Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.Comment: 15 pages, LaTeX, 5 figures PostScrip

The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)

Modeling and simulation with operator scaling

Self-similar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating stochastic processes with operator scaling. A simulation method for operator stable Levy processes is developed, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate practical applications. A classification of operator stable Levy processes in two dimensions is provided according to their exponents and symmetry groups. We conclude with some remarks and extensions to general operator self-similar processes.Comment: 29 pages, 13 figure

Central Glucagon-like Peptide-1 Receptor Signaling via Brainstem Catecholamine Neurons Counteracts Hypertension in Spontaneously Hypertensive Rats

Glucagon-like peptide-1 receptor (GLP-1R) agonists, widely used to treat type 2 diabetes, reduce blood pressure (BP) in hypertensive patients. Whether this action involves central mechanisms is unknown. We here report that repeated lateral ventricular (LV) injection of GLP-1R agonist, liraglutide, once daily for 15 days counteracted the development of hypertension in spontaneously hypertensive rats (SHR). In parallel, it suppressed urinary norepinephrine excretion, and induced c-Fos expressions in the area postrema (AP) and nucleus tractus solitarius (NTS) of brainstem including the NTS neurons immunoreactive to dopamine beta-hydroxylase (DBH). Acute administration of liraglutide into fourth ventricle, the area with easy access to the AP and NTS, transiently decreased BP in SHR and this effect was attenuated after lesion of NTS DBH neurons with anti-DBH conjugated to saporin (anti-DBH-SAP). In anti-DBH-SAP injected SHR, the antihypertensive effect of repeated LV injection of liraglutide for 14 days was also attenuated. These findings demonstrate that the central GLP-1R signaling via NTS DBH neurons counteracts the development of hypertension in SHR, accompanied by attenuated sympathetic nerve activity

Broad-band X-ray spectral evolution of GX 339-4 during a state transition

We report on X-ray and soft gamma-ray observations of the black-hole candidate GX 339-4 during its 2007 outburst, performed with the RXTE and INTEGRAL satellites. The hardness-intensity diagram of all RXTE/PCA data combined shows a q-shaped track similar to that observed in previous outbursts.The evolution in the diagram suggested that a transition from hard-intermediate state to soft-intermediate state occurred, simultaneously with INTEGRAL observations performed in March. The transition is confirmed by the timing analysis presented in this work, which reveals that a weak type-A quasi-periodic oscillation (QPO) replaces a strong type-C QPO. At the same time, spectral analysis shows that the flux of the high-energy component shows a significant decrease in its flux. However, we observe a delay (roughly one day) between variations of the spectral parameters of the high-energy component and changes in the flux and timing properties. The changes in the high-energy component can be explained either in terms the high-energy cut-off or in terms of a variations in the reflection component. We compare our results with those from a similar transition during the 2004 outburst of GX 339-4.Comment: 8 pages, 6 figures, accepted for publication in MNRAS Main Journa

Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes

The inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive a relationship between weak convergence of a Levy process to an infinite variance stable distribution when time approaches zero and weak convergence of a different Levy process as time approaches infinity. This allows us to get self contained conditions for a Levy process to converge to an infinite variance stable distribution as time approaches zero. We formulate our results both for general Levy processes and for the important class of tempered stable Levy processes. For this latter class, we give detailed results in terms of their Rosinski measures