Short-Range Inverse-Square Law Experiment in Space

The objective of ISLES (Inverse-Square Law Experiment in Space) is to perform a null test of Newton's law in space with a resolution of one part in 10⁵ or better at 100 m. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and probe large extra dimensions of string theory down to a few m. The experiment will be cooled to 2 K, which permits superconducting magnetic levitation of the test masses. This soft, low-loss suspension, combined with a low-noise SQUID, leads to extremely low intrinsic noise in the detector. To minimize Newtonian errors, ISLES employs a near null source, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a nominal distance of 100 m. The signal is detected by a superconducting differential accelerometer.     

A stabilization law for two semi-infinite interacting strings of characters

We consider a Markov chain that describes the evolution of two interacting strings of symbols. The transitions probalitities of this Markov chain depend only on the rightmost symbols of both strings. The main goal of the present paper is to prove a limit theorem (stabilization law): the distribution of the rightmost symbols converges to some limit correlation function.1 Partially supported by FAPESP (2002/01501-9) and RFBR (02-01-00415)2 Partially supported by RFBR (02-01-00415)     

Microdischarges Near Metal–Insulator Interfaces

Some statistical features of microdischarges running near the metal-insulator interfaces have been discussed. The study has verified an exponential character of statistical distributions of the time intervals between microdischarge pulses, power-law distribution of voltage peaks of these pulses (height of pulses) and very weak correlation effects among pulses, i.e. weak time-height correlation, time autocorrelation and height autocorrelation. A statistical parameter of the power law distribution of the heights of microdischarge pulses proved to be sensitive to the voltage load of the insulating interface metal-insulator.     

Sand Erosion in Axial Flow Conditions

A mathematical model of sand erosion in axial flow conditions is presented. The basic mass balance equations and sand erosion constitutive equation were given in Vardoulakis et al. (1996). As opposed to reference Vardoulakis et al. (1996), we consider here the extreme case where convection is null and hydrodynamic dispersion dominates. In addition, Brinkman's extension of Darcy's law is adopted to account for a smooth transition between channel flow and Darcian flow. The set of governing PDE's is presented in dimensionless form and is solved numerically. In concordance with the basic constitutive equation for erosion kinetics, the analysis shows that erosion progresses in time as a front of high transport concentration. This result is justified by the highly non-linear character of the erosion source term which dominates in the diffusion-like governing equation.     

On Pathwise Uniqueness of Stochastic Differential Equations Without Drift

We consider the stochastic differential equation: dX _t =(|X _t |)dB _t , where B is a Brownian motion and is a non-Hölder Borel function. A sufficient condition of pathwise uniqueness is given.     

On Certain Extensions of a Rotation Invariant Markov Process

Let (X _t ,P ^x ) be a rotation invariant (RI) Feller process on R ^d {0}, d2. We study certain type of strong Markov extensions of (X _t ,P ^x ) to R ^d . It turns out that that the unique (RI) extension always exists and is of that type. We give a kind of quasi-ergodicy condition (E) under which the (RI) extension is the only extension of that type. A class of processes fulfilling (E) is also characterized.     

Additive Kernels and Integral Representation of Potentials

Let P=(P _t ) _t>0 be a submarkovian semigroup of kernels on a measurable space (X,). An additive kernel of P is a kernel K from X into ]0,[ such that P _t K(x,A)=K(x,A+t) for every t>0,xX and every Borel subset A of ]0,[. It is proved in this paper that for every potential f of P, there exits an additive kernel K of P, unique (up to equivalence) such that f=K1=₀ K(,dt). This result is already well known for regular potentials of right processes. If U=(U _p ) _p>0 is a sub-Markovian resolvent of kernels on (X,), we give a notion of additive kernel of U and we prove a similar integral representation of potentials of U.     

Second class particles as microscopic characteristics in totally asymmetric nearest-neighbor -exclusion processes

We prove laws of large numbers for a second class particle in one-dimensional totally asymmetric -exclusion processes, under hydrodynamic Euler scaling. The assumption required is that initially the ambient particle configuration converges to a limiting profile. The macroscopic trajectories of second class particles are characteristics and shocks of the conservation law of the particle density. The proof uses a variational representation of a second class particle, to overcome the problem of lack of information about invariant distributions. But we cannot rule out the possibility that the flux function of the conservation law may be neither differentiable nor strictly concave. To give a complete picture we discuss the construction, uniqueness, and other properties of the weak solution that the particle density obeys.

     

Geometric Dynamics

A kinematic differential system on a Riemann (or semi-Riemann) manifold induces a Lorentz-Udrite world-force law, i.e., any local group with one parameter (any local flow) on a Riemann (or semi-Riemann) manifold induces the dynamics of the given vector field or of an associated particle, which will be called geometric dynamics.The cases of Riemann-Jacobi or Riemann-Jacobi-Lagrange structures are imposed by the behavior of an external tensor field of type (1,1). The case of the Finsler-Jacobi structure appears if the initial metric is chosen such that the energy of the given vector field is constant (Sec. 1). At the end of Sec. 1 are formulated open problems regarding some extensions of geometric dynamics.Adequate structures on the tangent bundle describe the geometric dynamics in the Hamilton language (Sec. 2).Section 3 proves the existence of a Finsler-Jacobi structure induced by an almost contact metric structure.The theory is applied to electromagnetic dynamical systems (the starting point of our theory), offering new principles of unification of the gravitation and the electromagnetism. Also, here, one enounces open problems regarding the geometric dynamics induced by the electric intensity and magnetizing force (Sec. 4).From the geometrical point of view, we create a wider class of Riemann-Jacobi, Riemann-Jacobi-Lagrange, or Finsler-Jacobi manifolds ensuring that all trajectories of a given vector field are geodesics. Having T₁M²ⁿ⁺¹ in mind, the problem of creating a wider class of Riemannian manifolds, in which there exists a vector field such that (1) all trajectories of the vector field are geodesics; (2) the flow defined by is incompressible; (3) the condition which corresponds to the property that is the associate vector field of the contact structure is satisfied;was studied intensively by S. Sasaki. The results were not satisfactory, but Sasaki discovered (, , )-structures [10].AMS Subject Classification (1991): 70H35, 53C22, 58F25, 83C22     

Zero–One Law for some Brownian Functionals

We prove that for a>0, (B _t) one-dimensional standard Brownian motion and ₀=inf{t>0 : B _t=0} the following zero–one law is valid