Computational modeling of cardiac tissue with strongly coupled electromechanics and orthotropic viscoelastic effects

Modeling of complex mechanisms leading to the functioning of the heart has been an active field of research since decades. Difficulties associated with in vivo experiments motivate the utilization of computational models in order to gain a better appreciation of heart electromechanics. Although rate dependent behaviour of the orthotropic passive heart tissue has been comprehensively studied in the literature [1], effects of this phenomenon on fully coupled cardiac electromechanics are unrevealed yet. Therefore, this contribution is concerned with the investigation of viscous effects on the electromechanical response of the myocardium. To this end, we adopt the fully implicit finite element framework which strongly couples the mechanical and electrophysiological problem of the myocardium in a mono- and bi-domain setting [2,3], respectively. Viscous effects, however, are consistently embedded into this framework by making use of the orthotropic viscoelastic material model for the passive myocardium, which considers different relaxation mechanisms for the different orientation directions [5]. The performance of the proposed model is assessed by comparing finite element simulations of spiral waves in heart tissue for elastic and viscoelastic formulations. We further investigate the influence of viscosity on the defibrillation phenomenon by means of the finite element formulation of bidomain electrophysiology. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational modeling of the propagation of acoustic pulses in hemodynamics

The present paper deals with the numerical simulation of the propagation of pulses of blood pressure and velocity in a blood vessel. The numerical solution of the system of linear hemodynamic equations is formed as a superposition of progressing waves (Riemann invariants) satisfying the transport equations. Considerable attention is paid to the construction of a difference scheme for the linear and quasilinear transport equations. Examples of computations are presented. The suggested algorithm can be generalized to the case of a quasilinear system of equations.     

Computational modeling for reasoning about the social behavior of humans

The number of computationally-based models of human social behavior is growing rapidly. In fact, the current ease of programming is resulting in a plethora of tools with impressive interfaces but little theoretical power under the hood. Further, the overabundance of new toolkits for building models is facilitating the excessively rapid growth of simple proof-of-concept, or intellective, models. The current state of models range from the simplistic to the elaborate, from the conceptual to the empirical, and from the purely notional to the validatable. This review briefly describes the state of human social behavioral modeling. Key issues surrounding analysis and validation are discussed.

Computational modeling of elastic and plastic multiple cracks by the fundamental solutions

The fundamental solutions of elasticity are used to establish a numerical method for elastic and plastic multiple crack problems in two dimensions. The continuous distributions of the point forces, dislocations, and the plastic sources are used systematically to model the crack, non-crack boundary, and the plastic deformation. Use of these singularities are guided strictly by the physical interpretation of the problem. We adopt Muskhelishvili's complex variable formalism that facilitate the analytical evaluation of the integrals representing the continuous distributions of the singularities. The resulting numerical method is concise and accurate enough to be used for elastic and plastic multiple crack problems.     

Smoothed particle hydrodynamics modeling of the thermal behavior of double skin facades in fires considering the effects of venetian blinds

At present, the fire safety of double skin facades (DSFs) is an important research area due to recent spikes in fires in high rise buildings involving glass DSF systems, and also due to our limited understanding of the thermal behavior of these systems. To overcome this lack of knowledge, a numerical framework is proposed for simulating the thermal performance of DSFs under fire conditions. The framework is based on the smoothed particle hydrodynamics technique and it can be used to compute numerical solutions and simulate the thermal degradation of DSFs under fire conditions. The numerical model was validated by comparing the predicted response parameters in a fire exposed DSF system with those measured in fire experiments. The validated numerical model was then employed to derive empirical equations linking temperature with both the time and location along the interior and exterior glass panes of DSFs. Finally, numerical simulations were conducted for the same DSF configuration but equipped with venetian blinds in order to examine the influence of the blinds on the fire performance of glass DSFs. An in-house MATLAB code was developed and implemented to conduct these numerical simulations. The results obtained from these numerical simulations clearly indicated that the “blind tilt angle” can significantly affect the fire spread characteristics and temperature distribution in DSFs, and thus it should be considered in the design of DSF systems for high rise buildings.     

Computational treatment of free convection effects on perfectly conducting viscoelastic fluid

We introduced a magnetohydrodynamic model of boundary-layer equations for a perfectly conducting viscoelastic fluid. This model is applied to study the effects of free convection currents with one relaxation time on the flow of a perfectly conducting viscoelastic fluid through a porous medium, which is bounded by a vertical plane surface. The state space approach is adopted for the solution of one-dimensional problems. The resulting formulation together with the Laplace transform technique is applied to a thermal shock problem and a problem for the flow between two parallel fixed plates, both without heat sources. Also a problem for the semi-infinite space in the presence of heat sources is considered. A discussion of the effects of cooling and heating on a perfectly conducting viscoelastic fluid is given. Numerical results are illustrated graphically for each problem considered.     

