Observational effects in black and white holes (dynamical wormholes)

The models of wormholes with a topology based on a Reissner-Nordström black and white hole are considered. In these models, there are one entrance in one universe (a black hole) and one exit into another universe (a white hole) corresponding to this entrance. The passage of matter through the wormhole in these models is possible only in one direction (from past to future). All models are considered under the assumption of spherical symmetry. It is shown that all models without a throat do not violate the null energy condition. The model of a Reissner-Nordström black hole containing no singularities inside the horizon has been constructed. The trajectories of particles and light rays passing from one universe into another have been constructed for the simplest Reissner-Nordström black and white hole. Distinctive features have been found for the images of objects from another universe observed through such objects. The characteristics of these images are compared with those for ordinary wormholes.     

Recent advances and open challenges in percolation

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation.     

Hexagonal discrete Boltzmann models with and without rest particles

We consider seven different hexagonal discrete Boltzmann models corresponding to one, two, three, and five hexagons with or without rest particles. In the microscopic collisions the number of particles associated with a given speed is not necessarily conserved, except for two models without rest particles. We compare different behaviors for the macroscopic quantities between models with and without rest particles and when the number of velocities (or hexagons) increases. We study similarity waves with two asymptotic states and consider two classes of solutions at one asymptotic state: either isotropic (densities associated with the same speed are equal) or anisotropic. Two macroscopic quantities seem useful for such studies: internal energy and mass ratio across the asymptotic states, which satisfy a relation deduced from continuous theory. Here we report results for the isotropic solutions, whoch only exist, for both models, in the subdomains where the propagation speed is larger than some well-defined value. Outside these subdomains, modifications occur when the rest particle desity becomes large. For both models we find a monotonic internal energy and subdomains with a mass ratio equal to the one in continuous theory.     

Models of collective cell motion for cell populations with different aspect ratio: Diffusion,proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape.     

Thermal radiation relaxation times near the boundary of a semi-infinite nongray medium

The effect of a nearby boundary on thermal radiation relaxation times in a semi-infinite medium has been examined for gray and exponential band models. Noticeable variations from relaxation time in an infinite medium are confined to a region within one wavelength of the boundary. A reflecting boundary has a lesser effect than a transparent one and the asymptotic behavior of the two band models are quite distinct for optically thick waves.     

Optimized 90° Polarization Shift Step Twists for Ku, K and Ka Bands

Optimized models for 90° polarization shift step twists for Ku, K and Ka bands are presented. The cross-section of the waveguide employed is similar to that of a rectangular one, with the difference that the walls of the shorter side are part of a circular one with the proper diameter. The optimized models have been found using the CST Microwave Studio simulation tool and in all cases the return loss is kept below -20 dB for a wide range of frequency spectrum. Two examples are given, one for Ku band and the other for K and Ka ones.     

Scale-invariant cellular automata and self-similar Petri nets

Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, “solve” the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior, whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.     

Lattice versions of quantum field theory models in two dimensions

The quantum inverse scattering method allows one to put quantum field theory models on a lattice in a way which preserves the dynamical structure. The trace identifies are discussed for these models.     

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

Fitting of deuterium quadrupole echo spectra with multiple motional models

Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine-d(5) in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine-d(3), which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra.     

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

Analysis of thermal regimes in media with bulk heat release

Traditional and Burnett models of heat and mass transfer in a two-element medium with heat release proportional to the fraction of one of the elements are considered. The models are analyzed using a computer program for multiparametric analysis. The varieties and characteristics of regimes in both models are investigated and compared. It is expedient to use the results of simulations, for example, in studying nonlinear processes of heat and mass transfer in new power-generating units.     

Fluctuations and large deviations in non-equilibrium systems

For systems in contact with two reservoirs at different densities or with two thermostats at different temperatures, the large deviation function of the density gives a possible way of extending the notion of free energy to non-equilibrium systems. This large deviation function of the density can be calculated explicitly for exclusion models in one dimension with open boundary conditions. For these models, one can also obtain the distribution of the current of particles flowing through the system and the results lead to a simple conjecture for the large deviation function of the current of more general diffusive systems.     

