Classical Formalism Research Articles

The Equivalence Postulate of Quantum Mechanics, Dark Energy, and the Intrinsic Curvature of Elementary Particles

The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underlie the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant underD-dimensional Möbius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of theD-dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrödinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. The author proposes that the quantum potential, which is always nontrivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multiparticle case the quantum potential, as well as the mass, is cumulative.

Notes on quantitative structure–property relationships (QSPR), part 3: Density functions origin shift as a source of quantum QSPR algorithms in molecular spaces

A general algorithm implementing a useful variant of quantum quantitative structure-property relationships (QQSPR) theory is described. Based on quantum similarity framework and previous theoretical developments on the subject, the present QQSPR procedure relies on the possibility to perform geometrical origin shifts over molecular density function sets. In this way, molecular collections attached to known properties can be easily used over other quantum mechanically well-described molecular structures for the estimation of their unknown property values. The proposed procedure takes quantum mechanical expectation value as provider of causal relation background and overcomes the dimensionality paradox, which haunts classical descriptor space QSPR. Also, contrarily to classical procedures, which are also attached to heavy statistical gear, the present QQSPR approach might use a geometrical assessment only or just some simple statistical outline or both. From an applied point of view, several easily reachable computational levels can be set up. A Fortran 95 program: QQSPR-n is described with two versions, which might be downloaded from a dedicated web site. Various practical examples are provided, yielding excellent results. Finally, it is also shown that an equivalent molecular space classical QSPR formalism can be easily developed.

A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models

In non-equilibrium molecular dynamics simulations, continuum mechanics quantities can be computed from the position and momentum of the particles based on the classical Irving-Kirkwood formalism. For practical purposes, the implementations of Irving-Kirkwood formulas often involve a spatial averaging using a smooth kernel function. The resulting formula for the stress has been known as Hardy stress. Usually results obtained this way still need to be further processed to reduce the fluctuation, e.g., by ensemble or time averaging. In this paper we extend Hardy's formulas by systematically incorporating both spatial and temporal averaging into the expression of continuum quantities. The derivation follows the Irving-Kirkwood formalism, and the average quantities still satisfy conservation laws in continuum mechanics. We will discuss the selection of kernel functions and present several numerical tests.

New simulation approach using classical formalism to water nuclear magnetic relaxation dispersions in presence of superparamagnetic particles used as MRI contrast agents

Superparamagnetic nanoparticles are used as negative contrast agents in magnetic resonance imaging: owing to their large magnetic moment the water proton spins are dephased, which accelerates the nuclear magnetic relaxation of an aqueous sample containing these particles. Transverse and longitudinal relaxation times depend on several parameters of the nanoparticles such as radius and magnetization and on experimental parameters such as the static magnetic field or echo time. In this work, we introduce a new simulation methodology, using a classical formalism, allowing the simulation of the NMR signal during transverse and longitudinal relaxation induced by superparamagnetic particles in an aqueous solution, which, to our knowledge has never been done before. Nuclear magnetic relaxation dispersion profiles are obtained for a wide range of nanoparticle radii and magnetizations. The results can be classified in two regimes--the well-known motional averaging and static regimes. This generalizes previous studies focusing on transverse relaxation at high magnetic field (larger than 1 T). Simulation results correspond to analytical theories in their validity range and so far unknown dependences of the relaxation with magnetization and radii of the NMR dispersions profiles are observed, which could be used to characterize experimental samples containing large superparamagnetic particles.

Mechanisms of planetary and stellar dynamos

AbstractWe review some of the recent progress on modeling planetary and stellar dynamos. Particular attention is given to the dynamo mechanisms and the resulting properties of the field. We present direct numerical simulations using a simple Boussinesq model. These simulations are interpreted using the classical mean-field formalism. We investigate the transition from steady dipolar to multipolar dynamo waves solutions varying different control parameters, and discuss the relevance to stellar magnetic fields. We show that owing to the role of the strong zonal flow, this transition is hysteretic. In the presence of stress-free boundary conditions, the bistability extends over a wide range of parameters.

