Computing probabilities of very rare events for Langevin processes: a new method based on importance sampling

Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections) for processes described by Langevin dynamics. As we demonstrate with numerical examples as well as an exactly solvable model, our method can converge to the desired answer at a rate which is orders of magnitude faster than that achieved with direct simulations of the process in question.Comment: 18 pages + 7 figures, to appear in Nucl.Phys.

Investigation of magnetopause reconnection models using two colocated, low‐altitude satellites: A unifying reconnection geometry

Ion precipitation data from two co-orbiting Defense Meteorological Satellite Program satellites (F6 and F8) are used to investigate magnetopause reconnection models. We examine differential fluxes between 30 eV and 30 keV, from a Southern Hemisphere, prenoon pass during the morning of January 10, 1990. Data from the first satellite to pass through the region (F6) show two distinct ion energy dispersions •-1 ø of latitude apart, between 76 ø and 79 ø magnetic latitude. The electron data exhibit similar features at around the same region but with no or little energy dispersion, consistent with their high velocities. We suggest that the two energy dispersions can be explained by two separate injections resulting from two bursts of magnetopause reconnection. Data from the second satellite (F8), which moved through the same region I rain later, reveal the same energy-dispersed structures, only further poleward and with less overall flux. This temporal evolution is consistent with two recently reconnected flux tubes releasing their plasma as they move antisunward away from dayside merging sites. However, an observed overlap between the two ion energy dispersions suggests a more complex reconnection geometry than usual models can accommodate. We propose a generalized reconnection scenario that unifies the Bursty Single X-Line and the Multiple X-Line Reconnection models. A simple time-of-flight particle precipitation model is constructed to reproduce the ion dispersions and their overlap. The modeling results suggest that for time-dependent reconnection the dispersion overlap is observed clearly at low altitudes only for a short period compared with the evolution timescale of the ion precipitation

Analysis of the second order exchange self energy of a dense electron gas

We investigate the evaluation of the six-fold integral representation for the second order exchange contribution to the self energy of a three dimensional electron gas at the Fermi surface.Comment: 6 page

Onsager reciprocity relations without microscopic reversibility

In this paper we show that Onsager--Machlup time reversal properties of thermodynamic fluctuations and Onsager reciprocity relations for transport coefficients can hold also if the microscopic dynamics is not reversible. This result is based on the explicit construction of a class of conservative models which can be analysed rigorously.Comment: revtex, no figure

Anomalous scaling of passive scalar in turbulence and in equilibrium

We analyze multi-point correlation functions of a tracer in an incompressible flow at scales far exceeding the scale $L$ at which fluctuations are generated (quasi-equilibrium domain) and compare them with the correlation functions at scales smaller than $L$ (turbulence domain). We demonstrate that the scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales

Cyclotron radiation and emission in graphene

Peculiarity in the cyclotron radiation and emission in graphene is theoretically examined in terms of the optical conductivity and relaxation rates to propose that graphene in magnetic fields can be a candidate to realize the Landau level laser, proposed decades ago [H. Aoki, Appl. Phys. Lett. {\bf 48}, 559 (1986)].Comment: 4 pages, 3 figure

Fluctuation relations for a driven Brownian particle

We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski and Gallavotti-Cohen in different special cases

The analysis of Polyakov loop and spin correlators in finite volumes

We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are investigated both for the $2d$ Ising model and in finite temperature $SU(2)$ gauge theory. We find that the leading matrix element shows similar scaling properties in both models. Just above the critical point we obtain for $SU(2)$ a Debye screening mass $~\mu_D/T\approx4~$, independent of the volume. Sorry, figures are not included and can be sent by ordinary mail.Comment: TALK GIVEN AT THE LATTICE '93 INTERNATIONAL SYMPOSIUM LATTICE FIELD THEORY, DALLAS, USA, OCTOBER 12--16, 1993 3 pages preprint HU BERLIN--IEP--93/5 and BIELEFELD BI-TP--93/63, November 199

A Trip from St. Paul Minn. to Los Angeles, California in a Ford Car

Diary of a cross country trip by automobile in 1920.https://digitalcommons.andrews.edu/books/1099/thumbnail.jp

Experiences with a Service Dog of an Adolescent with Spinal Muscular Atrophy

Adolescents with Spinal Muscular Atrophy (SMA) may receive occupational therapy services and may at times use service dogs. Literature suggests that service dogs can provide social and physical benefits to children and adults with physical disabilities, however little research has been published, especially with adolescents. A qualitative methodology was used to best gain insight on the daily life experiences with a service dog of a thirteen year old female adolescent with a diagnosis of SMA and her mother. Major themes that emerged from interviews included: A Process, A Special Bond, A Sense of Security, Increased Independence and Participation in Life, Empowering, Social Aspects, and The Future. The information gained from this study may lead occupational therapists to suggest clients apply for a service dog, assist client’s with the transition of obtaining a service dogs, and incorporate service dogs into occupational therapy interventions