rss_2.0Communications in Applied and Industrial Mathematics FeedSciendo RSS Feed for Communications in Applied and Industrial Mathematicshttps://sciendo.com/journal/CAIMhttps://www.sciendo.comCommunications in Applied and Industrial Mathematics Feedhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/6471177d2b88470fbea150a2/cover-image.jpghttps://sciendo.com/journal/CAIM140216A general review on the NLS equation with point-concentrated nonlinearityhttps://sciendo.com/article/10.2478/caim-2023-0004<abstract> <title style='display:none'>Abstract</title> <p>The paper presents a complete (to the best of the author’s knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the model, weak and strong local well-posedness, global well-posedness, classification and stability (orbital and asymptotic) of the standing waves, blow-up analysis and derivation from the standard NLS equation with shrinking potentials. Also some related problem is mentioned.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2023-00042023-10-13T00:00:00.000+00:00Modelling and predicting coastal zone depth profile evolution: a surveyhttps://sciendo.com/article/10.2478/caim-2023-0003<abstract> <title style='display:none'>Abstract</title> <p>We survey results concerning the problem of identifying depth profiles at coastal zone, which evolve in time due to natural as well as anthropic activities. This issue is relevant to control the modifications of the environment occurring near sea coastlines, but also in river's estuaries and harbors. One of the main goals is to predict the time evolution of the depth profile in the long-term (i.e., over years or decades, say), and to do this on the basis of <italic>real</italic> observed and measured <italic>data</italic>, available in several databases. Most mathematical models are formulated in terms of partial differential equations of the diffusive type, in one or two space dimensions. Consequently, from the mathematical standpoint, the aforementioned identification problem takes on the form of an inverse problem for some given parabolic equation associated with suitable initial and boundary conditions.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2023-00032023-09-16T00:00:00.000+00:00Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Lawhttps://sciendo.com/article/10.2478/caim-2023-0002<abstract> <title style='display:none'>Abstract</title> <p>This paper concerns the existence of global weak solutions <italic>á la Leray</italic> for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2023-00022023-06-21T00:00:00.000+00:00On an optimal control strategy in a kinetic social dynamics modelhttps://sciendo.com/article/10.2478/caim-2018-0014<abstract><title style='display:none'>Abstract</title><p> Kinetic models have so far been used to model wealth distribution in a society. In particular, within the framework of the kinetic theory for active particles, some important models have been developed and proposed. They involve nonlinear interactions among individuals that are modeled according to game theoretical tools by introducing parameters governing the temporal dynamics of the system. In this present paper we propose an approach based on optimal control tools that aims to optimize this evolving dynamics from a social point of view. Namely, we look for time dependent control variables concerning the distribution of wealth that can be managed, for instance, by the government, in order to obtain a given social profile.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00142018-12-19T00:00:00.000+00:00Selective model-predictive control for flocking systemshttps://sciendo.com/article/10.2478/caim-2018-0009<abstract><title style='display:none'>Abstract</title><p> In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of a controller, acting in order to enhance consensus. Two types of selective controls have been presented: an homogeneous control filtered by a selective function and a distributed control active only on a selective set. As a first step toward a reduction of computational cost, we introduce a model predictive control (MPC) approximation by deriving a numerical scheme with a feedback selective constrained dynamics. Next, in order to cope with the numerical solution of a large number of interacting agents, we derive the mean-field limit of the feedback selective constrained dynamics, which eventually will be solved numerically by means of a stochastic algorithm, able to simulate effciently the selective constrained dynamics. Finally, several numerical simulations are reported to show the effciency of the proposed techniques.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00092018-12-19T00:00:00.000+00:00A Continuous–Time Markov Chain Modeling Cancer–Immune System Interactionshttps://sciendo.com/article/10.2478/caim-2018-0018<abstract><title style='display:none'>Abstract</title><p>In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00182018-12-19T00:00:00.000+00:00Preface to the Special Issue Mathematical modelling for complex systems: multi-agents methodshttps://sciendo.com/article/10.2478/caim-2018-0019ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00192018-12-19T00:00:00.000+00:00High-Order Variational Time Integrators for Particle Dynamicshttps://sciendo.com/article/10.2478/caim-2018-0015<abstract><title style='display:none'>Abstract</title><p>The general family of Galerkin variational integrators are analyzed and a complete classification of such methods is proposed. This classification is based upon the type of basis function chosen to approximate the trajectories of material points and the numerical quadrature formula used in time. This approach leads to the definition of arbitrarily high order method in time. The proposed methodology is applied to the simulation of brownout phenomena occurring in helicopter take-off and landing.