Time-averaged MSD of Brownian motion

We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution

Shielding efficiency and E(J) characteristics measured on large melt cast Bi-2212 hollow cylinders in axial magnetic fields

We show that tubes of melt cast Bi-2212 used as current leads for LTS magnets can also act as efficient magnetic shields. The magnetic screening properties under an axial DC magnetic field are characterized at several temperatures below the liquid nitrogen temperature (77 K). Two main shielding properties are studied and compared with those of Bi-2223, a material that has been considered in the past for bulk magnetic shields. The first property is related to the maximum magnetic flux density that can be screened, Blim; it is defined as the applied magnetic flux density below which the field attenuation measured at the centre of the shield exceeds 1000. For a cylinder of Bi-2212 with a wall thickness of 5 mm and a large ratio of length over radius, Blim is evaluated to 1 T at T = 10 K. This value largely exceeds the Blim value measured at the same temperature on similar tubes of Bi-2223. The second shielding property that is characterized is the dependence of Blim with respect to variations of the sweep rate of the applied field, dBapp/dt. This dependence is interpreted in terms of the power law E = Ec(J/Jc)^n and allows us to determine the exponent n of this E(J) characteristics for Bi-2212. The characterization of the magnetic field relaxation involves very small values of the electric field. This gives us the opportunity to experimentally determine the E(J) law in an unexplored region of small electric fields. Combining these results with transport and AC shielding measurements, we construct a piecewise E(J) law that spans over 8 orders of magnitude of the electric field.Comment: 16 pages, 7 figure

Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

Reduced-symmetry two-dimensional solitons in photonic lattices

We demonstrate theoretically and experimentally a novel type of localized beams supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.Comment: 5 pages, 4 figure

New and old N=8 superconformal field theories in three dimensions

We show that an infinite family of N=6 d=3 superconformal Chern-Simons-matter theories has hidden N=8 superconformal symmetry and hidden parity on the quantum level. This family of theories is different from the one found by Aharony, Bergman, Jafferis and Maldacena, as well as from the theories constructed by Bagger and Lambert, and Gustavsson. We also test several conjectural dualities between BLG theories and ABJ theories by comparing superconformal indices of these theories.Comment: 16 pages, late

Separation of VUV/UV photons and reactive particles in the effluent of a He/O2 atmospheric pressure plasma jet

Cold atmospheric pressure plasmas can be used for treatment of living tissues or for inactivation of bacteria or biological macromolecules. The treatment is usually characterized by a combined effect of UV and VUV radiation, reactive species, and ions. This combination is usually beneficial for the effectiveness of the treatment but it makes the study of fundamental interaction mechanisms very difficult. Here we report on an effective separation of VUV/UV photons and heavy reactive species in the effluent of a micro scale atmospheric pressure plasma jet ($\mu$-APPJ). The separation is realized by an additional flow of helium gas under well-defined flow conditions, which deflects heavy particles in the effluent without affecting the VUV and UV photons. Both components of the effluent, the photons and the reactive species, can be used separately or in combination for sample treatment. The results of treatment of a model plasma polymer film and vegetative Bacillus subtilis and Escherichia coli cells are shown and discussed. A simple model of the He gas flow and reaction kinetics of oxygen atoms in the gas phase and at the surface is used to provide a better understanding of the processes in the plasma effluent. The new jet modification, called X-Jet for its appearance, will simplify the investigation of interaction mechanisms of atmospheric pressure plasmas with biological samples.Comment: 10 pages, 7 figures, submitted to Journal of Physics D: Applied Physic

Behavior of bulk high-temperature superconductors of finite thickness subjected to crossed magnetic fields

Crossed magnetic field effects on bulk high-temperature superconductors have been studied both experimentally and numerically. The sample geometry investigated involves finite-size effects along both (crossed) magnetic field directions. The experiments were carried out on bulk melt-processed Y-Ba-Cu-O (YBCO) single domains that had been pre-magnetized with the applied field parallel to their shortest direction (i.e. the c-axis) and then subjected to several cycles of the application of a transverse magnetic field parallel to the sample ab plane. The magnetic properties were measured using orthogonal pick-up coils, a Hall probe placed against the sample surface and Magneto-Optical Imaging (MOI). We show that all principal features of the experimental data can be reproduced qualitatively using a two-dimensional finite-element numerical model based on an E-J power law and in which the current density flows perpendicularly to the plane within which the two components of magnetic field are varied. The results of this study suggest that the suppression of the magnetic moment under the action of a transverse field can be predicted successfully by ignoring the existence of flux-free configurations or flux-cutting effects. These investigations show that the observed decay in magnetization results from the intricate modification of current distribution within the sample cross-section. It is also shown that the model does not predict any saturation of the magnetic induction, even after a large number (~ 100) of transverse field cycles. These features are shown to be consistent with the experimental data.Comment: 41 pages, 9 figures, accepted in Phys. Rev. B Changes : 8 references added, a few precisions added, some typos correcte

Landau theory of bi-criticality in a random quantum rotor system

We consider here a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin. We focus entirely on the case not considered previously, namely when the distribution of exchange interactions has non-zero mean. Inclusion of non-zero mean permits ferromagnetic and superconducting phases for M=1 and M=2, respectively. We find that quite generally, the Landau theory for this system can be recast as a zero-mean problem in the presence of a magnetic field. Naturally then, we find that a Gabay-Toulouse line exists for $M>1$ when the distribution of exchange interactions has non-zero mean. The solution to the saddle point equations is presented in the vicinity of the bi-critical point characterized by the intersection of the ferromagnetic (M=1) or superconducting (M=2) phase with the paramagnetic and spin glass phases. All transitions are observed to be second order. At zero temperature, we find that the ferromagnetic order parameter is non-analytic in the parameter that controls the paramagnet/ferromagnet transition in the absence of disorder. Also for M=1, we find that replica symmetry breaking is present but vanishes at low temperatures. In addition, at finite temperature, we find that the qualitative features of the phase diagram, for M=1, are {\it identical} to what is observed experimentally in the random magnetic alloy $LiHo_xY_{1-x}F_4$.Comment: 20 pages, 5 figure

Monte Carlo transient phonons transport in silicon and germanium at nanoscales

Heat transport at nanoscales in semiconductors is investigated with a statistical method. The Boltzmann Transport Equation (BTE) which characterize phonons motion and interaction within the crystal lattice has been simulated with a Monte Carlo technique. Our model takes into account media frequency properties through the dispersion curves for longitudinal and transverse acoustic branches. The BTE collisional term involving phonons scattering processes is simulated with the Relaxation Times Approximation theory. A new distribution function accounting for the collisional processes has been developed in order to respect energy conservation during phonons scattering events. This non deterministic approach provides satisfactory results in what concerns phonons transport in both ballistic and diffusion regimes. The simulation code has been tested with silicon and germanium thin films; temperature propagation within samples is presented and compared to analytical solutions (in the diffusion regime). The two materials bulk thermal conductivity is retrieved for temperature ranging between 100 K and 500 K. Heat transfer within a plane wall with a large thermal gradient (250 K-500 K) is proposed in order to expose the model ability to simulate conductivity thermal dependence on heat exchange at nanoscales. Finally, size effects and validity of heat conduction law are investigated for several slab thicknesses

Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation

The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity