On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree

In the present paper, we study a new kind of p-adic measures for q?+?1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition.     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.     

A point pattern matching algorithm based on QR decomposition

A new method for point pattern matching is proposed in this paper. First, we show how the orthogonal-triangular decomposition (QR decomposition) can be used for point pattern matching. Second, in order to improve the matching accuracy, we propose a simple but robust point-matching method relying on finding the first K similar neighbors emerging from candidate matches, to embed the QR decomposition method within the framework of iterative matching. The proposed method, when applied to a wide experimental data has shown higher accuracy than the existing methods in this area.     

Collapse of vortex lines in hydrodynamics

A new mechanism is proposed for collapse in hydrodynamics associated with the “breaking” of vortex lines. The collapse results in the formation of point singularities of the vorticity field, i.e., a generalized momentum curl. At the point of collapse the vorticity |Ω| increases as ((t ₀ ? t)^?1 and its spatial distribution for t → t ₀ approaches quasi-two-dimensional: in the “soft” direction contraction obeys the law l ₁ → (t ₀ ? t)^3/2 whereas in the other two “hard” directions it obeys l ₂ → (t ₀ ? t)^1/2. It has been shown that this collapse scenario takes place in the general case for three-dimensional integrable hydrodynamics with the Hamiltonian ? = ∫|Ω| d r.     

Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

We propose the P_N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P_N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.     

A rail noise prediction model for the Tehran-Karaj commuter train

Rail noise prediction models enable consideration of different scenarios for the optimal management of noise prevention and mitigation. This project is aimed at developing an equation that enables computation of L_A,max for the Tehran-Karaj commuter train, a type of Diesel-Electric Locomotive. The form of the proposed model is derived from equations for predicting L_A,max for a single locomotive pass-by, proposed in the manual prepared by Harris Miller Miller & Hanson Inc. for the US Federal Transit Administration, and in the French rail noise prediction model. The algorithm for predicting L_A,max for the Tehran-Karaj commuter train has been developed on the basis of the 50 measurements from 5 locations at distances of 25 m, 35 m, 45 m, 55 m, and 65 m from the centre of the track and at a height of 1.5 m. In the field measurements, the reference distance and the reference vehicle speed have respectively been set equal to 25 m and 80 km per hour. The reference L_A,max, length and the speed correction coefficients have been estimated from the field measurements and have been found to be 86.2 dB(A), 11.3, and 18.4 respectively. The fitness test (Kolmogorov-Smirnov) and regression analysis indicate satisfactory results.     

Fitting of two-tensor models without ad hoc assumptions to detect crossing fibers using clinical DWI data

Analysis of crossing fibers is a challenging topic in recent diffusion-weighted imaging (DWI). Resolving crossing fibers is expected to bring major changes to present tractography results based on the standard tensor model. Model free approaches, like Q-ball or diffusion spectrum imaging, as well as multi-tensor models are used to unfold the different diffusion directions mixed in a voxel of DWI data. Due to its seeming simplicity, the two-tensor model (TTM) is applied frequently to provide two positive-definite tensors and the relative population fraction modeling two crossing fiber branches. However, problems with uniqueness and noise instability are apparent. To stabilize the fit, several of the 13 physical parameters are fixed ad hoc, before fitting the model to the data. Our analysis of the TTM aims at fitting procedures where ad hoc parameters are avoided. Revealing sources of instability, we show that the model's inherent ambiguity can be reduced to one scalar parameter which only influences the fraction and the eigenvalues of the TTM, whereas the diffusion directions are not affected. Based on this, two fitting strategies are proposed: the parsimonious strategy detects the main diffusion directions without extra parameter fixation, to determine the eigenvalues and the population fraction an empirically motivated condition must be added. The expensive strategy determines all 13 physical parameters of the TTM by a fit to DWIs alone; no additional assumption is necessary. Ill-posedness of the model in case of noisy data is cured by denoising of the data and by L-curve regularization combined with global minimization performing a least-squares fit of the full model. By model simulations and real data applications, we demonstrate the feasibility of our fitting strategies and achieve convincing results. Using clinically affordable diffusion acquisition paradigms (encoding numbers: 21, 2*15, 2*21) and b values (b = 500–1500 s/mm²), this methodology can place the TTM parameters involved in crossing fibers on a more empirical basis than fitting procedures with technical assumptions.     

