Related papers: Integral representation for a relaxed optimal desi…
We prove a relaxation result for a quasi-convex bulk integral functional with variable exponent growth in a suitable space of bounded variation type. A key tool is a decomposition under mild assumptions of the energy into absolutely…
We use gradient Young measures generated by Lipschitz maps to define a relaxation of integral functionals which are allowed to attain the value $+\infty$ and can model ideal locking in elasticity as defined by Prager in 1957. Furthermore,…
We prove an integral representation result for a class of variational functionals appearing in the framework of hierarchical systems of structured deformations via a global method for relaxation. Some applications to specific relaxation…
For an integral functional defined on functions $(u,v)\in W^{1,1}\times L^1$ featuring a prototypical strong interaction term between $u$ and $v$, we calculate its relaxation in the space of functions with bounded variations and Radon…
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply…
An integral representation result is obtained for the relaxation of a class of energy functionals depend- ing on two vector fields with different behaviors, which may appear in the context of image decomposition and thermochemical…
In this work we analyze the relation between the multiplicative decomposition $\mathbf F=\mathbf F^{e}\mathbf F^{p}$ of the deformation gradient as a product of the elastic and plastic factors and the theory of uniform materials. We prove…
A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic…
We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure,…
Mathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Here we demonstrate…
We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the…
This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemical species in the host material. Such a modeling framework…
Integral representation results are obtained for the relaxation of some classes of energy functionals depending on two vector fields with different behaviors, which may appear in the context of image decomposition and thermochemical…
A polycrystalline solid is modelled as an ensemble of random irregular polyhedra filling the entire space occupied by the solid body, leaving no voids or flaws between them. Adjacent grains can slide with a relative velocity proportional to…
We consider the problem of optimal input design for estimating uncertain parameters in a discrete-time linear state space model, subject to simultaneous amplitude and l1/l2-norm constraints on the admissible inputs. We formulate this…
We consider the representation of the value of a class of optimal stopping problems of linear diffusions in a linearized form as an expected supremum of a known function. We establish an explicit integral representation of this representing…
The relationship between the refractive index decrement, $\delta$, and the real part of the atomic form factor, $f^\prime$, is used to derive a simple polynomial functional form for $\delta(E)$ far from the K-edge of the element. The…
We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…
For composite systems made of $N$ different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first…