What can we learn from the dynamics of the Covid-19 epidemic ?

We investigate the mechanisms behind quasi-periodic outbursts on the Covid-19 epidemics. Data for France and Germany show that the patterns of outbursts exhibit a qualitative change in early 2022, which appears in a change in their average period and which is confirmed by the time-frequency analysis. This provides a signal that can be used to discriminate among several mechanisms. Two main ideas have been proposed to explain periodicity in epidemics. One involves memory effects and another considers exchanges between epidemic clusters and a reservoir of population. We test these two approaches in the particular case of the Covid-19 epidemics and show that the "cluster model" is the only one that appears to be able to explain the observed pattern with realistic parameters. The last section discusses our results in the context of early studies of epidemics, and we stress the importance to work with models with a limited number of parameters, which moreover can be sufficiently well estimated, to draw conclusions on the general mechanisms behind the observations.

Risk factors for return visits and rehospitalizations to the child emergency psychiatric unit: A retrospective study over 2 years at Saint-Étienne University Hospital.

PURPOSE: This retrospective study aimed to achieve a better understanding of risk factors leading children and adolescents hospitalized in an emergency psychiatric ward to return visits, and to propose preventive devices. METHOD: From January 2, 2010 through February 29, 2012, 180 children and adolescents younger than 17 years were hospitalized in a total of 261 stays in the emergency psychiatric ward of University hospital of Saint-Étienne (France). We assessed clinical and sociodemographic characteristics of these patients and traced any of their return visits to the same unit through December 31, 2012. Risk factors for patients' repeated visits were calculated using multivariate analysis, and the cumulative incidence of returns using the Kaplan-Meier method for censored data. We used confidence interval of relative risk, considering 0.05 to reflect significance. RESULTS: Over the 2 years of the study, 77 (42.8%) of the 180 patients revisited the emergency psychiatric ward; 62 (80.7%) of these required further hospitalizations. Multivariate analysis linked the patients' psychiatric history (RR=2.5) and pursuit of vocational education (RR=4) with the risk of return. Return visits rose from 27.2% at 6 months to 41.2% at 2 years. CONCLUSION: Knowledge of risk factors would allow implementation of secondary or tertiary preventive devices. Students could undergo early screening of psychiatric pathologies using mobile screening teams which would save money, avoid hospitalizations, and when necessary, facilitate both hospitalization and return visits.

Crack in the frictional interface as a solitary wave.

We introduce and investigate a multiscale model for the propagation of rupture fronts in friction. Taking advantage of the correlation length for the motion of individual contacts in elastic theory, we introduce collective contacts which can be characterized by a master equation approach. The problem of the dynamics of a chain of those effective contacts under stress is studied. We show that it can be reduced to an analog of the Frenkel-Kontorova model. In some limits this allows us to derive analytical solutions for kinks describing the rupture fronts. Numerical simulations are used to study more complex cases.

Dependence of kinetic friction on velocity: master equation approach.

We investigate the velocity dependence of kinetic friction with a model that makes minimal assumptions on the actual mechanism of friction so that it can be applied at many scales, provided the system involves multicontact friction. Using a recently developed master equation approach, we investigate the influence of two concurrent processes. First, at a nonzero temperature, thermal fluctuations allow an activated breaking of contacts that are still below the threshold. As a result, the friction force monotonically increases with velocity. Second, the aging of contacts leads to a decrease of the friction force with velocity. Aging effects include two aspects: the delay in contact formation and aging of a contact itself, i.e., the change of its characteristics with the duration of stationary contact. All these processes are considered simultaneously with the master equation approach, giving a complete dependence of the kinetic friction force on the driving velocity and system temperature, provided the interface parameters are known.

Master equation approach to friction at the mesoscale.

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquakelike model which requires numerical studies. We show that this phenomenon can also be described by a master equation, which can be solved analytically in some cases and provides an efficient numerical solution for more general cases. We examine the effect of temperature and aging of the contacts and discuss the statistical properties of the contacts for different situations of friction and their implications, particularly regarding the existence of stick-slip.