Computer simulations of thermo-sensitive microgels: Quantitative comparison with experimental swelling data

In this work, a quantitative comparison between experimental swelling data of thermo-sensitive microgels and computer simulation results obtained from a coarse-grained model of polyelectrolyte network and the primitive model of electrolyte is carried out. Polymer-polymer hydrophobic forces are considered in the model through a solvent-mediated interaction potential whose depth increases with temperature. The qualitative agreement between simulation and experiment is very good. In particular, our simulations predict a gradual shrinkage with temperature, which is actually observed for the microgels studied in this survey. In addition, the model can explain the swelling behavior for different contents of ionizable groups without requiring changes in the hydrophobic parameters. Our work also reveals that the abruptness of the shrinkage of charged gels is considerably conditioned by the number of monomeric units per chain. The swelling data are also analyzed with the Flory-Rhener theory, confirming some limitations of this classical formalism.

The dynamics of sex ratio evolution Dynamics of global population parameters

Classical formalizations of the Fisherian theory of sex ratio evolution are based on the assumption that the number of grand offspring of a female serves as a measure of fitness. However, the classical population genetics approach also considers the contribution of male individuals to gene proliferation. The difference between the predictions of phenotypic and genetic models is that the phenotypic approach describes the primary sex ratio of 0.5 as the ESS value, while genetic models describe the stable state of a population by a combination of the stable states of the male and female subpopulations. In this paper, we formulate an alternative model of sex ratio evolution that is focused on the dynamics and quantitative properties of this process and that combine a rigorous genetic approach with a game theoretic strategic analysis. In the new model, females are the strategic agents and males are the passive carriers on unexpressed genes. Fitness functions in the new model are derived with respect to a “fitness exchange” effect, i.e. the contribution of male individuals to female fitness and vice versa. This new model shows that the dynamics of this system are complex and consist of two phases. The first, rapid, phase converges the system to a stable manifold (termed the male subpopulation equilibrium—MSE) where the male subpopulation state is in equilibrium, conditional on the current state of the female subpopulation. Double phase dynamics occur when the population state is not compatible with the current strategic composition of the population (determined by the value of the primary sex ratio) which can be caused by ecological factors. The trajectory of convergence to the MSE can be very complicated and may contain a dramatic change in the primary sex ratio. Thus, the primary sex ratio of 0.5 is unstable for perturbations of gene frequencies among male carriers. Therefore, the new model supports predictions of genetic models that the evolutionary stability of the sex ratio should be characterized by a combination of a stable value of the primary sex ratio and the male subpopulation equilibrium.

A statistical methodology to derive the scaling law for the H-mode power threshold using a large multi-machine database

In this paper, a refined set of statistical techniques is developed and then applied to the problem of deriving the scaling law for the threshold power to access the H-mode of confinement in tokamaks. This statistical methodology is applied to the 2010 version of the ITPA International Global Threshold Data Base v6b(IGDBTHv6b). To increase the engineering and operative relevance of the results, only macroscopic physical quantities, measured in the vast majority of experiments, have been considered as candidate variables in the models. Different principled methods, such as agglomerative hierarchical variables clustering, without assumption about the functional form of the scaling, and nonlinear regression, are implemented to select the best subset of candidate independent variables and to improve the regression model accuracy. Two independent model selection criteria, based on the classical (Akaike information criterion) and Bayesian formalism (Bayesian information criterion), are then used to identify the most efficient scaling law from candidate models. The results derived from the full multi-machine database confirm the results of previous analysis but emphasize the importance of shaping quantities, elongation and triangularity. On the other hand, the scaling laws for the different machines and at different currents are different from each other at the level of confidence well above 95%, suggesting caution in the use of the global scaling laws for both interpretation and extrapolation purposes.

Quantum hydrodynamics of strongly coupled electron fluids

We have extended the classical hydrodynamics formalism to include nonlocal quantum behavior via the phenomenological Bohm potential. We have then solved the quantum hydrodynamics equations to derive an expression for the dynamical structure factor, which describes the density-density correlations in the system. This formalism can be applied to high density strongly coupled electron fluids in the long wavelength domain. We show that at densities above 7×10(25) cm(-3) there are significant differences in the dispersion relation. Future experiments at large laser facilities could provide an experimental test of the theory.

