A mathematical formalization of the parallel replica dynamics

The purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics and molecular dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The aim of the approach is to efficiently generate a coarse-grained evolution (in terms of state-to-state dynamics) of a given stochastic process. The approach formally consists in concurrently considering several realizations of the stochastic process, and tracking among the realizations that which, the soonest, undergoes an important transition. Using specific properties of the dynamics generated, a computational speed-up is obtained. In the best cases, this speed-up approaches the number of realizations considered. By drawing connections with the theory of Markov processes and, in particular, exploiting the notion of quasi-stationary distribution, we provide a mathematical setting appropriate for assessing theoretically the performance of the approach, and possibly improving it

Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics

This paper is an introduction to the modelling of viscoelastic fluids, with an emphasis on micro-macro (or multiscale) models. Some elements of mathematical and numerical analysis are provided. These notes closely follow the lectures delivered by the second author at the Chinese Academy of Science during the Workshop "Stress Tensor Effects on Fluid Mechanics", in January 2010

Using nonequilibrium fluctuation theorems to understand and correct errors in equilibrium and nonequilibrium discrete Langevin dynamics simulations

Common algorithms for computationally simulating Langevin dynamics must discretize the stochastic differential equations of motion. These resulting finite time step integrators necessarily have several practical issues in common: Microscopic reversibility is violated, the sampled stationary distribution differs from the desired equilibrium distribution, and the work accumulated in nonequilibrium simulations is not directly usable in estimators based on nonequilibrium work theorems. Here, we show that even with a time-independent Hamiltonian, finite time step Langevin integrators can be thought of as a driven, nonequilibrium physical process. Once an appropriate work-like quantity is defined -- here called the shadow work -- recently developed nonequilibrium fluctuation theorems can be used to measure or correct for the errors introduced by the use of finite time steps. In particular, we demonstrate that amending estimators based on nonequilibrium work theorems to include this shadow work removes the time step dependent error from estimates of free energies. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. While these deviations can be large, they can be eliminated altogether by Metropolization or greatly diminished by small reductions in the time step. Through this connection with driven processes, further developments in nonequilibrium fluctuation theorems can provide additional analytical tools for dealing with errors in finite time step integrators.Comment: 11 pages, 4 figure

Extended skyrmion lattice scattering and long-time memory in the chiral magnet Fe1−x_{1-x}Cox_xSi

Small angle neutron scattering measurements on a bulk single crystal of the doped chiral magnet Fe$_{1-x}$Co$_x$Si with $x$=0.3 reveal a pronounced effect of the magnetic history and cooling rates on the magnetic phase diagram. The extracted phase diagrams are qualitatively different for zero and field cooling and reveal a metastable skyrmion lattice phase outside the A-phase for the latter case. These thermodynamically metastable skyrmion lattice correlations coexist with the conical phase and can be enhanced by increasing the cooling rate. They appear in a wide region of the phase diagram at temperatures below the $A$-phase but also at fields considerably smaller or higher than the fields required to stabilize the A-phase

Magnetic Fluctuations, Precursor Phenomena and Phase Transition in MnSi under Magnetic Field

The reference chiral helimagnet MnSi is the first system where skyrmion lattice correlations have been reported. At zero magnetic field the transition at $T_C$ to the helimagnetic state is of first order. Above $T_C$, in a region dominated by precursor phenomena, neutron scattering shows the build up of strong chiral fluctuating correlations over the surface of a sphere with radius $2\pi/\ell$, where $\ell$ is the pitch of the helix. It has been suggested that these fluctuating correlations drive the helical transition to first order following a scenario proposed by Brazovskii for liquid crystals. We present a comprehensive neutron scattering study under magnetic fields, which provides evidence that this is not the case. The sharp first order transition persists for magnetic fields up to 0.4 T whereas the fluctuating correlations weaken and start to concentrate along the field direction already above 0.2 T. Our results thus disconnect the first order nature of the transition from the precursor fluctuating correlations. They also show no indication for a tricritical point, where the first order transition crosses over to second order with increasing magnetic field. In this light, the nature of the first order helical transition and the precursor phenomena above $T_C$, both of general relevance to chiral magnetism, remain an open question

Dissolution and gettering of iron during contact co-firing

The dissolution and gettering of iron is studied during the final fabrication step of multicrystalline silicon solar cells, the co-firing step, through simulations and experiments. The post-processed interstitial iron concentration is simulated according to the as-grown concentration and distribution of iron within a silicon wafer, both in the presence and absence of the phosphorus emitter, and applying different time-temperature profiles for the firing step. The competing effects of dissolution and gettering during the short annealing process are found to be strongly dependant on the as-grown material quality. Furthermore, increasing the temperature of the firing process leads to a higher dissolution of iron, hardly compensated by the higher diffusivity of impurities. A new defect engineering tool is introduced, the extended co-firing, which could allow an enhanced gettering effect within a small additional tim

