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.

Continuous-flow IRMS technique for determining the 17O excess of CO2 using complete oxygen isotope exchange with cerium oxide

This paper presents an analytical system for analysis of all single substituted isotopologues (¹²C¹⁶O¹⁷O, ¹²C¹⁶O¹⁸O, ¹³C¹⁶O¹⁶O) in nanomolar quantities of CO₂ extracted from stratospheric air samples. CO₂ is separated from bulk air by gas chromatography and CO₂ isotope ratio measurements (ion masses 45 / 44 and 46 / 44) are performed using isotope ratio mass spectrometry (IRMS). The ¹⁷O excess (Δ¹⁷O) is derived from isotope measurements on two different CO₂ aliquots: unmodified CO₂ and CO₂ after complete oxygen isotope exchange with cerium oxide (CeO₂) at 700 °C. Thus, a single measurement of Δ¹⁷O requires two injections of 1 mL of air with a CO₂ mole fraction of 390 μmol mol⁻¹ at 293 K and 1 bar pressure (corresponding to 16 nmol CO₂ each). The required sample size (including flushing) is 2.7 mL of air. A single analysis (one pair of injections) takes 15 minutes. The analytical system is fully automated for unattended measurements over several days. The standard deviation of the ¹⁷O excess analysis is 1.7‰. Multiple measurements on an air sample reduce the measurement uncertainty, as expected for the statistical standard error. Thus, the uncertainty for a group of 10 measurements is 0.58‰ for Δ ¹⁷O in 2.5 h of analysis. 100 repeat analyses of one air sample decrease the standard error to 0.20‰. The instrument performance was demonstrated by measuring CO₂ on stratospheric air samples obtained during the EU project RECONCILE with the high-altitude aircraft Geophysica. The precision for RECONCILE data is 0.03‰ (1σ) for δ¹³C, 0.07‰ (1σ) for δ¹⁸O and 0.55‰ (1σ) for δ¹⁷O for a sample of 10 measurements. This is sufficient to examine stratospheric enrichments, which at altitude 33 km go up to 12‰ for δ¹⁷O and up to 8‰ for δ¹⁸O with respect to tropospheric CO₂ : δ¹⁷O ~ 21‰ Vienna Standard Mean Ocean Water (VSMOW), δ¹⁸O ~ 41‰ VSMOW (Lämmerzahl et al., 2002). The samples measured with our analytical technique agree with available data for stratospheric CO₂

Assessing TMS-induced D and I waves with spinal H-reflexes

Transcranial magnetic stimulation (TMS) of motor cortex produces a series of descending volleys known as D (direct) and I (indirect) waves. In the present study, we questioned whether spinal H-reflexes can be used to dissect D waves and early and late I waves from TMS. We therefore probed H-reflex facilitation at arrival times of D and I waves at the spinal level and thereby changed TMS parameters that have previously been shown to have selective effects on evoked D and different I waves. We changed TMS intensity and current direction and applied a double-pulse paradigm known as short-interval intracortical inhibition (SICI). Experiments were conducted in flexor carpi radialis (FCR) in the arm and soleus (SOL) in the leg. There were two major findings: 1) in FCR, H-reflex facilitation showed characteristic modulations with altered TMS parameters that correspond to the changes of evoked D and I waves; and 2) H-reflexes in SOL did not, possibly because of increased interference from other spinal circuits. Therefore, the most significant outcome of this study is that in FCR, H-reflexes combined with TMS seem to be a useful technique to dissect TMS-induced D and I waves. NEW & NOTEWORTHY Questions that relate to corticospinal function in pathophysiology and movement control demand sophisticated techniques to provide information about corticospinal mechanisms. We introduce a noninvasive electrophysiological technique that may be useful in describing such mechanisms in more detail by dissecting D and I waves from transcranial magnetic stimulation (TMS). Based on the combination of spinal H-reflexes and TMS in the flexor carpi radialis muscle, the technique was shown to measure selective effects on D and I waves from changing TMS parameters

Single polymer adsorption in shear: flattening versus hydrodynamic lift and corrugation effects

The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of flexible polymers. Surface friction due to small-wavelength surface potential corrugations is argued to weaken the surface attraction as well.Comment: 6 pages, 4 figure

