In this study, I have focused on metastable behaviours of a ferromagnetic system. The studies have been carried out particularly on Ising and Blume-Capel ferromagnet in presence of externally applied magnetic field using Monte Carlo simulation technique based on Metropolis algorithm. The metastable lifetime is found to decrease in presence of a quenched random field. The strength of the random field plays an equivalent role to temperature on metastable lifetime. Becker Döring’s theory of classical nucleation (originally proposed for the spin-1/2 Ising system), as well as Avrami’s law, have been verified in the random field Ising model. However, the nucleation regime is found to be affected by the stronger random field. The competitive nature of the metastable lifetime of surface and bulk has been studied by introducing a relative interfacial interaction strength (R). Surface reversal time is found to be different from the bulk reversal time. Depending on R, temperature, and the applied field, a competition between the surface reversal and bulk reversal is noticed based on faster reversal. The effect of uniaxial anisotropy (D, both positive and negative) on the metastable lifetime has been investigated. The linear dependency of the mean macroscopic reversal time on a suitably defined microscopic reversal time has been observed. The saturated magnetisation Mf , after the reversal, is noticed to be strongly dependent on D. That Mf , D, and h (field) are found to follow a proposed scaling relation. The metastable behaviours under the influence of graded and step-like variation of both the applied field and anisotropy have been explored. Motion of an interface, arising due to the presence of a stronger gradient of either field or anisotropy, has been studied. A competitive reversal by the field and anisotropy is observed when I consider the similar spatial modulation of both the field and anisotropy. Finally, Becker-Döring’s theory is also verified in spin-s (s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2) Ising and Blume-Capel models. Moreover, the decay of metastable volume fraction is found to follow Avrami’s law nicely for all values of s and both models considered. To join the webinar, click this link: https://meet.google.com/brv-nawn-ihg

Join Zoom Meeting https://zoom.us/j/91288928049 Meeting ID: 912 8892 8049 Passcode: Macdonald We study weights of highest weight modules $V$ over a Kac-Moody algebra $\mathfrak{g}$ (one may assume this to be $\mathfrak{sl}_n$ throughout the talk, without sacrificing novelty). We begin with several positive weight-formulas for arbitrary non-integrable simple modules, and mention the equivalence of several "first order" data that helps prove these formulas. We then discuss the notion of "higher order holes" in the weights, and use these to present two positive weight-formulas for arbitrary modules $V$. One of these is in terms of "higher order Verma modules", and we end by explaining BGG resolutions and Weyl-Kac type character formulas, for these modules in certain cases. (Joint with G.V.K. Teja and with Gurbir Dhillon.)

Towards the automation of Software-Defined Network (SDN) based Internet of Things (IoT) platforms, we are using formal analysis and synthesis techniques to ensure their safe behaviours. SDN, a flexible and low cost networking principle which provides dynamic distributed system applications, IoT is one such kind. There is a strong need for consistent and correct integration of IoT applications in the SDN environment. Using formal compositional verification methods for analyzing the safety of an SDN-IoT environment, we provide a detailed synthesis framework to model the abstract behaviour of IoT devices, SDN manager and automatically generate low level implementation code to be integrated with IoT applications.

Elasticity is a fundamental macroscopic property that emerges in any collection of interacting particles. However, at sufficiently low temperatures where thermal fluctuations are negligible, a free energetic description of such macroscopic properties is not available. Granular materials and glasses offer a paradigm where disorder in the arrangements of particles plays a fundamental role in determining the energy landscape, and thereby their stability, response and elasticity properties. Gradually introducing disorder into athermal crystalline packings can be used to build a relation between the well-established physics of crystals and that of amorphous solids. Such studies can also reveal interesting phenomena peculiar to athermal systems such as hidden order-disorder transitions. In this talk I will outline the development of exact theoretical techniques which can be used to characterize fluctuations in positions, forces and interaction energies in near-crystalline athermal systems, which offer a route towards understanding the emergent elasticity properties of ubiquitous amorphous solids.

Theoretical studies in Quantum Chromodynamics (QCD) show that at high temperature hadrons melt into quark-gluon plasma (QGP) via a transition known as confinement-deconfinement (CD) transition. In pure SU(N) gauge theories the CD transition is described by the Polyakov loop and the $Z_N$ (center of SU(N)) symmetry. This symmetry is spontaneously broken in the deconfined phase. When matter fields in the fundamental representation are included, the Euclidean action breaks this symmetry explicitly. The non-perturbative studies have shown in SU(2)-Higgs theory (scalar QCD) the partition function averages, in the continuum limit (for large number of temporal sites ($N_\tau$)), exhibit the corresponding $Z_2$ symmetry in parts of the phase diagram. In this talk, we will discuss our work on the $Z_N$ symmetry in SU(N)-Higgs theories. We present results of non-perturbative studies for $N=3$ which suggest that, the $Z_3$ symmetry is effectively realized,in the Higgs symmetric phase. The nature of the CD transition changes with $N_\tau$, becomes first order in the continuum limit (as if in pure SU(N) theory). In the same limit, in the deconfined phase the $Z_N$ states become degenerate. To understand the realization of $Z_N$ symmetry, next we will discuss our study on one dimensional gauged chain of matter fields. As in SU(N) gauge theories, the action breaks $Z_N$ symmetry explicitly. The analytic calculation of the partition function shows that the $Z_N$ symmetry is realized in the continuum limit for bosonic matter fields. To further probe the reason behind the realisation of $Z_N$ symmetry we consider a simple model of $Z_2$-Higgs theory in both 3+1 and 0+1 dimensions where it is shown that the density of states (DoS) exhibits $Z_2$ symmetry. As DoS, so entropy, dominate the thermodynamics (over the Boltzmann factor) in the Higgs symmetric phase, the $Z_2$ symmetry is realized.