Fluxon interaction with the finite-size dipole impurity

Interaction of the fluxon with the finite size dipole impurity in the long Josephson junction is investigated. The impurity has polarity and will be referred to as a dipole impurity because it also has a direction and, consequently, changes its sign under the space inversion transform $x\to ?x$. Such a model is used to describe the inductively coupled to the Josephson transmission line qubit and the misaligned Abrikosov vortex that penetrates into the long Josephson junction. We derive the approximate equations of motion for the fluxon centre of mass and its velocity. With the help of these equations we demonstrate that pinning and scattering of the fluxon on the impurity differs significantly from the case of the point impurity which is modelled by the derivative of the Dirac's δ-function.     

Dynamics of ball-like flames in extremely low-speed counterflow field in near-lean limit low-Lewis number mixture

For the understanding of ball-like flame behavior in counterflow field, transient three-dimensional computations with thermal-diffusion model were conducted for a low-Lewis number mixture near lean limit. Three types of flame behaviors were confirmed: stable spherical ball-like flame (spherical BLF) in A ≤ 0.010, stable non-spherical ball-like flame (non-spherical BLF) in 0.01 < A < 0.089 and splitting ball-like flame (splitting BLF) in A ≥ 0.089, where A is ordinary stretch rate normalized with laminar burning velocity S_L and thermal diffusivity α. Analysis of flame structure for non-spherical BLF located its center at the stagnation point showed that the maximum temperature on the stagnation plane was higher than that on the counterflow axis because of the small difference between the flame curvatures on the stagnation plane and that on the counterflow axis. With the increase of stretch rate, the maximum temperature of the non-spherical BLF on the stagnation plane increased and the position of maximum temperature got away from the stagnation point. The maximum temperature on the counterflow axis decreased and the position of maximum temperature got closer to the stagnation point. Existence of unburned fuel was also confirmed near the stagnation point at A = 0.085. Thus, net fuel velocity was newly introduced to evaluate the effect of the unburned fuel diffusion. The profile of the net fuel velocity revealed two peaks in the case of A < 0.050 and four peaks in the case of A > 0.050. In the case A > 0.050, the inner two peaks were found to be due to the diffusion of unburned fuel to the outward direction. The analyses on the peak positions showed that the flame splitting occurs when the positions of the inner two peaks of the net fuel velocity are located outside of the reference flame ball radius.     

Two-Dimensional EspEn: A New Approach to Analyze Image Texture by Irregularity

Image processing has played a relevant role in various industries, where the main challenge is to extract specific features from images. Specifically, texture characterizes the phenomenon of the occurrence of a pattern along the spatial distribution, taking into account the intensities of the pixels for which it has been applied in classification and segmentation tasks. Therefore, several feature extraction methods have been proposed in recent decades, but few of them rely on entropy, which is a measure of uncertainty. Moreover, entropy algorithms have been little explored in bidimensional data. Nevertheless, there is a growing interest in developing algorithms to solve current limits, since Shannon Entropy does not consider spatial information, and SampEn2D generates unreliable values in small sizes. We introduce a proposed algorithm, EspEn (Espinosa Entropy), to measure the irregularity present in two-dimensional data, where the calculation requires setting the parameters as follows: m (length of square window), r (tolerance threshold), and ρ (percentage of similarity). Three experiments were performed; the first two were on simulated images contaminated with different noise levels. The last experiment was with grayscale images from the Normalized Brodatz Texture database (NBT). First, we compared the performance of EspEn against the entropy of Shannon and SampEn2D. Second, we evaluated the dependence of EspEn on variations of the values of the parameters m, r, and ρ. Third, we evaluated the EspEn algorithm on NBT images. The results revealed that EspEn could discriminate images with different size and degrees of noise. Finally, EspEn provides an alternative algorithm to quantify the irregularity in 2D data; the recommended parameters for better performance are m = 3, r = 20, and ρ = 0.7.     

