Higher order correlations for fluctuations in the presence of fields

The higher order moments of the fluctuations for the thermodynamical systems in the presence of fields are investigated in the framework of a theoretical method. The metod uses a generalized statistical ensemble consonant with the adequate expression for the generalized internal energy. The applications refer to the case of a system in magnetoquasistatic field. In the case of linear magnetic media one finds that for the description of the magnetic induction fluctuations the Gaussian approximation is good enough. For nonlinear media the coresponding fluctuations are non-Gaussian, they having a non-null asymmetry. Aditionally the respective fluctuations have characteristics of leptokurtic, mesokurtic and platykurtic type, depending of the value of the magnetic field strength comparatively with a scaling factor of the magnetization curve.Comment: 10 pages, REVTe

On a fractional differential equation with infinitely many solutions

We present a set of restrictions on the fractional differential equation $x^{(\alpha)}(t)=g(x(t))$, $t\geq0$, where $\alpha\in(0,1)$ and $g(0)=0$, that leads to the existence of an infinity of solutions starting from $x(0)=0$. The operator $x^{(\alpha)}$ is the Caputo differential operator

Can dissipation prevent explosive decomposition in high-energy heavy ion collisions?

We discuss the role of dissipation in the explosive spinodal decomposition scenario of hadron production during the chiral transition after a high-energy heavy ion collision. We use a Langevin description inspired by microscopic nonequilibrium field theory results to perform real-time lattice simulations of the behavior of the chiral fields. We show that the effect of dissipation can be dramatic. Analytic results for the short-time dynamics are also presented.Comment: 9 latex pages, 4 eps figures, version to appear in Phys. Lett.

Model and computer simulation of nanosecond laser material ablation

A computer model to simulate the evolution of parameters describing laser ablation processes was developed. The absorbed laser energy, the heat diffusion, the phase transformations and the shielding effect of the ablated material were taken into account. The temporal development of the ablated volume, pore depth and extension of the melt zone were calculated for single pulses of 500, 100, 20, 5 and 1ns. Simulations were performed for pulse energies of 50μJ and spot diameters of 10μm. From temporal evolution curves of the ablated volumes, the stoppage of the ablation process was evidenced before the end of the processing pulse. Comments with respect to optimal pulse duration (in the ns regime) are also formulate

On gauge unification in Type I/I' models

We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In both cases it is difficult to arrange for the multiplet structure to give the MSSM result. For the case of power law running there is also enhanced sensitivity to the spectrum at the unification scale. For the case of logarithmic running there is a fine tuning problem associated with the light closed string Kaluza Klein spectrum which requires gauge mediated supersymmetry breaking on the ``visible'' brane with a dangerously low scale of supersymmetry breaking. Evading these problems in low string scale models requires a departure from the MSSM structure, which would imply that the success of gauge unification in the MSSM is just an accident.Comment: 10 pages, LaTeX, 2 figures; minor change

Unification and Extra Space-Time Dimensions

We analyse the phenomenological implications of a particular class of supersymmetric models with additional space-time dimensions below the unification scale. Assuming the unification of the gauge couplings and using a two-loop calculation below the scale of the additional space-time dimensions, we show that the value of $\alpha_3(M_z)$ is further increased from the two-loop Minimal Supersymmetric Standard Model prediction. We consider whether decompactification threshold effects could bring $\alpha_3(M_z)$ into agreement with experiment and discuss the associated level of fine tuning needed.Comment: 11 pages, LaTeX, submitted to Phys. Lett.

Asymptotic integration of (1+α)(1+\alpha)-order fractional differential equations

\noindent{\bf Abstract} We establish the long-time asymptotic formula of solutions to the $(1+\alpha)$--order fractional differential equation ${}_{0}^{\>i}{\cal O}_{t}^{1+\alpha}x+a(t)x=0$, $t>0$, under some simple restrictions on the functional coefficient $a(t)$, where ${}_{0}^{\>i}{\cal O}_{t}^{1+\alpha}$ is one of the fractional differential operators ${}_{0}D_{t}^{\alpha}(x^{\prime})$, $({}_{0}D_{t}^{\alpha}x)^{\prime}={}_{0}D_{t}^{1+\alpha}x$ and ${}_{0}D_{t}^{\alpha}(tx^{\prime}-x)$. Here, ${}_{0}D_{t}^{\alpha}$ designates the Riemann-Liouville derivative of order $\alpha\in(0,1)$. The asymptotic formula reads as $[a+O(1)]\cdot x_{{\scriptstyle small}}+b\cdot x_{{\scriptstyle large}}$ as $t\rightarrow+\infty$ for given $a$, $b\in\mathbb{R}$, where $x_{{\scriptstyle small}}$ and $x_{{\scriptstyle large}}$ represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation ${}_{0}^{\>i}{\cal O}_{t}^{1+\alpha}x=0$, $t>0$.Comment: 16 page