The Classical Two-Component Spinor Formalisms for General Relativity I

The classical two-component spinor formalisms for general relativity as built up by Infeld and van der Waerden afford an elegant approach to spacetime geometry. Deeply involved in the inner structure of these frameworks is the beautiful theory of spin densities of Schouten. In this work Schouten’s theory is presented in detail. The elementary aspects of the spin-affine geometry borne by the formalisms are then described in a systematic way. It is particularly shown that the symmetric parts of any admissible spin connections behave covariantly under the action of the Weyl gauge group.

The Classical Two-Component Spinor Formalisms for General Relativity II

The Classical Two-Component Spinor Formalisms for General Relativity II

Efficiency and rate of spontaneous emission in organic electroluminescent devices

We examine spontaneous emission in organic electroluminescent devices and investigate the influence of the local photonic mode density on the emissive properties of molecular emitters. Spontaneous emission in organic electroluminescent devices is modeled by means of an approximate closed-form solution for the exciton rate equation, which yields the efficiency of conversion of electrical charges into molecular excited states. The exciton decay rate and the efficiency of conversion of molecular excitation into far-field radiated photons are described using a state-of-the-art classical electromagnetic formalism suitable to model multilayered organic light-emitting diodes (OLEDs). We present an in-depth analysis of the influence of optical microcavities and the corresponding resonant modes on the luminescent properties of organic molecules. Near-field coupling and coupling to metallic reflectors are demonstrated as the main effects responsible for environment-induced modifications of the rate and efficiency of spontaneous emission. The extent to which the excitonic decay rate is modified by the optical microcavity (Purcell effect) is shown to be strictly dependent on the intrinsic luminescence quantum yield of the molecular emitter. The modeling formalism is successfully validated against experimental results obtained on three series of small-molecule $p$-$i$-$n$ OLED samples, featuring phosphorescent or fluorescent molecular emitters, with a widely varying thickness of the optical microcavity. We demonstrate that, within its limits of validity, the theoretical treatment in this work provides a rigorous quantitative description of spontaneous emission in organic luminescent devices and allows for the identification of the factors determining the OLED internal and external quantum efficiencies.

Uncertainty Evaluation in Modelling of Acoustic Phenomena with Uncertain Parameters Using Interval Arithmetic

Uncertainty assessment in modelling of acoustic phenomena with uncertain parameters using interval arithmetic on the example of the reverberation time estimation, are presented in the paper. The application of the classical interval analysis formalism as well as its expansions are shown. Statistical methods of estimation of the reverberation time are based on parameters, which are related, among others, to the geometry of the analysed room, characteristics of sound absorption, and interior transmission. Values of these parameters are usually di cult to determine, which has a signi cant in uence on the modelling result. The interval analysis allows to determine the variability interval of the parameter being estimated. The authors determined the in uence of the input parameters uncertainty on the estimated reverberation time, calculated according to the Sabine, Eyring Norris and Millington Sette formulae. The uncertainty analysis was performed for the literature data, related to the reverberation time calculations of the room of a certi ed acoustics.

Harmonic radiation of a relativistic nonlinear inverse Compton scattering using two laser wavelengths

The use of two different wavelength lasers in the nonlinear regime of the inverse Compton scattering interaction is proposed in order to provide a new strategy for controlling scattered photon energy distributions in the x-ray to $\ensuremath{\gamma}$-ray spectral region. In this nonlinear interaction, the component of the relativistic electron's trajectory driven by a longer-wavelength laser with the normalized vector potential ${a}_{\mathrm{L}}\ensuremath{\sim}1$ is a large oscillatory figure-8; in the proposed scenario a rapid small-amplitude oscillation induced by a shorter-wavelength laser is superimposed upon this figure-8. Thus, the electron's momentum is mainly supplied from longer-wavelength laser, while the high-frequency part of the acceleration is given by shorter-wavelength laser. In this way, the harmonics radiated at high frequency from the oscillating electron can be strongly modified by the nonlinear motion initiated by the low frequency, large ${a}_{\mathrm{L}}$ laser resulting in the generation of the harmonics with the photon energy of $4{\ensuremath{\gamma}}^{2}\mathrm{h\Elzxl{}}({\ensuremath{\omega}}_{\mathrm{L},\mathrm{short}}+n{\ensuremath{\omega}}_{\mathrm{L},\mathrm{long}})$. In this paper, the electron's kinetics in the two-wavelength laser field and the concomitant emitted radiation spectrum are examined, with numerical illustrations based on a classical Lienard-Wiechert potential formalism provided.

