A characterization of Markovian homogeneous multicomponent Gaussian fields

Necessary and sufficient conditions are given for a certain class of homogeneous multicomponent Gaussian generalized stochastic fields to possess a Markov property equivalent to Nelson's. The class of Markov fields so characterized has as a subclass the class of Markov fields which lead by Nelson's Reconstruction Theorem to some covariant (free) quantum fields.     

Renormalization group analysis of relaxational dynamics in systems with many-component order-parameter II

A general discussion of scaling fields and scaling variables in the dynamic renormalization group is given using path probability formalism. It is shown that scaling variables are the derivatives of the action with respect to scaling fields. The general ideas are illustrated on the multicomponent relaxational model in the large-n limit, where scaling fields and scaling variables are calculated explicitly and flow lines, crossover and universality are discussed. Critical points of higher order are also included in the investigation.     

Evidence for magnetic field induced changes of the phase of tunneling states: spontaneous echoes in (KBr)(1-x)(KCN)(x) in magnetic fields

Recently it was discovered that, in contrast to expectations, the low-temperature dielectric properties of some multicomponent glasses depend strongly on magnetic fields. The low-temperature dielectric response of these materials is governed by atomic tunneling systems. We now have investigated the influence of magnetic fields on the coherent properties of atomic tunneling states in a crystalline host in two-pulse echo experiments. As in glasses, we observe a very strong magnetic field dependence of the echo amplitude. Moreover, for the first time we have direct evidence that the magnetic fields change the phase of coherent tunneling systems.     

Direct coupling of magnetic fields to tunneling systems in glasses

We report on investigations of spontaneous polarization echoes in the nonmagnetic multicomponent glass BaO-Al2O3-SiO2 in static magnetic fields. While the echo decay is only marginally influenced, the echo amplitude depends strongly on magnetic fields. It seems that the intrinsic magnetic moment of tunneling systems causes dephasing effects which are detected in our echo experiments. In addition we find a strong increase of the echo amplitude with magnetic fields. This result shows that the coupling of the tunneling systems to magnetic fields is surprisingly strong and cannot be understood on the basis of current theories.     

Symmetry transformations and reciprocity relations in the theory of multicomponent dielectric media

Characteristics of the formation of a dipole electric field are established for multicomponent fiber composites having a regular distribution of inclusions in the matrix. It is shown that these media are characterized by symmetry transformations of the average electric fields. These symmetry transformations yield reciprocity relations for the effective parameters. Various forms of these relations are given and their physical interpretation is presented.     

A homogeneous multicomponent cosmological model with interacting spinor,scalar, and vector fields in the presence of dark energy

The evolution of a homogeneous multicomponent cosmological model with interacting spinor, vector, and scalar fields in the presence of dark energy described by the ideal liquid with the corresponding state equation is considered. The source of the vector and spinor fields is the kinetic energy of the inflation (scalar) field that is modeled by introduction of Lagrangians for the spinor and vector fields interacting with the scalar field through the squared gradient. A system of the dynamic Einstein–Proca–Klein–Fock and ideal liquid equations in the presence of interaction of the cosmological model components is solved. The role of individual components in the process of model evolution is elucidated.     

Fast crystallization of structural steel during laser processing of the surface

The size, shape, and structure of the molten zone appearing on the surface of Fe-C multicomponent alloy upon laser recrystallization are studied. The laser scan rate varies between 0.01 to 0.167 m/s. A set of equations for the temperature and concentration fields is derived within a model of locally nonequilibrium crystallization. The use of the hypothesis for marginal stability, as applied to crystal growth, makes it possible to find the characteristic size of the crystal structure. The mathematical simulation of recrystallization upon laser processing is in good agreement with experimental data. The results of the simulation can be used for predicting the mechanical properties in the molten zone as a function of the energy parameters of the radiation and thermophysical properties of the alloy.     

Theory of field effects on transport properties of polyatomic gases in the transition regime

A simple method is presented for describing the effects of external magnetic or electric fields on the transport properties of polyatomic gases over the entire range from the continuum to the Knudsen regime. Instead of treating bulk and boundary-layer effects separately, both molecular and surface scattering are included from the beginning in the collisional part of the Boltzmann equation, and the surface is treated as one component of a multicomponent mixture. A simple first-order solution of this problem is sufficient to account for the dependence of the transport coefficients on the Knudsen number in the presence of a field. Detailed results for the longitudinal and transverse viscomagnetic effects in a single gas are presented, and shown to be in good agreement with experimental data for CO and N₂.     

Multicomponent transport algorithms for partially ionized mixtures

We investigate iterative methods for solving linear systems arising from the kinetic theory of gases and providing multicomponent transport coefficients of partially ionized plasmas. We consider the situations of weak and strong magnetic fields as well as electron temperature nonequilibrium and the linear systems are investigated in their natural constrained singular symmetric form. Stationary iterative techniques are considered with new more singular formulations of the transport linear systems as well as orthogonal residuals algorithms. The new formulations are derived by considering generalized inverses with nullspaces of increasing dimension. Numerical tests are performed with high temperature air and iterative techniques lead to fast and accurate evaluation of the transport coefficients for all ionization levels and magnetic field intensities.     

