Narrow Results

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKähler manifolds. We also mention some of their applications to time-dependent mechanics.

We consider wave packet propagation in mesoscopic quantum systems. A number of approaches are compared to look at the general solution of a time-dependent Schrödinger equation and the validity of the Ehrenfest theorem. Detailed calculations are presented to illustrate the results of a charged particle motion in the time-dependent systems, and show that the Ehrenfest theorem is not directly applicable in topologically nontrivial systems.

The performance degradation of a hybrid solar cell is modelled considering the variation of depletion width over time. The p-i-n structure of a TiO₂/perovskite/HTL photovoltaic is investigated. Several different time-dependent approaches are compared and a new model is introduced based on the variation of defect density over time in depletion region. This phenomenon consequently manifests itself in the device degradation. Our approach leads to rather complicated time-dependent equation for the defect density which takes into account also the non-uniformity of electric field in the depletion region. The thickness of TiO₂ nano layer is taken 50 nm and perovskite layer is 330 nm. The nanoscale thickness of TiO₂ layer warrants the carrier transport through tunneling mechanism.

In this paper, we study the decaying dynamics in the mirror-field interaction by means of the intrinsic decoherence scheme. Factorization of the mirror-field Hamiltonian with the use of displacement operators allows us to calculate the explicit solution to Milburn’s equation for arbitrary initial conditions. We show expectation values, correlations, and Husimi functions for the solutions obtained.

A framework is developed that enables the modeling of the various mechanisms of epidemic processes. A model within the framework is completely characterized by a set of transmission functions. These functions support the modeling of the infectivity of a new infective as a function of its age-of-infection. They also support the presence of a, possible time-dependent, outside source of infection and allow for the introduction of an inhibitor function that accounts for the decreasing number of available susceptibles in the course of the epidemic. In addition this inhibitor function could describe the effects of an inoculation program, or a governmental information campaign, or improvements in general health care on the course of the epidemic. The proposed models deliver a complete stochastic description of the infectious-age structure of the population at any moment of time. In particular the size of the epidemic, that is the probability distribution of the number of new infectives, is worked out. By letting time tend to infinity an analytical expression for the final size of the epidemic is found. This leads to new recursive procedures for the determination of this final size. Ludwig's recursive scheme for this purpose is considerably extended. Finally, using a specific type of model from within the framework as a building block, a compound model is introduced that describes an epidemic with a structured population of infectives. Although such a compound model goes beyond the boundaries of the framework, still important characteristics present in the framework are preserved in such a model. The size of the epidemic at a certain moment of time, according to a compound model, as well as its final size are easily found. Moreover, for the infinite case simple expressions for the final size distribution and its first moment are found. This leads to a precise quantitative threshold theorem, that discriminates between a minor outbreak or a major build-up for such an epidemic.

A model is developed that describes evolution with respect to time of an infectious disease introduced into a population of susceptibles. The proposed model incorporates at one end Bailey's simple stochastic epidemic and at the other end the Reed-Frost chain-binomial models and is the natural stochastic analogue of Kermack and McKendrick's deterministic model. The epidemic process is characterized by the size of the population and by two infectivity functions. The first one relates to a time dependent outside source of infection. The second one describes the infectivity of an individual as a function of his age-of-infection, that is the time elapsed since his own infection. The proposed model consists of a set of partial differential equations which governs, steered by the given infectivity functions, the evolution with respect to time of a set of density functions. These density functions deliver a complete stochastic description of the infectious-age structure of the population at any moment of time. An expression for the size of the epidemic, that is the probability distribution of the number of infectives, as a function of time follows. Also expressions for the expected arrival times of infectives, useful for the inverse problem, are developed. By letting time tend to infinity earlier results for the final size of the epidemic are confirmed.

Background: Remodeling process affects the mineral content of osteons and imparts heterogeneity through secondary mineralization; the aim of the present study is to assess the elastic and plastic time-dependent mechanical properties of osteons reflecting different mineral content as well as interstitial tissue of human femoral cortical bone by nanoindentation. Methods: Four trapezoiform blocks approximately 3mm thick were cut from the distal end of different human femoral diaphysis. Osteons with different apparent mineral degrees were classified by means of gray levels imaging using Environmental Scanning Electron Microscopy (ESEM). Nanoindentation tests were performed in the longitudinal direction of the bone axis using a four-stage protocol (load-hold-unload-hold) and the experimental curves were fitted by a mechanical model allowing the determination of the time-dependent mechanical properties. Results: Apparent low mineral content impact negatively the mechanical response of bone material at the micro-scale. Mechanical response varies among osteons exhibiting different mineral degrees. The values of the apparent elastic modulus double when the strain rate is analyzed at the extreme values ($\dot{\epsilon }=\mathrm{\text{zero}}$ and infinity) whatever the bone component. Conclusions: These results evidence the mechanical heterogeneity of bone microstructure due to remodeling process. The quantification of the time-dependent mechanical properties could be useful to improve numerical models of bone behavior and provide new insights to build up original biomimetic materials.

