Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

VL - 2 UR - http://dx.doi.org/10.3934/mine.2020011 ER - TY - JOUR T1 - Ground state energy of mixture of Bose gases JF - Reviews in Mathematical Physics Y1 - 2019 A1 - Alessandro Michelangeli A1 - Phan Thanh Nam A1 - Alessandro Olgiati AB -We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N−1), we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

VL - 31 UR - https://doi.org/10.1142/S0129055X19500053 ER - TY - JOUR T1 - Nutations in growing plant shoots: The role of elastic deformations due to gravity loading JF - Journal of the Mechanics and Physics of Solids Y1 - 2019 A1 - Daniele Agostinelli A1 - Alessandro Lucantonio A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Circumnutations KW - Flutter instability KW - Gravitropism KW - Hopf bifurcation AB -The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

UR - https://doi.org/10.1016/j.jmps.2019.103702 ER - TY - JOUR T1 - Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness JF - SIAM Journal on Applied Mathematics Y1 - 2018 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -We analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

VL - 78 UR - https://doi.org/10.1137/17M1147354 ER - TY - JOUR T1 - An authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production JF - JOURNAL OF INDUSTRIAL TEXTILES Y1 - 2018 A1 - Rafiei, S. A1 - Noroozi, B. A1 - Luca Heltai A1 - Haghi, A. K. VL - 47 ER - TY - RPRT T1 - Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping Y1 - 2018 A1 - Lorenzo Nardini A1 - Filippo Riva AB -In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

UR - http://preprints.sissa.it/xmlui/handle/1963/35319 U1 - 35629 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - On Krylov solutions to infinite-dimensional inverse linear problems Y1 - 2018 A1 - Noe Caruso A1 - Alessandro Michelangeli A1 - Paolo Novati AB - We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35327 U1 - 35638 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Minimizing movements for mean curvature flow of droplets with prescribed contact angle JF - Journal de Mathématiques Pures et Appliquées Y1 - 2018 A1 - Giovanni Bellettini A1 - Matteo Novaga A1 - Shokhrukh Kholmatov KW - Capillary functional KW - Mean curvature flow with prescribed contact angle KW - Minimizing movements KW - Sets of finite perimeter AB -We study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the solutions constructed as a limit of an approximation algorithm of Almgren–Taylor–Wang and Luckhaus–Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. Résumé Nous étudions le mouvement par courbure moyenne d'une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit éventuellement non constant. En utilisant les solutions construites comme limites d'un algorithme d'approximation dû à Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l'existence d'une évolution faible, et sa compatibilité avec une solution au sens des distributions. Nous démontrons également plusieurs résultats de comparaison.

VL - 117 UR - http://www.sciencedirect.com/science/article/pii/S0021782418300825 ER - TY - JOUR T1 - On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One JF - Journal of Nonlinear Science Y1 - 2018 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -The aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith's criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

VL - 28 UR - https://doi.org/10.1007/s00332-017-9407-0 ER - TY - ABST T1 - A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics Y1 - 2018 A1 - Efthymios N. Karatzas A1 - Giovanni Stabile A1 - Leo Nouveau A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza ER - TY - RPRT T1 - Truncation and convergence issues for bounded linear inverse problems in Hilbert space Y1 - 2018 A1 - Noe Caruso A1 - Alessandro Michelangeli A1 - Paolo Novati AB - We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35326 U1 - 35637 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - On the 1D wave equation in time-dependent domains and the problem of debond initiation Y1 - 2017 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

PB - SISSA UR - http://preprints.sissa.it/handle/1963/35302 U1 - 35608 U2 - Mathematics ER - TY - JOUR T1 - Minimizers of anisotropic perimeters with cylindrical norms JF - Communications on Pure & Applied Analysis Y1 - 2017 A1 - Giovanni Bellettini A1 - Matteo Novaga A1 - Shokhrukh Kholmatov KW - anisotropic Bernstein problem; KW - minimal cones KW - Non parametric minimal surfaces KW - Sets of finite perimeter AB -We study various regularity properties of minimizers of the Φ–perimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

VL - 16 UR - http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d ER - TY - JOUR T1 - A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations JF - Journal of Dynamics and Differential Equations Y1 - 2017 A1 - Lorenzo Nardini VL - 29 UR - https://doi.org/10.1007/s10884-015-9461-y ER - TY - JOUR T1 - Real topological string amplitudes JF - Journal of High Energy Physics Y1 - 2017 A1 - Narain, K. S. A1 - Nicolò Piazzalunga A1 - Alessandro Tanzini AB -We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'= −\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

VL - 2017 UR - https://doi.org/10.1007/JHEP03(2017)080 ER - TY - JOUR T1 - Symplectic geometry of the moduli space of projective structures in homological coordinates JF - Inventiones Mathematicae Y1 - 2017 A1 - Marco Bertola A1 - Dmitry Korotkin A1 - Chaya Norton UR - https://arxiv.org/abs/1506.07918 ER - TY - JOUR T1 - Existence and uniqueness of dynamic evolutions for a peeling test in dimension one JF - Journal of Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini KW - Dynamic debonding KW - Dynamic energy release rate KW - Dynamic fracture KW - Griffith's criterion KW - Maximum dissipation principle KW - Wave equation in time-dependent domains AB -In this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