Nonlinear analysis of the dynamics of DNA breathing.

The base pairs that encode the genetic information in DNA show large amplitude localized excitations called DNA breathing. We discuss the experimental observations of this phenomenon and its theoretical analysis. Starting from a model introduced to study the thermal denaturation of DNA, we show that it can qualitatively describe DNA breathing but is quantitatively not satisfactory. We show how the model can be modified to be quantitatively correct. This defines a nonlinear lattice model, which is interesting in itself because it has nonlinear localized excitations, forming a new class of discrete breather.

Experimental and theoretical studies of sequence effects on the fluctuation and melting of short DNA molecules.

Understanding the melting of short DNA sequences probes DNA at the scale of the genetic code and raises questions which are very different from those posed by very long sequences, which have been extensively studied. We investigate this problem by combining experiments and theory. A new experimental method allows us to make a mapping of the opening of the guanines along the sequence as a function of temperature. The results indicate that non-local effects may be important in DNA because an AT-rich region is able to influence the opening of a base pair which is about 10 base pairs away. An earlier mesoscopic model of DNA is modified to correctly describe the timescales associated with the opening of individual base pairs well below melting, and to properly take into account the sequence. Using this model to analyze some characteristic sequences for which detailed experimental data on the melting is available (Montrichok et al 2003 Europhys. Lett. 62 452), we show that we have to introduce non-local effects of AT-rich regions to get acceptable results. This brings a second indication that the influence of these highly fluctuating regions of DNA on their neighborhood can extend to some distance.

Modeling friction on a mesoscale: master equation for the earthquakelike model.

The earthquakelike model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach naturally describes stick-slip and smooth-sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the studies of the properties of the contacts.

Modeling DNA beacons at the mesoscopic scale.

We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free-energy landscape. Melting profiles, dependence of melting temperature on loop length, and kinetic time scales are in semiquantitative agreement with experimental data obtained from fluorescent DNA beacons forming poly(T) loops. Variation in strand rigidity is not sufficient to account for the large activation enthalpy of closing and the strong loop length dependence observed in hairpins forming poly(A) loops. Implications for modeling single strands of DNA or RNA are discussed.

Bubbles and denaturation in DNA.

The local opening of DNA is an intriguing phenomenon from a statistical-physics point of view, but is also essential for its biological function. For instance, the transcription and replication of our genetic code cannot take place without the unwinding of the DNA double helix. Although these biological processes are driven by proteins, there might well be a relation between these biological openings and the spontaneous bubble formation due to thermal fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois (PBD) model, have fairly accurately reproduced some experimental denaturation curves and the sharp phase transition in the thermodynamic limit. It is, hence, tempting to see whether these models could be used to predict the biological activity of DNA. In a previous study, we introduced a method that allows to obtain very accurate results on this subject, which showed that some previous claims in this direction, based on molecular-dynamics studies, were premature. This could either imply that the present PBD model should be improved or that biological activity can only be predicted in a more complex framework that involves interactions with proteins and super helical stresses. In this article, we give a detailed description of the statistical method introduced before. Moreover, for several DNA sequences, we give a thorough analysis of the bubble-statistics as a function of position and bubble size and the so-called l-denaturation curves that can be measured experimentally. These show that some important experimental observations are missing in the present model. We discuss how the present model could be improved.

Transition from smooth sliding to stick-slip motion in a single frictional contact.

We show that the transition from smooth sliding to stick-slip motion in a single planar frictional junction always takes place at an atomic-scale relative velocity of the substrates.

The dynamics of water in nanoporous silica studied by dielectric spectroscopy.