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00152018-12-19T00:00:00.000+00:00The Political Replacement Effect in a Kinetic Model of Social Dynamics with Phase Transitionhttps://sciendo.com/article/10.2478/caim-2018-0013<abstract><title style='display:none'>Abstract</title><p>The political replacement effect is an interesting socio-political hypothesis introduced by Acemoglu and Robinson and statistically tested. It may determine, under some conditions, the phenomenon of innovation blocking, possibly leading to economic backwardness in a society. In a previous paper, we have introduced a kinetic model with stochastic evolutive game-type interactions, analyzing the relationship between the level of political competition in a society and the degree of economic liberalization. In the present paper we model we model the possibility of having a sort of phase transition occurring in the system when the phenomenon of blocking of the introduction of technological innovation, intended in a broad sense, appears. Crossing a critical point, the rules of interactions change by means of slightly different transition probabilities nevertheless determining very significant differences in the resulting long-term solutions.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00132018-12-19T00:00:00.000+00:00Student interactions during class activities: a mathematical modelhttps://sciendo.com/article/10.2478/caim-2018-0011<abstract><title style='display:none'>Abstract</title><p> This paper aims at bridging Mathematical Modelling and Mathematics Education by studying the opinion dynamics of students who work in small groups during mathematics classrooms. In particular, we propose a model which hinges upon the pioneering work of Hegselmann and Krause on opinion dynamics and integrates recent results of interactionist research in Mathematical Education. More precisely, the proposed model incorporates the following features: 1) the feelings of each student towards the classmates (building upon the so-called \I can" -\you can" framework); 2) the different levels of preparation of the students; 3) the presence of the teacher, who may or may not intervene to drive the students towards the correct solution of the problem. Several numerical experiments are presented to assess the capability of the model in reproducing typical realistic scenarios.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00112018-12-19T00:00:00.000+00:00An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomenahttps://sciendo.com/article/10.2478/caim-2018-0010<abstract><title style='display:none'>Abstract</title><p>In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00102018-12-19T00:00:00.000+00:00A contribution to the mathematical modeling of immune-cancer competitionhttps://sciendo.com/article/10.2478/caim-2018-0012<abstract><title style='display:none'>Abstract</title><p>This paper deals with the modeling of interactions between the immune system and cancer cells, in the framework of the mathematical kinetic theory for active particles. The work deepens a previous paper of Belloquid et al. that assumes spatial homogeneity and discrete values of the activity of cancer and immune cells. A number of simulations are made with the aim to investigate how the state of the various cell populations evolves in time depending on the choice of the free parameters.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00122018-12-19T00:00:00.000+00:00Heat rectification in He II counterflow in radial geometrieshttps://sciendo.com/article/10.2478/caim-2018-0017<abstract><title style='display:none'>Abstract</title><p> We consider heat rectification in radial flows of turbulent helium II, where heat flux is not described by Fourier's law, but by a more general law. This is different from previous analyses of heat rectification, based on such law. In our simplified analysis we show that the coupling between heat flux and the gradient of vortex line density plays a decisive role in such rectification. Such rectification will be low at low and high values of the heat rate, but it may exhibit a very high value at an intermediate value of the heat rate. In particular, for a given range of values for the incoming heat ow, the outgoing heat flow corresponding to the exchange of internal and external temperatures would be very small. This would imply difficulties in heat removal in a given range of temperature gradients.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00172018-12-05T00:00:00.000+00:00A fractional spline collocation-Galerkin method for the time-fractional diffusion equationhttps://sciendo.com/article/10.1515/caim-2018-0007<abstract><title style='display:none'>Abstract</title><p> The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented. </p></abstract>ARTICLEtruehttps://sciendo.com/article/10.1515/caim-2018-00072018-03-24T00:00:00.000+00:00On preconditioner updates for sequences of saddle-point linear systemshttps://sciendo.com/article/10.1515/caim-2018-0003<abstract><title style='display:none'>Abstract</title><p> Updating preconditioners for the solution of sequences of large and sparse saddle- point linear systems via Krylov methods has received increasing attention in the last few years, because it allows to reduce the cost of preconditioning while keeping the efficiency of the overall solution process. This paper provides a short survey of the two approaches proposed in the literature for this problem: updating the factors of a preconditioner available in a block LDL<sup>T</sup> form, and updating a preconditioner via a limited-memory technique inspired by quasi-Newton methods.