VL - 261 UR - http://www.sciencedirect.com/science/article/pii/S0022039616301772 ER - TY - JOUR T1 - Liquid crystal elastomer strips as soft crawlers JF - Journal of the Mechanics and Physics of Solids Y1 - 2015 A1 - Antonio DeSimone A1 - Paolo Gidoni A1 - Giovanni Noselli KW - Crawling motility KW - Directional surfaces KW - Frictional interactions KW - Liquid crystal elastomers KW - Soft biomimetic robots AB -In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

VL - 84 UR - http://www.sciencedirect.com/science/article/pii/S0022509615300430 ER - TY - JOUR T1 - Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations JF - Computers and Mathematics with Applications Y1 - 2015 A1 - Federico Negri A1 - Andrea Manzoni A1 - Gianluigi Rozza AB -This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

VL - 69 ER - TY - JOUR T1 - Buckling dynamics of a solvent-stimulated stretched elastomeric sheet Y1 - 2014 A1 - Alessandro Lucantonio A1 - Matthieu Roché A1 - Paola Nardinocchi A1 - Howard A. Stone AB - When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet. PB - Royal Society of Chemistry UR - http://urania.sissa.it/xmlui/handle/1963/34967 U1 - 35197 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Crawling on directional surfaces JF - International Journal of Non-Linear Mechanics Y1 - 2014 A1 - Paolo Gidoni A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bio-mimetic micro-robots KW - Cell migration KW - Crawling motility KW - Directional surfaces KW - Self-propulsion AB -In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