Rotationless formulation for large deformations in flexible multibody dynamics

AbstractEspecially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method.In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state‐of‐the‐art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the role of coherent states in quantum foundations

Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that useful connections arise among them. The topics discussed are: (1) a truly natural formulation of phase space path integrals; (2) how this analysis implies that the usual classical formalism is ``simply a subset'' of the quantum formalism, and thus demonstrates a universal coexistence of both the classical and quantum formalisms; and (3) how these two insights lead to a complete analytic solution of a formerly insoluble family of nonlinear quantum field theory models.

Modeling of Systems With Position-Dependent Mass Revisited: A Port-Hamiltonian Approach

It is known that straightforward application of the classical Lagrangian and Hamiltonian formalism to systems with mass varying explicitly with position may lead to discrepancies in the formulation of the equations of motion. Systems with mass varying explicitly with position often arise from situations where the partitioning of a closed system of constant mass leads to open subsystems that exchange mass among themselves. One possible solution is to introduce additional nonconservative generalized forces that account for these effects. However, it remains unclear how to systematically interconnect the Lagrangian or Hamiltonian subsystems. In this note, systems with mass varying explicitly with position and their properties are studied in the port-Hamiltonian modeling framework. The port-Hamiltonian formalism combines the classical Lagrangian and Hamiltonian approach with network modeling and is applicable to various engineering domains. One of the strong aspects of the port-Hamiltonian formalism is that power-preserving interconnections between port-Hamiltonian subsystems results in another port-Hamiltonian system with composite energy and interconnection structure. The motion of a heavy cable being deployed from a reel by the action of gravity is used as an example.

Pluralism and Deformalisation as Mechanisms in the Achievement of More Equitable and Just Outcomes - The Move from 'Classical Formalism' to Deformalisation

By tracing the development and evolvement of certain legal theories over the centuries, as well as consequences emanating from such developments, this paper highlights how and why a shift from the model of „classical formalism“ towards more deformalised models has arisen. The paper also illustrates how deformalisation and „a corresponding loss of certainty“ could be harnessed in order to provide for greater „realism“ and externalities, whilst still attaining a respectable level of consistency. Developments and efforts aimed at exploring the applicability of classical formalism and deformalised models should be regarded as „an endeavour to establish a consistency of terms, as well as a probing into how far principles, notions, and rules for decision making can be generalised, and rectification when generalisations have gone too far.“ Unity, as well as „a common law of mankind“ are goals which are still capable of being achieved even where fragmentation, diversification and pluralisation of the law occur. Such processes of specialisation, where correspondingly countered by the appropriate level of generality as well as the ability to apply rules – such that they are consistently applied in similar situations, are capable of achieving more equitable, just and unifying goals as opposed to a model which merely strives for the achievement of legal certainty. Looking beyond the borders of legal theory may indeed provide the much needed redress in situations where generalisations exceed the required limits.

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g ϕ 4 classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost “identical” formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.

Spherical galaxy models as equilibrium configurations in non-extensive statistics

Considering galaxies as self - gravitating systems of many collisionless particles allows to use methods of statistical mechanics inferring the distribution function of these stellar systems. Actually, the long range nature of the gravitational force contrasts with the underlying assumptions of Boltzmann statistics where the interactions among particles are assumed to be short ranged. A particular generalization of the classical Boltzmann formalism is available within the nonextensive context of Tsallis q -statistics, subject to non -additivity of the entropies of sub - systems. Assuming stationarity and isotropy in the velocity space, it is possible solving the generalized collsionless Boltzmann equation to derive the galaxy distribution function and density profile. We present a particular set of nonextensive models and investigate their dynamical and observable properties. As a test of the viability of this generalized context, we fit the rotation curve of M33 showing that the proposed approach leads to dark matter haloes in excellent agreement with the observed data.