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.1515/caim-2018-00032018-02-28T00:00:00.000+00:00Some results on discrete eigenvalues for the Stochastic Nonlinear Schrödinger Equation in fiber opticshttps://sciendo.com/article/10.1515/caim-2015-0006<abstract><title style='display:none'>Abstract</title><p> We study a stochastic Nonlinear Schrödinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber. Since the stochastic NLSE is not exactly integrable by means of the NFT, then we use a perturbation approach, where we assume that the signal-to-noise ratio is high. The zeroth-order perturbation leads to the deterministic NLSE while the first-order perturbation allows to describe the statistics of the discrete eigenvalues. This is important to understand the properties of the channel for recently devised optical transmission techniques, where the information is encoded in the nonlinear Fourier spectrum. </p></abstract>ARTICLEtruehttps://sciendo.com/article/10.1515/caim-2015-00062018-03-24T00:00:00.000+00:00On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networkshttps://sciendo.com/article/10.2478/caim-2018-0016<abstract><title style='display:none'>Abstract</title><p> We identify sufficient conditions for the stability of some well-known finite difference schemes for the solution of the multivariable reaction-diffusion equations that model chemical reaction networks. Since the equations are mainly nonlinear, these conditions are obtained through local linearization. A recurrent condition is that the Jacobian matrix of the reaction part evaluated at some positive unknown solution is either D-semi-stable or semi-stable. We demonstrate that for a single reversible chemical reaction whose kinetics are monotone, the Jacobian matrix is D-semi-stable and therefore such schemes are guaranteed to work well.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00162018-12-05T00:00:00.000+00:00The chord length distribution function of a non-convex hexagonhttps://sciendo.com/article/10.1515/caim-2018-0002<abstract><title style='display:none'>Abstract</title><p> In this paper we obtain the chord length distribution function of a non-convex equilateral hexagon and then derive the associated density function. Finally, we calculate the expected value of the chord length. </p></abstract>ARTICLEtruehttps://sciendo.com/article/10.1515/caim-2018-00022018-02-28T00:00:00.000+00:00Loss of mass and performance in skeletal muscle tissue: a continuum modelhttps://sciendo.com/article/10.1515/caim-2018-0001<abstract><title style='display:none'>Abstract</title><p> We present a continuum hyperelastic model which describes the mechanical response of a skeletal muscle tissue when its strength and mass are reduced by aging. Such a reduction is typical of a geriatric syndrome called sarcopenia. The passive behavior of the material is described by a hyperelastic, polyconvex, transversely isotropic strain energy function, and the activation of the muscle is modeled by the so called active strain approach. The loss of ability of activating of an elder muscle is then obtained by lowering of some percentage the active part of the stress, while the loss of mass is modeled through a multiplicative decomposition of the deformation gradient. The obtained stress-strain relations are graphically represented and discussed in order to study some of the effects of sarcopenia. </p></abstract>ARTICLEtruehttps://sciendo.com/article/10.1515/caim-2018-00012018-02-28T00:00:00.000+00:00A particle model reproducing the effect of a conflicting flight information on the honeybee swarm guidancehttps://sciendo.com/article/10.2478/caim-2018-0021<abstract><title style='display:none'>Abstract</title><p> The honeybee swarming process is steered by few scout individuals, which are the unique informed on the location of the target destination. Theoretical and experimental results suggest that bee coordinated flight arises from visual signals. However, how the information is passed within the population is still debated. Moreover, it has been observed that honeybees are highly sensitive to conflicting directional information. In fact, swarms exposed to fast-moving bees headed in the wrong direction show clear signs of disrupted guidance. In this respect, we here present a discrete mathematical model to investigate different hypotheses on the behaviour both of informed and uninformed bees. In this perspective, numerical realizations, specifically designed to mimic selected experiments, reveal that only one combination of the considered assumptions is able to reproduce the empirical outcomes, resulting thereby the most reliable mechanism underlying the swarm dynamics according to the proposed approach. Specifically, this study suggests that (i) leaders indicate the right flight direction by repeatedly streaking at high speed pointing towards the target and then slowly coming back to the trailing edge of the bee cloud; and (ii) uninformed bees, in turn, gather the route information by adapting their movement to all the bees sufficiently close to their position.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00212018-12-14T00:00:00.000+00:00en-us-1