Mildly flavoring domain walls in Sp(N) SQCD

We consider supersymmetric domain walls of four-dimensional $$ \mathcal{N} $$ N = 1 Sp(N) SQCD with F = N + 1 and F = N + 2 flavors.First, we study numerically the differential equations defining the walls, classifying the solutions. When F = N + 2, in the special case of the parity-invariant walls, the naive analysis does not provide all the expected solutions. We show that an infinitesimal deformation of the differential equations sheds some light on this issue.Second, we discuss the 3d$$ \mathcal{N} $$ N = 1 Chern-Simons-matter theories that should describe the effective dynamics on the walls. These proposals pass various tests, including dualities and matching of the vacua of the massive 3d theory with the 4d analysis. However, for F = N +2, the semiclassical analysis of the vacua is only partially successful, suggesting that yet-to-be-understood strong coupling phenomena are into play in our 3d$$ \mathcal{N} $$ N = 1 gauge theories.

Deformations of Courant pairs and Poisson algebras

We study the deformation of Courant pairs with a commutative algebra base. We consider the deformation cohomology bi-complex and describe a universal infinitesimal deformation. In a sequel, we formulate an extension of a given deformation of a Courant pair to another with extended base, which leads to describe the obstruction in extending a given deformation. We also discuss the construction of versal deformation of Courant pairs. As an application, we compute universal infinitesimal deformation of Poisson algebra structures on the three-dimensional complex Heisenberg Lie algebra. We compare the second deformation cohomology spaces of these Poisson algebra structures by considering them in the category of Leibniz pairs and Courant pairs, respectively.

Continuum Mechanics of Solids

Continuum mechanics of Solids presents a unified treatment of the major concepts in Solid Mechanics for beginning graduate students in the many branches of engineering. The fundamental topics of kinematics in finite and infinitesimal deformation, mechanical and thermodynamic balances plus entropy imbalance in the small strain setting are covered as they apply to all solids. The major material models of Elasticity, Viscoelasticity, and Plasticity are detailed and models for Fracture and Fatigue are discussed. In addition to these topics in Solid Mechanics, because of the growing need for engineering students to have a knowledge of the coupled multi-physics response of materials in modern technologies related to the environment and energy, the book also includes chapters on Thermoelasticity, Chemoelasticity, Poroelasticity, and Piezoelectricity. A preview to the theory of finite elasticity and elastomeric materials is also given. Throughout, example computations are presented to highlight how the developed theories may be applied.

On Deformations of 1-motives

According to a well-known theorem of Serre and Tate, the infinitesimal deformation theory of an abelian variety in positive characteristic is equivalent to the infinitesimal deformation theory of its Barsotti–Tate group. We extend this result to 1-motives.

Deformation of complex Finsler metrics

The aim of this paper is to describe the infinitesimal deformation (M, V) of a complex Finsler space family {(M, Lt)}t∈ℝ and to study some of its geometrical objects (metric tensor, non-linear connection, etc). In this circumstances the induced non-linear connection on (M, V) is defined. Moreover we have elaborate the inverse problem, the problem of the first order deformation of the metric. A special part is devoted to the study of particular cases of the perturbed metric.