Epidemic model on a network: analysis and applications to COVID-19

We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic

The closed-edge structure of graphite and the effect of electrostatic charging

The properties of graphite, and of few-layer graphene, can be strongly influenced by the edge structure of the graphene planes, but there is still much that we do not understand about the geometry and stability of these edges. We present an experimental and theoretical study of the closed edges of graphite crystals, and of the effect of an electric field on their structure. High-resolution transmission electron microscopy is used to image the edge structure of fresh graphite and of graphite that has been exposed to an electric field, which experiences a separation of the graphene layers. Computer simulations based on density functional theory are used to rationalise and quantify the preference for the formation of multiple concentric loops at the edges. A model is also presented to explain how the application of an electric field leads to the separation of the folded edges

Condensation transition in DNA-polyaminoamide dendrimer fibers studied using optical tweezers

When mixed together, DNA and polyaminoamide (PAMAM) dendrimers form fibers that condense into a compact structure. We use optical tweezers to pull condensed fibers and investigate the decondensation transition by measuring force-extension curves (FECs). A characteristic plateau force (around 10 pN) and hysteresis between the pulling and relaxation cycles are observed for different dendrimer sizes, indicating the existence of a first-order transition between two phases (condensed and extended) of the fiber. The fact that we can reproduce the same FECs in the absence of additional dendrimers in the buffer medium indicates that dendrimers remain irreversibly bound to the DNA backbone. Upon salt variation FECs change noticeably confirming that electrostatic forces drive the condensation transition. Finally, we propose a simple model for the decondensing transition that qualitatively reproduces the FECs and which is confirmed by AFM images.Comment: Latex version, 4 pages+3 color figure

Non-equilibrium Lorentz gas on a curved space

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries

DNA loop statistics and torsional modulus

The modelling of DNA mechanics under external constraints is discussed. Two analytical models are widely known, but disagree for instance on the value of the torsional modulus. The origin of this embarassing situation is located in the concept of writhe. This letter presents a unified model for DNA establishing a relation between the different approaches. I show that the writhe created by the loops of DNA is at the origin of the discrepancy. To take this into account, I propose a new treatment of loop statistics based on numerical simulations using the most general formula for the writhe, and on analytic calculations with only one fit parameter. One can then compute the value of the torsional modulus of DNA without the need of any cut-off.Comment: 8 pages, 1 figure. Accepted by Europhysics Letter

Evaluation of Eta Model seasonal precipitation forecasts over South America

International audienceSeasonal forecasts run by the Eta Model over South America were evaluated with respect to precipitation predictability at different time scales, seasonal, monthly and weekly for one-year period runs. The model domain was configured over most of South America in 40km horizontal resolution and 38 layers. The lateral boundary conditions were taken from CPTEC GCM forecasts at T62L28. The sea surface temperature was updated daily with persisted anomaly during the integrations. The total time integration length was 4.5 months. The Eta seasonal forecasts represented reasonably well the large scale precipitation systems over South America such as the Intertropical Convergence Zone and the South Atlantic Convergence Zone. The total amounts were comparable to observations. The season total precipitation forecasts from the driver model exhibited large overestimate. In general, the largest precipitation errors were found in ASON season and the smallest in FMAM. The major error areas were located along the northern and northeastern coast and over the Andes. These areas were present in both models. The monthly precipitation totals indicated that the intra-seasonal variability, such as the monsoonal onset, was reasonably captured by the model. The equitable threat score and the bias score showed that the Eta Model forecasts had higher precipitation predictability over the Amazon Region and lower over Northeast Brazil. The evaluation of the precipitation forecast range showed that at the fourth month the forecast skill was still comparable to the first month of integration. Comparisons with the CPTEC GCM forecasts showed that the Eta improved considerably the forecasts from the driver model. Five-member ensemble runs were produced for the NDJF rainy season. Both driver model and Eta Model forecasts showed some internal variability in the SACZ and over the Andes regions. Comparison of the Eta Model seasonal forecasts against climatology showed that in general the model produced additional useful information over the climatology. Transient variability was evaluated by tracking the frontal passages along the eastern coast. The frontal timing was no longer captured by the model but some indication of the frequency and of the northward movement was given by the model forecast. Weekly precipitation totals were evaluated for the São Francisco Basin. Some parameters, such as the mean and the standard deviation of the 7-day total precipitation, were comparable to observations. The correlations between the forecast and the observed 7-day series were positive, but low

Dynamic force spectroscopy of DNA hairpins. II. Irreversibility and dissipation

We investigate irreversibility and dissipation in single molecules that cooperatively fold/unfold in a two state manner under the action of mechanical force. We apply path thermodynamics to derive analytical expressions for the average dissipated work and the average hopping number in two state systems. It is shown how these quantities only depend on two parameters that characterize the folding/unfolding kinetics of the molecule: the fragility and the coexistence hopping rate. The latter has to be rescaled to take into account the appropriate experimental setup. Finally we carry out pulling experiments with optical tweezers in a specifically designed DNA hairpin that shows two-state cooperative folding. We then use these experimental results to validate our theoretical predictions.Comment: 28 pages, 12 figure

Dynamical aspects of inextensible chains

In the present work the dynamics of a continuous inextensible chain is studied. The chain is regarded as a system of small particles subjected to constraints on their reciprocal distances. It is proposed a treatment of systems of this kind based on a set Langevin equations in which the noise is characterized by a non-gaussian probability distribution. The method is explained in the case of a freely hinged chain. In particular, the generating functional of the correlation functions of the relevant degrees of freedom which describe the conformations of this chain is derived. It is shown that in the continuous limit this generating functional coincides with a model of an inextensible chain previously discussed by one of the authors of this work. Next, the approach developed here is applied to a inextensible chain, called the freely jointed bar chain, in which the basic units are small extended objects. The generating functional of the freely jointed bar chain is constructed. It is shown that it differs profoundly from that of the freely hinged chain. Despite the differences, it is verified that in the continuous limit both generating functionals coincide as it is expected.Comment: 15 pages, LaTeX 2e + various packages, 3 figures. The title has been changed and three references have been added. A large part of the manuscript has been rewritten to improve readability. Chapter 4 has been added. It contains the construction of the generating functional without the shish-kebab approximation and a new derivation of the continuous limit of the freely jointed bar chai

Elasticity model of a supercoiled DNA molecule

Within a simple elastic theory, we study the elongation versus force characteristics of a supercoiled DNA molecule at thermal equilibrium in the regime of small supercoiling. The partition function is mapped to the path integral representation for a quantum charged particle in the field of a magnetic monopole with unquantized charge. We show that the theory is singular in the continuum limit and must be regularised at an intermediate length scale. We find good agreement with existing experimental data, and point out how to measure the twist rigidity accurately.Comment: Latex, 4 pages. The figure contains new experimental data, giving a new determination of the twist rigidit

A charged particle in a magnetic field - Jarzynski Equality

We describe some solvable models which illustrate the Jarzynski theorem and related fluctuation theorems. We consider a charged particle in the presence of magnetic field in a two dimensional harmonic well. In the first case the centre of the harmonic potential is translated with a uniform velocity, while in the other case the particle is subjected to an ac force. We show that Jarzynski identity complements Bohr-van Leeuwen theorem on the absence of diamagnetism in equilibrium classical system.Comment: 5 pages, minor corrections made and journal reference adde