Broad-band dielectric spectroscopy is used to investigate the dynamics of hydration water on the surface of the cylindrical pores of a nanostructured silica material (MCM-41, with pore diameter of 3.2 nm) at various hydrations, in the temperature range 250-150 K. We focus our attention on orientational relaxations that shift from 0.5 MHz at 250 K to less than 1 Hz at 150 K. The measurements distinguish the relaxation of the hydroxyl groups at the surface of silica from the orientational dynamics of hydration water which strongly depends on the degree of hydration. Although it is significantly faster than the dynamics of water in ice, the orientational relaxation of "non-freezing" water has an activation energy comparable to that in ice when the hydration layer is complete and approximately two-molecule thick.

Model for DNA hairpin denaturation.

We investigate the thermal denaturation of DNA hairpins using molecular dynamics simulations of a simple model describing the molecule at a scale of a nucleotide. The model allows us to analyze the different interacting features that determine how an hairpin opens, such as therole of the loop and the properties intrinsic to the stem.

Can we model DNA at the mesoscale?

Modelling DNA is useful for understanding its properties better but it is also challenging because many of these properties involve hundreds of base pairs or more, or time scales which are much longer than the time scales accessible to molecular dynamics. It is therefore necessary to develop models at a mesoscale, which include enough details to describe the properties of interest, for instance the biological sequence, while staying sufficiently simple and realistic.We discuss here two examples: a dynamical model to study the mechanical denaturation of DNA, which probes the sequence on various scales, and a model for the self assembly of DNA which describes the formation of hairpins and allows us to study its kinetics.

Nonintegrable Schrodinger discrete breathers.

In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrödinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.

Dynamics and melting of a thin confined film.

Molecular dynamics is used to investigate the melting of a thin lubricant film confined between two crystalline surfaces. The dynamics of the film is significantly affected by the substrate, both in the solid and in the molten phases. The solid phase, able to sustain shear stress, shows, however, large diffusional motions of the atoms. The melting temperature depends strongly on the confinement. A phenomenological microscopic theory, based on the Lindemann criterion, is proposed to explain this effect.

Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier.

We address the problem of heat conduction in 1D nonlinear chains; we show that, acting on the parameter which controls the strength of the on-site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the chain by the same amount. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.

Physical aspects of the weakly hydrated protein surface.

We review the physical properties of water on the surface of weakly hydrated proteins and present some theoretical models used to understand them. The first part concerns mainly structural properties and introduces a model for two-dimensional clusters of water molecules. The second part is devoted to dynamical properties of the hydrated protein surface. Dielectric measurements which provide an evidence for proton conductivity due to the percolation of the network of surface water molecules and for the glass dynamics of migrating protons when temperature is lowered are reviewed. These results can be associated with the concept of frustration and analyzed with two models, an Ising model to describe the proton jumps and the model of two-dimensional surface water which exhibits a glassy dynamiques of the water molecules. Biological implications of these properties of hydration water are briefly discussed.

Glass transition in protein hydration water.

A model of two-dimensional water is studied in order to analyze recent dielectric measurements on protein hydration water. The frustration introduced by the coupling of the water molecules to the protein surface prevents a true crystallization and induces a smooth transition to a glassy state that is detected by its structure factor and the stretched exponential behavior of the cage correlation function that measures the rate of change of the hydrogen bond network around each molecule. The spectrum of the fluctuations in the vicinity of the glass transition exhibits 1/f(alpha) noise in agreement with the dielectric measurements. The results suggest that two-dimensional water, which can be probed by dielectric measurements, could be an interesting system to study the glassy behavior of water.

Friction in a solid lubricant film.

Molecular-dynamics study of a thin (one to five layers) lubricant film between two substrates in moving contact are performed using Langevin equations with an external damping coefficient depending on distance and velocity of atoms relative the substrates, motivated by microscopic configurations. They show that the minimal friction coefficient is obtained for the solid-sliding regime. A detailed analysis of the results, the comparison with other microscopic modeling approaches of friction, and the evaluation of quantities that can be compared to experiments, such as the velocity of the transition from stick slip to smooth sliding, are used to discuss the relevance of the microscopic simulations of friction.