Electric-field-induced energy spectra and dispersions of ZnO/MgxZn1−xO MQWs

The energy spectra and dispersion relations of carriers in the presence of an electric field applied along the growth direction in ZnO/Mg_xZn_1−xO multiple quantum wells (MQW) are calculated using the asymptotic transfer method (ATM) on the basis of the quasistationary state approximation. The energy spectra of the carriers induce some quasi-bound levels under electric fields. The dispersion relations for the energy of the ground state and lower excitation states still have parabolic shapes for both the electrons and the heavy holes in the presence of a moderate electric field. Our results also reveal that the number of energy levels increases with increasing number of ZnO quantum wells and that the energies increase with both increasing Mg composition x and electric field strength.     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Production of dimuons from high-energy polarized proton-proton collisions

The high-energy process p+p→μ⁺+μ^?+X for dimuons with large invariant mass is studied in the case that the protons are polarized. In general, the cross section $\text{d}\text{σ/}\text{d}\text{Q}{}^2\text{d}\text{y}\text{d}\text{Ω}$ is determined by nine structure functions, and several interesting correlations between the polarization direction and the observed cross section are possible. In the Drell-Yan parton model for the process, the structure of the cross section is much simpler: there are six linear relations among the structure functions. An experimental test of these relations would provide a stringent test of the Drell-Yan model.     

Construction of π± photoproduction amplitudes at high energy from dispersion relations and local duality

We investigate the charged-pion photoproduction amplitudes at all energies. We first show that low-energy s-channel helicity amplitudes exhibit, in most cases, a Bessel-function structure of zeroes. At high energy we therefore parametrize the imaginary parts of helicity amplitudes according to the Harari model, and compute the real parts using fixed-t dispersion relations as proposed recently. Such an evaluation of scattering amplitudes presents some very nice properties. In particular, it allows one to understand from duality arguments how the Born contribution may survive with full strength in the forward direction but not at large t-values. Furthermore FESR are identically satisfied by the model.     

P-n codoping induced enhancement of ferromagnetism in Mn-doped In2O3: A first-principles study

We have performed first-principles density functional theory calculation in order to investigate the feasibility of “p-n codoping method” in improving magnetic property of In₂O₃ based diluted magnetic semiconductors. We find that the ferromagnetic state is favored in Mn-doped In₂O₃, and Sn doping can increase magnetic moment in Mn-doped In₂O₃. These findings are in line with our earlier experimental observation. Along with previous works, we now have enough evidences to support that p-n codoping is a valid method to improve magnetism of oxides based diluted magnetic semiconductors.     

The spectral-line moment-based (SLMB) modeling of the wide band and global blackbody-weighted transmission function and cumulative distribution function of the absorption coefficient in uniform gaseous media

The spectral-line moment-based (SLMB) modeling is proposed for the calculation of radiative properties of gases on any spectral width. The associated mathematical formulation is obtained by applying several concepts of the k-distribution methods such as the reordering of the wavenumber scale by monotonic variations of the absorption coefficient, together with the application of the k-moment method's principles. This approach gives both a general formula for the BTF and a simple and readily applicable approximation for the blackbody-weighted cumulated k-distribution function of the absorption coefficient. The model is applied for the computation of wide band BTFs and cumulative k-distributions for uniform columns of CO₂ and H₂O in the temperature range (300-2400 K) at atmospheric pressure. Model parameters are deduced from line-by-line (LBL) spectra calculated using the HITEMP database. Comparisons with LBL reference data as well as with contemporary modeling approaches (SLW, FSK, SNB) are performed and discussed.