We report in this paper quantum dynamics calculation of state-selected reaction probabilities for a benchmark chemical reaction H₂ + CH₃ → H + CH₄ on an ab initio potential energy surface. The quantum dynamics calculation is based on the recently developed semirigid vibrating rotor target (SVRT) model and involves six degrees of freedom. The present result is the first such high-level quantum dynamics calculation of microscopic reaction probability for a chemical reaction between two molecules with at least one of the reagents being larger than a diatomic molecule.

It is important to investigate the time-dependent deformation of MEMS devices such as thermally driven micro beams because it affect theirs reliability. In this paper, time-dependent buckling of clamped-clamped polysilicon micro beams under high stress and temperature has been modeled by Finite Element Analysis (FEA). A thermo-mechanical, non-linear model has been developed in this analysis. The temperature dependency of polysilicon properties have also been formulated and modeled in this analysis. Depending on input current, two different polysilicon mechanical behaviors, pure elastic buckling and elasto-plastic deformation have been studied. The goal is to consider the changes of elasto-plastic behavior and thermal properties of polysilicon with temperature in this model. The clamped-clamped micro beam of 2μm wide, 2μm thick and 100μ m long is modeled. For buckling phenomenon to occur, this clamped-clamped beam is self-heated by an electrical current input. These micro beams are made of heavily doped polysilicon and are fabricated by surface micro machining technology. The simulation results show the importance of temperature-dependent properties of polysilicon on deflections of micro beams under compressive stress. A comparison is made between the time dependant results obtained from FEA and the experimental results in the literature.

Modeling the flow of non-Newtonian fluids in porous media is a challenging subject. Several approaches have been proposed to tackle this problem. These include continuum models, numerical methods, and pore-scale network modeling. The latter proved to be more successful and realistic than the rest. The reason is that it captures the essential features of the flow and porous media using modest computational resources and viable modeling strategies. In this article we present pore-scale network modeling techniques for simulating non-Newtonian flow in porous media. These techniques are partially validated by theoretical analysis and comparison to experimental data.

We consider the coupling of two-dimensional (2D) and one-dimensional (1D) models to form a single hybrid 2D–1D model for time-dependent linear wave problems. The 1D model is used to represent a 2D computational domain where the solution behaves approximately in a 1D way. This hybrid model, if designed properly, is a more efficient way to solve the full 2D model over the entire problem. Two important issues related to such hybrid 2D–1D models are (a) the design of the hybrid model and its validation (with respect to the original problem) and (b) the way the 2D–1D coupling is done, and the coupling error generated. This paper focuses on the second issue. The method used in this paper to couple the 1D and 2D models is the one proposed by Panasenko. This method has been used for mixed-dimensional coupling in many steady-state problems, and here it is being used for the first time for time-dependent problems. The hybrid formulation is derived, and the numerical accuracy and efficiency of the method are explored for a couple of basic problems.

In healthy individuals, dehydration of the body leads to release of the hormone vasopressin from the pituitary. Via the bloodstream, vasopressin reaches the collecting duct cells in the kidney, where the water channel Aquaporin-2 (AQP2) is expressed. After stimulation of the vasopressin V2 receptor by vasopressin, intracellular AQP2-containing vesicles fuse with the apical plasma membrane of the collecting duct cells. This leads to increased water reabsorption from the pro-urine into the blood and therefore to enhanced retention of water within the body.

Using existing biological data we propose a mathematical model of AQP-2 trafficking and regulation in collecting duct cells. Our model includes the vasopressin receptor, adenylate cyclase, protein kinase A, and intracellular as well as membrane located AQP2. To model the chemical reactions we used ordinary differential equations (ODEs) based on mass action kinetics. We employ known protein concentrations and time series data to estimate the kinetic parameters of our model and demonstrate its validity.

Through generating, testing and ranking different versions of the model, we show that some model versions can describe the data well as soon as important regulatory parts such as the reduction of the signal by internalization of the vasopressin-receptor or the negative feedback loop representing phosphodiesterase activity are included.

We perform time-dependent sensitivity analysis to identify the reactions that have the greatest influence on the cAMP and membrane located AQP2 levels over time. We predict the time courses for membrane located AQP2 at different vasopressin concentrations, compare them with newly generated data and discuss the competencies of the model.