1,721,111 research outputs found
Shape and size in medicine, biotechnology, materials science and social sciences
No full textThis special issue gathers together papers presented during the workshop Shape and Size in Medicine, Biotechnology, Materials Science and Social Sciences, Milano, Italy, 16-17 February 201
A journey through multiscale, some episodes from approximation and modelling
No full textThe present notes contains both a survey of and some novelties about mathematical problems which emerged in multiscale based approach in approximation of evolutionary partial differential equations. Specifically, we present a relaxed systems approximation for nonlinear diffusion problems, which can tackle also the cases of degenerate and strongly degenerate diffusion equations. Relaxation schemes take advantage of the replacement of the original partial differential equation with a semi-linear hyperbolic system of equations, with a stiff source term, tuned by a relaxation parameter ε. When ε→0+, the system relaxes onto the original PDE: in this way, a consistent discretization of the relaxation system for vanishing ε yields a consistent discretization of the original PDE. The advantage of this procedure is that numerical schemes obtained in this fashion do not require to solve implicit nonlinear problems and possess the robustness of upwind discretizations. We also review a unified framework, including BGK-based diffusive relaxation methods and new relaxed numerical schemes. A stability analysis for the new methods is sketched and high order extensions are provided. Finally some numerical tests in one and two dimensions are shown with preliminary results for nonlocal problems and multiscale hyperbolic systems
New dimension in Biology: two examples of 3D phenomenological models
No full textAlthough computational and experimental models for cell migration and dynamics on two-dimensional (2D) substrata have described how various molecular and cellular properties and biochemical processes are integrated to accomplish cell functions, biologists are increasingly turning to threedimensional cell cultures, where they are discovering biological activities
that more closely mirror what happens in living organisms.
In fact, the in situ environment of a cell in living organism has a threedimensional
architecture. This “new dimension” may represent a challenge
in mathematical and computational modelling in order to better understand
physiological and biochemical processes. We report here two examples regarding
phenomenological description of early stages of vascular network
assembly and, respectively, of olfactory system in embryogenesis
A chemo-mechanical model for the single myofibril in striated muscle contraction
No full textBased on the framework of sliding-filament theory and on the cross-bridges dynamics, a mathematical model for the simulation of the force response and length change of individual myofibril is presented. The myofibril is modeled as a group of segments placed in series, each segment represents a half-sarcomere with active and elastic properties. A multiple-state cross-bridge formalism relates the half Sarcomere force to the chemical kinetics of ATP hydrolysis. The corresponding system of nonlinear nonlocal partial differential equations of the model is analyzed. A numerical approach is introduced and some numerical tests are performed. The proposed in-silico model enables the study of biologically relevant process in the muscle contraction process, also in the case of muscular diseases, with reasonable computational effort
Multiscale and adaptivity : modeling numerics and applications : C.I.M.E. Summer School, Cetraro, Italy 2009
No full textA convergent adaptive wavelet-Rothe method for elastoplastic hardening
No full textThis paper is concerned with the development of adaptive wavelet methods for the hardening problem in elastoplasticity. We propose a Rothe method using some implicit scheme in time. Then, we consider a standard elastic predictor-plastic corrector method. The (non-linear) correction is performed by some convergent scheme such as a Newton-Raphson iteration or suitable modifications of it. Thus, it remains to solve Helmholtz-type problems with varying right-hand sides. These are solved by the convergent adaptive wavelet method introduced by Cohen, Dahmen, and DeVore.
In the plastic correction, the trial strain might have to be corrected according to pointwise formulated hardening conditions. We propose an adaptive corrector method based on biorthogonal B-splines. This allows a fully adaptive stress correction. We obtain an overall convergent method. Some preliminary numerical results are presented
Criteri per la indivuazione delle caratteristiche di impianti di prova per modelli di micro-turbine idrauliche a reazione
No full textIn questo lavoro viene proposto un metodo semplice per individuare quali caratteristiche di portata e prevalenza debba avere un impianto di prova a circuito chiuso per modelli di turbine idrauliche a reazione con indice caratteristico nq compreso fra 20 e 300. Vengono ricavate le relazioni che legano, in questo campo, la portata al salto ed alle caratteristiche geometriche e funzionali del modello: dimensione, indice caratteristico e velocità di rotazione. Queste relazioni sono dedotte dai criteri usuali di dimensionamento delle turbine a reazione e in particolare dalla dipendenza del coefficiente di velocità periferica dall'indice caratteristico
Comparison of computational methods for the estimation of the dielectrophoretic force acting on biological cells and aggregates in silicon labonchip
No full textDielectrophoresis (DEP) is a promising method for particles manipulation without physical contact in silicon lab-on-chip devices. It exploits the dielectric properties of cells and aggregates suspended in a microfluidic sample under the action of high-gradient electric fields. The force is approximated by a truncation of a multipole expansion which, for single cell, reduces to the first order contribution. When the cells aggregate is “big” further terms should be considered involving higher order field derivatives. Here, we compare different force approximations, depending on the aggregate's dimension and on the non-uniformity of the electric field. Numerical modeling has been performed by using COMSOL Multiphysics to compute the electric field, to quantify the DEP forces and to simulate the particles tracings that have been compared with experimental results developed in several settings
Sull'ottimizzazione di gruppi combinati gas-vapore con sezione a vapore a due pressioni
No full textScopo dello studio è la determinazione dei massimi rendimenti ottenibili dai gruppi combinati gas-vapore costituiti da turbine a gas a ciclo di Brayton e da sezioni a vapore a due livelli di pressione. In linea con le più diffuse realizzazioni industriali nel settore, il vapore di bassa pressione è impiegato allo stato fisico di vapore saturo secco. Lo studio è stato condotto per turbine a gas di attuale e futura generazione considerando, per ciascuna di esse, un campo di rapporti di compressione sufficientemente ampio da contenere tutte le realizzazioni industriali
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