Jarzynski equality for the Jepsen gas

We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres.Comment: 7 pages, 4 figures, submitted to Europhys. Let

Stochastically perturbed flows: Delayed and interrupted evolution

We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed evolution, in which the flow alternates with a quiescent state in which the variate remains frozen at its current value for random intervals of time; and interrupted evolution, in which the variate is also re-set in the quiescent state to a random value drawn from a fixed distribution. In the former case, the effect of the delay upon the first passage time statistics is analyzed. In the latter case, the conditions under which an extended stationary distribution can exist as a consequence of the competition between an attractor in the flow and the random re-setting are examined. We elucidate the role of the normalization condition in eliminating the singularities arising from the unstable critical points of the flow, and present a number of representative examples. A simple formula is obtained for the stationary distribution and interpreted physically. A similar interpretation is also given for the known formula for the stationary distribution in a full-fledged dichotomous flow.Comment: 27 pages; no figures. Submitted to Stochastics and Dynamic

Efficiency at maximum power: An analytically solvable model for stochastic heat engines

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.Comment: 6 pages, 3 figure

Stochastic Stokes' drift of a flexible dumbbell

We consider the stochastic Stokes drift of a flexible dumbbell. The dumbbell consists of two isotropic Brownian particles connected by a linear spring with zero natural length, and is advected by a sinusoidal wave. We find an asymptotic approximation for the Stokes drift in the limit of a weak wave, and find good agreement with the results of a Monte Carlo simulation. We show that it is possible to use this effect to sort particles by their flexibility even when all the particles have the same diffusivity.Comment: 12 pages, 1 figur

Using the VALGENT-3 framework to assess the clinical and analytical performance of the RIATOL qPCR HPV genotyping assay

Background and objective: The VALGENT framework is developed to assess the clinical performance of HPV tests that offer genotyping capability. Samples from the VALGENT-3 panel are used to identify an optimal viral concentration threshold for the RIATOL qPCR HPV genotyping assay (RIATOL qPCR) to assure non-inferior accuracy to detect high-grade cervical intraepithelial neoplasia (CIN), compared to Qiagen Hybrid Capture 2 (HC2), a standard comparator test validated for cervical cancer screening. Study design: The VALGENT-3 panel comprised 1300 samples from women participating in the Slovenian cervical cancer screening programme, enriched with 300 samples from women with abnormal cytology. In follow-up, 126 women were diagnosed with CIN2+ (defined as diseased) and 1167 women had two consecutive negative Pap smears (defined as non-diseased). All 1600 samples were analyzed with the RIATOL qPCR. Viral concentration was expressed as viral log10 of the number of copies/ml. A zone of viral concentration cut-offs was defined by relative ROC analysis where the sensitivity and specificity were not inferior to HC2. Results: The RIATOL qPCR had a sensitivity and specificity for CIN2+ of 97.6% (CI: 93.2-99.5%) and 85.1% (CI: 82.9-87.1%), respectively, when the analytical cut off was used. At a cut off of 6.5, RIATOL qPCR had a sensitivity of 96.0% (CI: 91.0-98.7%) and a specificity of 89.5% (87.6-91.2%). At optimized cut off, accuracy of the qPCR was non-inferior to the HC2 with a relative sensitivity of 1.00 [CI: 0.95-1.05 (p= 0.006)] and relative specificity of 1.00 [CI: 0.98-1.01 (p= 0.0069)]. Conclusions: The RIATOL qPCR has a high sensitivity and specificity for the detection of CIN2+. By using a fixed cut-off based on viral concentration, the test is non-inferior to HC2. HPV tests that provide viral concentration measurements or other quantifiable signals allow flexibility to optimize accuracy required for cervical cancer screening

Long-lived states of oscillator chain with dynamical traps

A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise. Locally they manifest themselves via distortion of the particle arrangement symmetry. Depending on the system parameters the particle arrangement is characterized by the corresponding distributions taking either a bimodal form, or twoscale one, or unimodal onescale form which, however, deviates substantially from the Gaussian distribution. The individual particle velocities exhibit also a number of anomalies, in particular, their distribution can be extremely wide or take a quasi-cusp form. A large number of different cooperative structures and superstructures made of these formations are found in the visualized time patterns. Their evolution is, in some sense, independent of the individual particle dynamics, enabling us to regard them as dynamical phases.Comment: 8 pages, 5 figurs, TeX style of European Physical Journa

Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States

We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or antiferromagnetic ordered states. We discuss the phase diagram, the order of the transitions, and the critical behaviour. For global coupling we show analytically that the critical exponent of the magnetization exhibits a transition from the value 1/2 to a non-universal behaviour depending on the ratio of noise strength to the magnitude of the spatial coupling.Comment: 4 pages, 5 figure