Ferromagnetism and colossal magnetoresistance from phase competition

We report a multicomponent theory for the coexistence of charge ordering (CO), and antiferromagnetic (AFM) and ferromagnetic (FM) spin ordering. This kind of state is invoked for manganites by Moreo et al., Science 283, 2034 (1999) and observed in recent experiments. We show that doping an AFM or CO state always generates a FM component. FM, AFM, and CO necessarily coexist in a particle-hole asymmetric system. Melting of large AFM-CO orders by small magnetic fields and colossal magnetoresistance (CMR) arise whenever the CO and AFM order parameters have similar magnitude and momentum structure. Hole doping favors FM metallic states while electron doping favors AFM-CO states, as in CMR manganites.     

Physically self-consistent basis for modern cosmology

Cosmoparticle physics appeared as a natural result of internal development of cosmology seeking physical grounds for inflation, baryosynthesis, and nonbaryonic dark matter and of particle physics going outside the Standard Model of particle interactions. Its aim is to study the foundations of particle physics and cosmology and their fundamental relationship in the combination of respective indirect cosmological, astrophysical, and physical effects. The ideas on new particles and fields predicted by particle theory and on their cosmological impact are discussed, as well as the methods of cosmoparticle physics to probe these ideas, are considered with special analysis of physical mechanisms for inflation, baryosynthesis, and nonbaryonic dark matter. These mechanisms are shown to reflect the main principle of modern cosmology, putting, instead of formal parameters of cosmological models, physical processes governing the evolution of the big-bang universe. Their realization on the basis of particle theory induces additional model-dependent predictions, accessible to various methods of nonaccelerator particle physics. Probes for such predictions, with the use of astrophysical data, are the aim of cosmoarcheology studying astrophysical effects of new physics. The possibility of finding quantitatively definite relationships between cosmological and laboratory effects on the basis of cosmoparticle approach, as well as of obtaining a unique solution to the problem of physical candidates for inflation, mechanisms of baryogenesis, and multicomponent dark matter, is exemplified in terms of gauge model with broken family symmetry, underlying horizontal unification and possessing quantitatively definite physical grounds for inflation, baryosynthesis, and effectively multicomponent dark-matter scenarios.     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

On the application of the theory of Lorentzian plasma to calculation of transport properties of multicomponent arc plasmas

The application of the Lorentzian plasma theory for the calculation of the properties of multicomponent electric arc plasma is considered. It is shown that this model gives satisfactory results in the temperature range, which is corresponding to the weakly ionized arc plasma and arc plasma with dominant first ionization. The calculations are provided for the arc plasmas of noble gases and their mixtures between them and also that with metals. It is also pointed that the discrepancy between the electron temperature and gas temperature can be significant even at relatively weak electric fields, that fact must be taken into account under the simulation of arc discharges.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on ? may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.     

Immiscible multicomponent lattice Boltzmann model for fluids with high relaxation time ratio

An immiscible multicomponent lattice Boltzmann model is developed for fluids with high relaxation time ratios, which is based on the model proposed by Shan and Chen (SC). In the SC model, an interaction potential between particles is incorporated into the discrete lattice Boltzmann equation through the equilibrium velocity. Compared to the SC model, external forces in our model are discretized directly into the discrete lattice Boltzmann equation, as proposed by Guo et al. We develop it into a new multicomponent lattice Boltzmann (LB) model which has the ability to simulate immiscible multicomponent fluids with relaxation time ratio as large as 29.0 and to reduce ‘spurious velocity’. In this work, the improved model is validated and studied using the central bubble case and the rising bubble case. It finds good applications in both static and dynamic cases for multicomponent simulations with different relaxation time ratios.     

Space charge generation in flows of weakly conductive media with large difference of charged particles' mobilities

Electrification in boundary domains of flows of partially ionized multicomponent gas mixtures through channels whose conducting walls are exposed to a constant potential is studied. In such media, in the absence of applied electric fields, electrification is due to significantly different values of mobility of charged particles of opposite signs. The influence of the interaction of electrons and gas ions with the walls of the channel on the value of the space electric charge, the thickness and structure of the charged boundary layer and the value of the convective electric current is analyzed.     

Gradient properties of the renormalisation group equations in multicomponent systems

The existence of a metric, which enables the renormalisation group β functions of a multicomponent field theory to be written as a gradient, has very important implications for the asymptotic behavior of the renormalisation group equations. It is shown that a very simple metric exists in a field theory with n-component Bose fields and arbitrary φ⁴ interaction, when the β functions are calculated perturbatively up to and including the 2-loop diagrams. This same metric is shown to work for all irreducible diagrams, but it must and can be modified to accommodate reducible 3-loop contributions. The prospects and outlook of this aspect of the renormalisation group are discussed.     

Light-cone quantisation of the Liouville and Toda field theories

The Toda field is a multicomponent field in two space-time dimensions satisfying a generalisation of the Liouville equation ?²? + exp ? = 0. We define the quantum field theory, and solve for the fields in terms of their initial values on a forward light-cone, demonstrating that our solution is regular. We give an explicit result for the Liouville equation which is the quantum version of the well-known classical solution. We also discuss the energy-momentum spectrum, and the conformal properties of the theory.