Analysis of a non-hyperbolic system modelling two-phase fluid flows: the effects of surface tension

The paper considers a system of partial differential equations of convection dispersion type, modelling a stratified two-phase fluid flow. Local existence in time is proved for a sufficiently smooth initial data, given in the set of physically admissible states. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Bifurcation for a free boundary problem with surface tension modeling the growth of multi-layer tumors

This paper is devoted to the study of the bifurcation of a free boundary problem modeling the growth of tumors with the effect of surface tension being considered. The existence of infinitely many branches of bifurcation solutions is proved. The method of analysis is based on reducing the problem to an operator equation in certain Hölder space with a nonlinear Fredholm operator of index 0. The desired result then follows from the Crandall-Rabinowitz bifurcation theorem.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Endogenizing the sticks and carrots: modeling possible perverse effects of counterterrorism measures

We present a novel model capable of distinguishing between the effects of negative incentives (“sticks”) and positive incentives (“carrots”) for influencing the behavior of intelligent and adaptable adversaries. Utilities are developed for the defender and the terrorist. The defender is assumed to have a unit cost of defense, and unit costs of providing negative and positive incentives. The terrorist likewise has a unit cost of attack, which may either increase or decrease if the defender provides negative incentives, and enjoys a unit benefit of positive incentives. We show that the potential for perverse effects of counterterrorism (e.g., the emergence of hatred) can cause defenders to rely on positive incentives and decrease their reliance on negative incentives at equilibrium, with use of negative incentives completely eliminated in situations where these would be moderately effective when applied. With low potential for perverse effects of counterterrorism, the defender should rely on effective negative incentives.     

Influence of edge effects on the state of stress and strength of carbon composites in tension

Conclusions A difference has been found between the theoretical and experimental strength values. The theoretical strength of flat strips with straight edges, obtained on the basis of the two-dimensional solution within the elastic range for a composite with fiber angle < 30°, is higher than the actual strength. The difference is due to the failure to take account of interlaminar shear. The strength tensor is applied to a monolayer with respect to which the internal state of stress and the nature of the interrelationship between the layers are not taken into account. In this connection, it is desirable to supplement the given criterion with a condition which would take account of the difference between the stresses _xy in adjacent layers. If the directions of reinforcement > 30°, then the agreement between the theoretical strength of flat strips of variable width, obtained on the basis of the two-dimensional solution within the elastic range using the tensor strength criterion, is in good agreement with the actual strength obtained experimentally. The big differences between the actual and theoretical strengths for the three-dimensional solution are attributable to the physical and geometric nonlinearity in the boundary zone between the elementary layers of the composite.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 263–270, March–April, 1985.     

Semiparametric modeling of the spatiotemporal trends in natural gas consumption: Methodology,results, and consequences

Household consumption of natural gas is usually considered to be quite stable as cooking, space, and water heating belong to basic needs. The improvement of technologies together with possibilities of switching to alternative sources can, however, lead to a decreasing consumption trend. Knowing more about such trend, especially of its spatial distribution, can be useful for strategic planning. In this paper, we describe a general statistical methodology allowing to study the spatiotemporal behavior of consumption. It is based on semiparametric modeling. Formalized error and sensitivity analyses are part of the methodology. Presented methods are illustrated on large‐scale data from the Czech Republic.     

The effects of impulsive releasing methods of natural enemies on pest control and dynamical complexity

In the present paper the different releasing methods including constant releasing and proportional to the predator population are considered and analyzed. The effects of these releasing methods of natural enemies on dynamical behavior are investigated. We firstly take into account the model with an impulsive effect at fixed moments, and the results imply that under some conditions the pest may serve to extinction. Several types of attractors can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of natural enemies released are crucial. Secondly, the model with unfixed moments is further investigated. Different periodic solutions also exist and the maximum amplitude of the host is always less than the economic threshold. Comparing the results obtained for the two models concludes that the proportional releasing predator has strong effects on the dynamical behavior.     

The day-of-the-week effects on the volatility: The role of the asymmetry

In this paper, we propose to evaluate whether asymmetry influences the day-of-the-week effects on volatility. We also investigate empirically the impact of the day-of-the-week effect in major international stock markets using GARCH family models from a forecast framework. Indeed the existence of calendar effects might be interesting only if their incorporation in a model results in better volatility forecasts.     

Numerical modeling of baffle location effects on the flow pattern of primary sedimentation tanks

Computational fluid dynamics (CFD) is used extensively by engineers to model and analyze complex issues related to hydraulic design, planning studies for future generating stations, civil maintenance and supply efficiency. In order to find the optimal position of a baffle in a rectangular primary sedimentation tank, computational investigations are performed. Also laboratory experiments are conducted to verify the numerical results and the measured velocity fields which were by Acoustic Doppler Velocimeter (ADV) are used. The GMRES algorithm as a pressure solver was used in the computational modeling. The results of computational investigations performed in the present study indicate that the favorable flow field (uniform in the settling zone) would be enhanced for the case that the baffle position provide small circulation regions volume and dissipate the kinetic energy in the tank. Also results show that the GMRES algorithm can obtain the good agreement between the results of numerical models and experimental tests.     

Virtual modeling of residual stress in drawn wire due to the skin pass effect

The wire drawing technological process is wide use in industry. The effect of skin‐pass is apply for reduction of residual stress in final product. The finite element method is applied to simulate the effect of skin‐pass in wire drawing process. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preface to the special issue on “Mathematical modeling and analysis in health and natural sciences”

Ricerche di Matematica -