Time reversed elastic nonlinearity diagnostic applied to mock osseointegration monitoring applying two experimental models

This study broadens vibration-like techniques developed for osseointegration monitoring to the nonlinear field. The time reversed elastic nonlinearity diagnostic is applied to two mock models. The first one consists of tightening a dental implant at different torques in a mock cortical bone; the second one allows one to follow glue curing at the interface between a dental implant and a mock jaw. Energy is focused near the implant interface using the time reversal technique. Two nonlinear procedures termed pulse inversion and the scaling subtraction method, already used successfully in other fields such as contrast agents and material characterization, are employed. These two procedures are compared for both models. The results suggest that nonlinear elasticity can provide new information regarding the interface, complementary to the linear wave velocity and attenuation. The curing experiment exhibits an overall low nonlinear level due to the fact that the glue significantly damps elastic nonlinearity at the interface. In contrast, the torque experiment shows strong nonlinearities at the focus time. Consequently, a parallel analysis of these models, both only partially reflecting a real case, enables one to envisage future in vivo experiments.     

The alignment of the vacuum in theories of technicolor

We study a class of models of dynamical weak-interaction symmetry breaking suggested by the work of Weinberg and Susskind. We demonstrate in these models some simple relations which determine the alignment of weakly gauged subgroups and the masses of pseudo-Goldstone bosons. We illustrate these methods by computing the spectrum of pseudo-Goldstone bosons in three models recently examined by Dimopoulos. These models are seen to contain a very light charged Higgs boson, whose mass we estimate by the use of chiral perturbation theory. In one of these models, we observe that the energetically preferred vacuum is a phenomenologically unpleasant one.     

Getting off the track

The production of MeV/amu heavy-ion and MeV cluster-ion beams has allowed continuous damage tracks to be made in a wide variety of materials. Using simple phenomenological models of the track-formation process one can estimate in advance the morphology of the tracks that will result from a particular set of irradiation parameters, i.e., target material, ion type and energy. In this talk I shall discuss the use of these models and how they are applied in a specific example: the pinning of quantized magnetic-flux vortices in a high-temperature superconductor. For this application one must also employ models for the interaction of the vortex and the column of damage. On the basis of such simulations it is found that although damage tracks are extremely useful for increasing the flux pinning, and hence the critical current, it would be even better if one could control the track positions and radii over a wider range of values. A new development in nanotechnology will be discussed that may, indeed, allow this to be accomplished easily and inexpensively.     

Time domain simulation in photonics: A comparison of nonlinear dispersive polarisation models

The paper investigates and compares a range of different models currently used for modelling nonlinear optical phenomena. The models are implemented in the numerical time domain Transmission Line Modelling (TLM) method and include a Kerr model and different formulations of the Duffing model. The models are used to simulate an all-optical limiter for a CW input and results compared with ones available in the literature. This enables a comparison to be made between the different models, from which it is concluded that the Duffing model has some advantages, when modelling materials and phenomena involving more than one frequency, arising from its ability to describe dispersive effects. These conclusions are further supported by the simulation results obtained for a pulse input.     

Image restoration with dual-prior constraint models based on Split Bregman

In order to utilizing the local and non-local information in the image, we proposed a novel sparse scheme for image restoration in this paper. The new scheme includes two important contributions. The first one is that we extended the image prior model in conventional total variation to the dual-prior models for combining the local smoothness and non-local sparsity under regularization framework. The second one is we developed a modified iterative Split Bregman majorization method to solve the objective function with dual-prior models. The experimental results show that the proposed scheme achieved the state-of-the-art performance compared to the current restoration algorithms.     

Finite-Time Fluctuations in the Degree Statistics of Growing Networks

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barabási-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.