VL - 61 UR - http://www.sciencedirect.com/science/article/pii/S0020746214000213 ER - TY - JOUR T1 - Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost Y1 - 2014 A1 - Giovanni Noselli A1 - Amabile Tatone A1 - Antonio DeSimone KW - Cell migration AB - We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34449 U1 - 34591 U2 - Mathematics ER - TY - JOUR T1 - A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model JF - Proceedings of the Royal Society A 470, 20140333 (2014) Y1 - 2014 A1 - Giovanni Noselli A1 - Antonio DeSimone AB - We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations. PB - Royal Society Publishing U1 - 34594 U2 - Mathematics ER - TY - JOUR T1 - Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Howard A. Stone AB - It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch. PB - American Institute of Physics UR - http://urania.sissa.it/xmlui/handle/1963/35113 U1 - 35370 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Swelling-induced and controlled curving in layered gel beams Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Matteo Pezzulla AB - We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method. PB - Royal Society of London UR - http://urania.sissa.it/xmlui/handle/1963/34987 U1 - 35229 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawlers in viscous environments: linear vs nonlinear rheology JF - International Journal of Non-Linear Mechanics 56, 142-147 (2013) Y1 - 2013 A1 - Antonio DeSimone A1 - Federica Guarnieri A1 - Giovanni Noselli A1 - Amabile Tatone AB - We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling. PB - Elsevier U1 - 34590 U2 - Mathematics ER - TY - RPRT T1 - Minimal partitions and image classification using a gradient-free perimeter approximation Y1 - 2013 A1 - Samuel Amstutz A1 - Nicolas Van Goethem A1 - Antonio André Novotny KW - Image classification, deblurring, optimal partitions, perimeter approximation AB - In this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring. PB - SISSA UR - http://hdl.handle.net/1963/6976 U1 - 6964 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Reduced basis method for parametrized elliptic optimal control problems JF - SIAM Journal on Scientific Computing Y1 - 2013 A1 - Federico Negri A1 - Gianluigi Rozza A1 - Andrea Manzoni A1 - Alfio Quarteroni AB - We propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique. VL - 35 ER - TY - JOUR T1 - Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control JF - IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 Y1 - 2013 A1 - Claudio Altafini A1 - Francesco Ticozzi A1 - K. Nishio AB - In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control UR - http://hdl.handle.net/1963/6503 U1 - 6448 U2 - Mathematics U4 - 1 ER - TY - Generic T1 - Reduction strategies for PDE-constrained oprimization problems in Haemodynamics T2 - European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 Y1 - 2012 A1 - Gianluigi Rozza A1 - Andrea Manzoni A1 - Federico Negri KW - inverse problems AB - Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation. JF - European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 UR - http://hdl.handle.net/1963/6338 U1 - 6268 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - Topological sensitivity analysis for high order elliptic operators Y1 - 2012 A1 - Samuel Amstutz A1 - Antonio André Novotny A1 - Nicolas Van Goethem KW - Topological derivative, Elliptic operators, Polarization tensor AB - The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders. PB - SISSA UR - http://hdl.handle.net/1963/6343 U1 - 6272 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy JF - Comm. Pure Appl. Math. 60 (2007) 1559-1622 Y1 - 2007 A1 - Stefano Bianchini A1 - Bernard Hanouzet A1 - Roberto Natalini AB - We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition. UR - http://hdl.handle.net/1963/1780 U1 - 2764 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Boundary-clustered interfaces for the Allen–Cahn equation JF - Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 Y1 - 2007 A1 - Andrea Malchiodi A1 - Wei-Ming Ni A1 - Juncheng Wei PB - Mathematical Sciences Publishers UR - http://hdl.handle.net/1963/5089 U1 - 4905 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Smooth toric DM stacks Y1 - 2007 A1 - Barbara Fantechi A1 - Etienne Mann A1 - Fabio Nironi AB - We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks. UR - http://hdl.handle.net/1963/2120 U1 - 2123 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Some existence results for the Toda system on closed surfaces JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 Y1 - 2007 A1 - Andrea Malchiodi A1 - Cheikh Birahim Ndiaye AB - Given a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$. UR - http://hdl.handle.net/1963/1775 U1 - 2769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Classification of stable time-optimal controls on 2-manifolds JF - J. Math. Sci. 135 (2006) 3109-3124 Y1 - 2006 A1 - Ugo Boscain A1 - Igor Nikolaev A1 - Benedetto Piccoli UR - http://hdl.handle.net/1963/2196 U1 - 2048 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Experimental and modeling studies of desensitization of P2X3 receptors. JF - Molecular pharmacology. 2006 Jul; 70(1):373-82 Y1 - 2006 A1 - Elena Sokolova A1 - Andrei Skorinkin A1 - Igor Moiseev A1 - Andrei A. Agrachev A1 - Andrea Nistri A1 - Rashid Giniatullin AB - The function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain. PB - the American Society for Pharmacology and Experimental Therapeutics UR - http://hdl.handle.net/1963/4974 U1 - 4799 U2 - Neuroscience U3 - Neurobiology U4 - -1 ER - TY - JOUR T1 - Multiple clustered layer solutions for semilinear Neumann problems on a ball JF - Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 Y1 - 2005 A1 - Andrea Malchiodi A1 - Wei-Ming Ni A1 - Juncheng Wei PB - Elsevier UR - http://hdl.handle.net/1963/3532 U1 - 732 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II JF - Indiana Univ. Math. J. 53 (2004) 297-392 Y1 - 2004 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/1663 U1 - 2455 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A finite element approximation of the Griffith\\\'s model in fracture mechanics JF - Numer. Math., 2003, 95, 653 Y1 - 2003 A1 - Matteo Negri AB - The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown. PB - SISSA Library UR - http://hdl.handle.net/1963/1548 U1 - 2570 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I JF - Comm. Math. Phys. 235 (2003) no.3, 427-466 Y1 - 2003 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni PB - Springer UR - http://hdl.handle.net/1963/1633 U1 - 2485 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Linearized elasticity as gamma-limit of finite elasticity JF - Set-Valued Anal. 10 (2002), p.165-183 Y1 - 2002 A1 - Gianni Dal Maso A1 - Matteo Negri A1 - Danilo Percivale PB - Springer UR - http://hdl.handle.net/1963/3052 U1 - 1281 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions concentrating on spheres to symmetric singularly perturbed problems JF - C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 Y1 - 2002 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni AB - We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. PB - SISSA Library UR - http://hdl.handle.net/1963/1594 U1 - 2524 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dieletric breakdown: optimal bounds JF - Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 Y1 - 2001 A1 - Adriana Garroni A1 - Vincenzo Nesi A1 - Marcello Ponsiglione PB - SISSA Library UR - http://hdl.handle.net/1963/1569 U1 - 2549 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence Y1 - 2001 A1 - Matteo Negri KW - Mumford-Shah functional PB - SISSA UR - http://hdl.handle.net/1963/5399 U1 - 5226 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Numerical minimization of the Mumford-Shah functional JF - Calcolo, 2001, 38, 67 Y1 - 2001 A1 - Matteo Negri A1 - Maurizio Paolini PB - SISSA Library UR - http://hdl.handle.net/1963/1461 U1 - 3079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional JF - Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 Y1 - 1999 A1 - Matteo Negri AB - We compute explicitly the anisotropy effect in the H1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations. PB - Taylor and Francis UR - http://hdl.handle.net/1963/1276 U1 - 3179 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of variational problems for Dirichlet forms in varying domains JF - Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 Y1 - 1998 A1 - Gianni Dal Maso A1 - Virginia De Cicco A1 - Lino Notarantonio A1 - Nicoletta A. Tchou PB - SISSA UR - http://hdl.handle.net/1963/6440 U1 - 6377 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Topological "observables" in semiclassical field theories JF - Phys. Lett. B 297 (1992) 82-88 Y1 - 1992 A1 - Margherita Nolasco A1 - Cesare Reina AB -We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}} \rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

PB - Elsevier UR - http://hdl.handle.net/1963/3541 U1 - 1160 U2 - Mathematics U3 - Mathematical Physics ER -