Brownian Motion and Polymer Statistics on Certain Curved Manifolds

We have calculated the probability distribution function G(R,L|R',0) of the end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a cylinder, a cone and a curved torus in 3-D. We showed that: surface curvature induces a geometrical localization area; at short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at large scales, (R-R')^2 is constant for the sphere, it is linear in L for the cylinder and reaches different constant values for the torus. The cone vertex induces (function of opening angle and R') contraction of the chain for all lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to appear in Phys. Rev

Path-integral analysis of fluctuation theorems for general Langevin processes

We examine classical, transient fluctuation theorems within the unifying framework of Langevin dynamics. We explicitly distinguish between the effects of non-conservative forces that violate detailed balance, and non-autonomous dynamics arising from the variation of an external parameter. When both these sources of nonequilibrium behavior are present, there naturally arise two distinct fluctuation theorems.Comment: 24 pages, one figur

Path Integral Approach to the Non-Relativistic Electron Charge Transfer

A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom or more generally the problem of rearrangement collisions is formulated in terms of influence functionals. It has been shown that the electron charge transfer process can be treated either as electron transition problem or as elastic scattering of ion and atom in the some effective potential field. The first-order Born approximation for the electron charge transfer cross section has been reproduced to prove the adequacy of the path integral approach for this problem.Comment: 19 pages, 1 figure, to appear in Journal of Physics B: Atomic, Molecular & Optical, vol.34, 200

Entropy, time irreversibility and Schroedinger equation in a primarily discrete space-time

In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time structure is determined by a condition that mimics the Heisenberg uncertainty relations and the motion in this space-time model is chosen as simple as possible. From these two assumptions we define a path-entropy that measures the number of closed paths associated with a given energy of the system preparation. This entropy has a dynamical character and depends on the time interval on which we count the paths. We show that it exists an like-equilibrium condition for which the path-entropy corresponds exactly to the usual thermodynamic entropy and, more generally, the usual statistical thermodynamics is reobtained. This result derived without using the Gibbs ensemble method shows that the standard thermodynamics is consistent with a motion that is time-irreversible at a microscopic level. From this change of paradigm it becomes easy to derive a $H-theorem$. A comparison with the traditional Boltzmann approach is presented. We also show how our approach can be implemented in order to describe reversible processes. By considering a process defined simultaneously by initial and final conditions a well defined stochastic process is introduced and we are able to derive a Schroedinger equation, an example of time reversible equation.Comment: latex versio

Threefold onset of vortex loops in superconductors with a magnetic core

A magnetic inclusion inside a superconductor gives rise to a fascinating complex of {\it vortex loops}. Our calculations, done in the framework of the Ginzburg-Landau theory, reveal that {\it loops always nucleate in triplets} around the magnetic core. In a mesoscopic superconducting sphere, the final superconducting state is characterized by those confined vortex loops and the ones that eventually spring to the surface of the sphere, evolving into {\it vortex pairs} piercing through the sample surface.Comment: 6 pages, 6 figures (low resolution), latex2

Mol Cell Proteomics

Protein biochips have a great potential in future parallel processing of complex samples as a research tool and in diagnostics. For the generation of protein biochips, highly automated technologies have been developed for cDNA expression library production, high throughput protein expression, large scale analysis of proteins, and protein microarray generation. Using this technology, we present here a strategy to identify potential autoantigens involved in the pathogenesis of alopecia areata, an often chronic disease leading to the rapid loss of scalp hair. Only little is known about the putative autoantigen(s) involved in this process. By combining protein microarray technology with the use of large cDNA expression libraries, we profiled the autoantibody repertoire of sera from alopecia areata patients against a human protein array consisting of 37,200 redundant, recombinant human proteins. The data sets obtained from incubations with patient sera were compared with control sera from clinically healthy persons and to background incubations with anti-human IgG antibodies. From these results, a smaller protein subset was generated and subjected to qualitative and quantitative validation on highly sensitive protein microarrays to identify novel alopecia areata-associated autoantigens. Eight autoantigens were identified by protein chip technology and were successfully confirmed by Western blot analysis. These autoantigens were arrayed on protein microarrays to generate a disease-associated protein chip. To confirm the specificity of the results obtained, sera from patients with psoriasis or hand and foot eczema as well as skin allergy were additionally examined on the disease-associated protein chip. By using alopecia areata as a model for an autoimmune disease, our investigations show that the protein microarray technology has potential for the identification and evaluation of autoantigens as well as in diagnosis such as to differentiate alopecia areata from other skin diseases