Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Stability and sensitivity analysis of Be-CoDiS, an epidemiological model to predict the spread of human diseases between countries. Validation with data from the 2014-16 West African Ebola Virus Disease epidemic.

Ebola virus disease is a lethal human and primate disease that requires a particular attention from the international health authorities due to important recent outbreaks in some Western African countries and isolated cases in European and North-America continents. Regarding the emergency of this situation, various decision tools, such as mathematical models, were developed to assist the authorities to focus their efforts in important factors to eradicate Ebola. In a previous work, we have proposed an original deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries by taking into consideration the movement of people between geographical areas. This model was validated by considering numerical experiments regarding the 2014-16 West African Ebola Virus Disease epidemic. In this article, we propose to perform a stability analysis of Be-CoDiS. Our first objective is to study the equilibrium states of simplified versions of this model, limited to the cases of one an two countries, and to determine their basic reproduction ratios. Then, in order to give some recommendations for the allocation of resources used to control the disease, we perform a sensitivity analysis of those basic reproduction ratios regarding the model parameters. Finally, we validate the obtained results by considering numerical experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.

Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out on the citizen supercomputer Ibercivis. Upon dilution, the pure model’s first-order transition becomes of the second order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their random field Ising model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.

Bathymetric Terrain Model of the Puerto Rico Trench and the Northeastern Caribbean Region for Marine Geological Investigations

Multibeam bathymetric data collected in the Puerto Rico Trench and northeastern Caribbean region are compiled into a seamless bathymetric terrain model for broad-scale geological investigations of the trench system. These data, collected during eight separate surveys between 2002 and 2013 and covering almost 180,000 square kilometers, are published here in large-format map sheet and digital spatial data. This report describes the common multibeam data collection and processing methods used to produce the bathymetric terrain model and corresponding data-source polygon. Details documenting the complete provenance of the data are provided in the metadata in the Data Catalog section.

Linear chaos for the Quick-Thinking-Driver model.

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

On the well-posedness of a mathematical model for lithium-ion batteries.

We discuss the well-posedness of a mathematical model that is used in the literature for the simulation of lithium-ion batteries. First, a mathematical model based on a macrohomogeneous approach is presented, following previous work. Then it is shown, from a physical and a mathematical point of view, that a boundary condition widely used in the literature is not correct. Although the errors could be just sign typos (which can be explained as carelessness in the use of d/dx versus d/dn, with n the outward unit vector) and authors using this model probably use the correct boundary condition when they solve it in order to do simulations, readers should be aware of the right choice. Therefore, the deduction of the correct boundary condition is done here, and a mathematical study of the well-posedness of the corresponding problem is presented.

Spin glass phase in the four-state three-dimensional Potts model

We perform numerical simulations, including parallel tempering, a four-state Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the critical temperature and the value of the critical exponents. Nevertheless, the extrapolation to infinite volume is hampered by strong scaling corrections. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the “random permutation” Potts glass.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

Effective nonlinear model of resonant tunneling nanostructures

We introduce a model of a nonlinear double-barrier structure to describe in a simple way the effects of electron-electron scattering while remaining analytically tractable. The model is based on a generalized effective-mass equation where a nonlinear local field interaction is introduced to account for those inelastic scattering phenomena. Resonance peaks seen in the transmission coefficient spectra for the linear case appear shifted to higher energies depending on the magnitude of the nonlinear coupling. Our results are in good agreement with self-consistent solutions of the Schrodinger and Poisson equations. The calculation procedure is seen to be very fast, which makes our technique a good candidate for a rapid approximate analysis of these structures.

Variability of the ocean heat content during the last millennium - an assessment with the ECHO-g Model

Studies addressing climate variability during the last millennium generally focus on variables with a direct influence on climate variability, like the fast thermal response to varying radiative forcing, or the large-scale changes in atmospheric dynamics (e. g. North Atlantic Oscillation). The ocean responds to these variations by slowly integrating in depth the upper heat flux changes, thus producing a delayed influence on ocean heat content (OHC) that can later impact low frequency SST (sea surface temperature) variability through reemergence processes. In this study, both the externally and internally driven variations of the OHC during the last millennium are investigated using a set of fully coupled simulations with the ECHO-G (coupled climate model ECHAMA4 and ocean model HOPE-G) atmosphere-ocean general circulation model (AOGCM). When compared to observations for the last 55 yr, the model tends to overestimate the global trends and underestimate the decadal OHC variability. Extending the analysis back to the last one thousand years, the main impact of the radiative forcing is an OHC increase at high latitudes, explained to some extent by a reduction in cloud cover and the subsequent increase of short-wave radiation at the surface. This OHC response is dominated by the effect of volcanism in the preindustrial era, and by the fast increase of GHGs during the last 150 yr. Likewise, salient impacts from internal climate variability are observed at regional scales. For instance, upper temperature in the equatorial Pacific is controlled by ENSO (El Nino Southern Oscillation) variability from interannual to multidecadal timescales. Also, both the Pacific Decadal Oscillation (PDO) and the Atlantic Multidecadal Oscillation (AMO) modulate intermittently the interdecadal OHC variability in the North Pacific and Mid Atlantic, respectively. The NAO, through its influence on North Atlantic surface heat fluxes and convection, also plays an important role on the OHC at multiple timescales, leading first to a cooling in the Labrador and Irminger seas, and later on to a North Atlantic warming, associated with a delayed impact on the AMO.

