theories of Semenov and Frank-Kamenetskii. The aim is to examine the contributions of the radical termination step and the temperature dependent pre-exponential factor on the critical parameters within the framework of classical stationary and non-stationary theories. In the non-stationary case, a more general expression for the critical Semenov parameter (cr) and critical temperature (θ cr) were obtained by asymptotic procedure. In the stationary case, numerical estimates for the critical Frank-Kamenetskii parameter (δ cr) and the critical temperature (θ cr) were obtained by variational method technique. It was observed that the Semenov and Frank-Kamenetskii parameters are greatly influenced by the termination step and the variable pre-exponential factor. Apart from elucidating hitherto unknown features in the theory of thermal explosion, the results are more general as some known results are easily recovered.

Photo-thermo-refractive (PTR) glass is an optically transparent photosensitive oxide glass. Upon heating, the UV-exposed regions of this glass undergo copious crystallization of NaF nano-crystals giving rise to a permanent, localized refractive index change. But the unexposed parts of the glass also undergo some crystallization which causes unwanted light scattering. Holographic optical elements produced from PTR glass have been used in special laser systems. In this article we report, for the first time since the invention of PTR glass about half-century ago, the steady-state nucleation rates, nucleation time-lags and crystal growth rates for UV-unexposed PTR glass estimated in a wide temperature range, from T g~4 70°C up to 750°C. A self-consistent description of these data is presented in the framework of CNT using the interfacial free energy of the critical nuclei and the effective diffusion coefficient as adjustable parameters. The diffusivity calculated from crystallization kinetics and that estimated from viscous flow via the Stokes-Einstein-Eyring equation show a decoupling phenomenon.

The dynamics of a non-planar vortex in a two-dimensional easy-plane ferromagnet of finite size is studied. Spin dynamics simulations show small cycloidal oscillations of the vortex around its mean path. In contrast to an earlier phenomenological theory we give a physical explanation: The oscillations occur due to the interaction of the vortex with coherent spin waves which are excited by this vortex at the moment when it starts to move, in order to conserve the total energy and angular momentum. The calculation of these quantities yields the frequencies and amplitudes of the cycloidal oscillations in good agreement with the simulation data. PACS. 75.10.Hk Classical spin models -05.45.Yv Solitons -75.40.Mg Numerical simulation studies

For a wide class of antiferromagnetic models we prove the existence of a phase transition using an extended Peierls argument, taking into account a result of Dobrushin [R. L. Dobrushin, Funct. Anal. Appl. 2:44 (1968); in English, 2:302 (1968)] for an antiferromagnetic Ising model and the results of Malyshev [V. Malyshev, Comm. Math. Phys. 40:75-82 (1975)] for ferromagnetic models (such as the anisotropic rotator). In particular we review a result of Fr6hlich, Israel, Lieb, and Simon [J. Fr6hlich et al., J. Stat. Phys. 22(3):297-347 (198)] obtained when reflection positivity holds.

We construct a new class of non-topological soliton stars which appears in global non-abelian field theories coupled to classical Einstein gravity. It is the analogue of the Q-stars recently found in abelian theories. If mu (of order 10- to 104 GeV) is a free-particle inverse Compton wavelength and mPl is the Planck mass, these objects have energy densities ε ~ mu4, radii r ~ mPl/mu2, global charges q ~ mPl3/mu3, and masses M ~ mPl3/mu2 obeying a generalized Chandrasekhar limit. We give an explicit SO(3) example which demonstrates their very simple structure: the stellar surface reproduces the non-abelian Q-ball, but within the star the fields are no longer constant.