Effective dynamics using conditional expectations

The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(x)$, where $x$ describes the configuration of the system in a high-dimensional space $\R^n$, and $\xi$ is a smooth function with value in $\R$ (typically a reaction coordinate). It is well known that, given a Boltzmann-Gibbs distribution on $x \in \R^n$, the equilibrium properties on $\xi(x)$ are completely determined by the free energy. On the other hand, the question of the effective dynamics on $\xi(x)$ is much more difficult to address. Starting from an overdamped Langevin equation on $x \in \R^n$, we propose an effective dynamics for $\xi(x) \in \R$ using conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones. We check numerically on some toy examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarse-grained dynamics

Pharmacokinetics of secnidazole in healthy volunteers after single oral dose

Introduction: Secnidazole is an anti infective agent which belongs to the 5-nitroimidazole class. Method: The objective of the trial was to characterize the pharmacokinetics of secnidazole after oral administration of a 2g dose, as microgranules formulation in healthy subjects. Blood samples were collected before, 1, 2, 3, 6, 9, 12, 24, 36, 48, 72, 96, 120, 168 and 240 h after dosing. Urines were collected in 24-h-fractions for the first five days and in 48 h-fraction for the last sample. The cumulative urinary excretion was captured for each subject from urine concentration (lg/L). Pharmacokinetic parameters were obtained by a non-compartmental approach (WinNonlin Pharsight). The assay was performed by ultra-performance liquid chromatography coupled with mass spectrometry detection (UPLC-MS/MS, Quattro Premier, Waters) after simple protein precipitation of 50 lL plasma sample. Chromatographic separation was done on a C18 Acquity column (50 mm · 2.1 mm, id 1.7 lm, Waters), in isocratic mode (80% water/0.1% formic acid and 20% acetonitrile). Ornidazole was used as internal standard. The detection was operated in positive mode and multiple reaction monitoring was used for quantification (186 > 128 ion transition for secnidazole). The lower limit of quantification was 10 and 100 lg/L for plasma and urine samples respectively. Results: Sixteen subjects (8 female, 8 male) were included. Population characteristics such as: age ranged from 23 to 50 years (mean ± SD: 38 ± 9.2 years), weight ranged from 51 to 90 Kg (mean ± SD = 64.6 ± 10.1 Kg) and body mass index (BMI) ranged from 19.9 to 24.2 Kg/m 2 (mean ± SD = 21.9 ± 1.5 Kg/m 2 ;). Secnidazole exposure achieved a maximal concentration (Cmax) with a mean of 37.9 ± 8.5 mg/L (range 20–56 mg/L) and at a median time associated with the Cmax (Tmax) of 6 h (range 3–6 h). The area under the curve to the last measurable time (AUC0_t) and the total area under the curve (AUC0_¥) were 1281.9 ± 416.4 mg h/L and 1304.2 ± 444.1 mg h/L (mean ± SD) respectively. The Cl/F and V/F were 1.7 ± 0.5 L/h and 40.2 ± 9.2 L respectively and the elimination half-life (t1/2) was 17.5 ± 4.3 h (mean ± SD). The mean amount of secnidazole excreted in the 168-h urine collection was 310.47 mg (15.5% of the administered dose). For example, for the subject number 5, the observed parameters are: Cmax 37.3 mg/L, Tmax 3 h, AUC0_¥ 1029.5 mg h/L and t1/2 15.6 h. Conclusion: After a 2 g single oral dose, secnidazole presents a good absorption profile and relatively long elimination half life ensuring probable sufficient exposure with once a day administration

Universality of the helimagnetic transition in cubic chiral magnets: Small angle neutron scattering and neutron spin echo spectroscopy studies of Fe1−x_{1-x}Cox_xSi

We present a comprehensive Small Angle Neutron Scattering (SANS) and Neutron Spin Echo Spectroscopy (NSE) study of the structural and dynamical aspects of the helimagnetic transition in Fe$_{1-x}$Co$_x$Si with $x$ = 0.30. In contrast to the sharp transition observed in the archetype chiral magnet MnSi, the transition in Fe$_{1-x}$Co$_x$Si is gradual and long-range helimagnetic ordering coexists with short-range correlations over a wide temperature range. The dynamics are more complex than in MnSi and involve long relaxation times with a stretched exponential relaxation which persists even under magnetic field. These results in conjunction with an analysis of the hierarchy of the relevant length scales show that the helimagnetic transition in Fe$_{1-x}$Co$_x$Si differs substantially from the transition in MnSi and question the validity of a universal approach to the helimagnetic transition in chiral magnets