A model intercomparison of changes in the Atlantic thermohaline circulation in response to increasing atmospheric CO2 concentration

As part of the Coupled Model Intercomparison Project, integrations with a common design have been undertaken with eleven different climate models to compare the response of the Atlantic thermohaline circulation ( THC) to time-dependent climate change caused by increasing atmospheric CO2 concentration. Over 140 years, during which the CO2 concentration quadruples, the circulation strength declines gradually in all models, by between 10 and 50%. No model shows a rapid or complete collapse, despite the fairly rapid increase and high final concentration of CO2. The models having the strongest overturning in the control climate tend to show the largest THC reductions. In all models, the THC weakening is caused more by changes in surface heat flux than by changes in surface water flux. No model shows a cooling anywhere, because the greenhouse warming is dominant.

Climate simulation for 125 kyr BP with a coupled ocean-atmosphere general circulation model

The ECHAM-1 T21/LSG coupled ocean-atmosphere general circulation model (GCM) is used to simulate climatic conditions at the last interglacial maximum (Eemian. 125 kyr BP). The results reflect thc expected surface temperature changes (with respect to the control run) due to the amplification (reduction) of the seasonal cycle of insolation in the Northern (Southern) Hemisphere. A number of simulated features agree with previous results from atmospheric GCM simulations e.g. intensified summer southwest monsoons) except in the Northern Hemisphere poleward of 30 degrees N. where dynamical feedback, in the North Atlantic and North Pacific increase zonal temperatures about 1 degrees C above what would be predicted from simple energy balance considerations. As this is the same area where most of the terrestrial geological data originate, this result suggests that previous estimates of Eemian global average temperature might have been biased by sample distribution. This conclusion is supported by the fact that the estimated global temperature increase of only 0.3 degrees C greater than the control run ha, been previously shown to be consistent a with CLIMAP sea surface temperature estimates. Although the Northern Hemisphere summer monsoon is intensified. globally averaged precipitation over land is within about 1% of the present, contravening some geological inferences bur not the deep-sea delta(13)C estimates of terrestrial carbon storage changes. Winter circulation changes in the northern Arabian Sea. driven by strong cooling on land, are as large as summer circulation changes that are the usual focus of interest, suggesting that interpreting variations in the Arabian Sea. sedimentary record solely in terms of the summer monsoon response could sometimes lead to errors. A small monsoonal response over northern South America suggests that interglacial paleotrends in this region were not just due to El Nino variations.

Critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions

We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulations and a finite-size scaling analysis. By using a field programmable gate array, we have been able to thermalize a large number of samples of systems with large volume. This has allowed us to observe a spin-glass ordered phase in d=4 and to study the critical properties of the transition. In d=3, our results are consistent with the presence of a Kosterlitz-Thouless transition, but also with different scenarios: transient effects due to a value of the lower critical dimension slightly below 3 could be very important.

Temperatures at the last interglacial simulated by a coupled ocean-atmosphere climate model

The last interglacial (Eemian, 125,000 years ago) has generally been considered the warmest time period in the last 200,000 years and thus sometimes been used as a reference for greenhouse projections. Herein we report results from a coupled ocean-atmosphere climate model of the surface temperature response to changes in the radiative forcing at the last interglacial. Although the model generates the expected summer warming in the northern hemisphere, winter cooling of a comparable magnitude occurs over North Africa and tropical Asia. The global annual mean temperature for the Eemian run is 0.3 degrees C cooler than the control run. Validation of simulated sea surface temperatures (SSTs) against reconstructed SSTs supports this conclusion and also the assumption that the flux correction, fitted for the present state, operates satisfactorily for modest perturbations. Our results imply that contrary to conventional expectations, Eemian global temperatures may already have been reached by the mid 20th century.