Series studies of the Potts model. I: The simple cubic Ising model

The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising ($q=2$) case we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to $u^{26}$ from $u^{20}$. The high-temperature series for the zero-field partition function is extended from $v^{18}$ to $v^{22}$. Subsequent analysis gives critical exponents in agreement with those from field theory.Comment: submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24 page

Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves

A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy transform approach to fields with nonanalytic behaviour on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized (``dynamical'') monodromy data which evolve from data specified on the initial characteristics (the wavefronts).Comment: 4 pages, RevTe

Microscopic/stochastic timesteppers and coarse control: a kinetic Monte Carlo example

Coarse timesteppers provide a bridge between microscopic / stochastic system descriptions and macroscopic tasks such as coarse stability/bifurcation computations. Exploiting this computational enabling technology, we present a framework for designing observers and controllers based on microscopic simulations, that can be used for their coarse control. The proposed methodology provides a bridge between traditional numerical analysis and control theory on the one hand and microscopic simulation on the other

Self-consistent analysis of hadron production in pppp and AAAA collisions at mid-rapidity

The self-consistent approach based on similarity of inclusive spectra of hadrons produced in $pp$ and $AA$ collisions is reviewed. This approach allows us to describe rather well the ratio of proton to anti-proton yields in $AA$ collisions as a function of the initial energy at a wide range from a few GeV to a few TeV. We suggest its modification due to the quark-gluon dynamics to describe the inclusive spectra of hadrons produced in $pp$ collision as a function of the transverse momentum $p_t$ at mid-rapidity. The extension of this approach to analyze the pion $p_t$-spectra produced in $AA$ collision at high and middle energies and mid-rapidity is given. The satisfactory description of experimental data on these spectra in $pp$ and $AA$ collisions within the offered approach is shown.Comment: 15 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1504.0784

Non-local Coulomb interactions and metal-insulator transition in Ti2_2O3_3: a cluster LDA+DMFT approach

We present an ab initio quantum theory of the metal-insulator transition in Ti$_2$O$_3$. The recently developed cluster LDA+DMFT scheme is applied to describe the many-body features of this compound. The conventional single site DMFT cannot reproduce a low temperature insulating phase for any reasonable values of the Coulomb interaction. We show that the non-local Coulomb interactions and the strong chemical bonding within Ti-Ti pair is the origin of the small gap insulating ground state of Ti$_2$O$_3$

Mid-rapidity dependence of hadron production in p−pp-p and A−AA-A collisions

The calculation of inclusive spectra of pions produced in $pp$ and $AA$ collisions as a function of rapidity $y$ is presented within the self-similarity approach. It is shown that at not large rapidities $y$ one can obtain the analytical form of the self-similarity function $\Pi(y,p_t)$ dependent of $y$ and hadron transverse momentum $p_t$. A satisfactory description of data on the rapidity spectra at $|y|\leq$ 0.3 is illustrated within a good agreement. The universal energy dependence of these spectra is also shown.Comment: 6 pages, 3 figure

B→γγB \to \gamma \gamma in an ACD model

We present a full calculation of the amplitudes for $B_{d[s]} \to \gamma \gamma$ in a simple ACD model that extends an incomplete one in a previous paper. We find cancellations between the contributions from different KK towers and a small decrease relative to the SM predictions. It is conjectured that radiative QCD corrections might actually lead to an enhancement in the branching ratios and {\bf CP} asymmetries, but no more than modest ones.Comment: 3 pages, 2 figure

The Fermion Generations Problem in the Gust in the Free World-Sheet Fermion Formulation

In the framework of the four dimensional heterotic superstring with free fermions we present a revised version of the rank eight Grand Unified String Theories (GUST) which contain the $SU(3)_H$-gauge family symmetry. We also develop some methods for building of corresponding string models. We explicitly construct GUST with gauge symmetry $G = SU(5) \times U(1)\times (SU(3) \times U(1))_H$ and $G = SO(10)\times (SU(3) \times U(1))_H$ or $E(6)\times SU(3)_H$ $\subset E(8)$ and consider the full massless spectrum for our string models. We consider for the observable gauge symmetry the diagonal subgroup $G^{symm}$ of the rank 16 group $G \times G$ $\subset SO(16) \times SO(16)$ or $\subset E(8) \times E(8)$. We discuss the possible fermion matter and Higgs sectors in these theories. We study renormalizable and nonrenormolizable contributions to the superpotential. There has to exist "superweak" light chiral matter ($m_H^f < M_W$) in GUST under consideration. The understanding of quark and lepton mass spectra and family mixing leaves a possibility for the existence of an unusually low mass breaking scale of the $SU(3)_H$ family gauge symmetry (some TeV).Comment: 68 page

Wavelength limits on isobaricity of perturbations in a thermally unstable radiatively cooling medium

Nonlinear evolution of one-dimensional planar perturbations in an optically thin radiatively cooling medium in the long-wavelength limit is studied numerically. The accepted cooling function generates in thermal equilibrium a bistable equation of state $P(\rho)$. The unperturbed state is taken close to the upper (low-density) unstable state with infinite compressibility ($dP/d\rho= 0$). The evolution is shown to proceed in three different stages. At first stage, pressure and density set in the equilibrium equation of state, and velocity profile steepens gradually as in case of pressure-free flows. At second stage, those regions of the flow where anomalous pressure (i.e. with negative compressibility) holds, create velocity profile more sharp than in pressure-free case, which in turn results in formation of a very narrow (short-wavelength) region where gas separates the equilibrium equation of state and pressure equilibrium sets in rapidly. On this stage, variation in pressure between narrow dense region and extended environment does not exceed more than 0.01 of the unperturbed value. On third stage, gas in the short-wavelength region reaches the second (high-density) stable state, and pressure balance establishes through the flow with pressure equal to the one in the unperturbed state. In external (long-wavelength) regions, gas forms slow isobaric inflow toward the short-wavelength layer. The duration of these stages decreases when the ratio of the acoustic time to the radiative cooling time increases. Limits in which nonlinear evolution of thermally unstable long-wavelength perturbations develops in isobaric regime are obtained.Comment: 21 pages with 7 figures, Revtex, accepted in Physics of Plasma