Speaker: Dr. Harsita Srivastava (NIT-J)

Date and Time: Tuesday, 22/07/2025 from 11:00 AM to 12:00 PM

Mode: Online

Google Meet link: https://meet.google.com/bas-tfye-crn

Title:  ANALYSIS OF INITIAL AND BOUNDARY VALUE PROBLEMS FOR NON-IDEAL COMPRESSIBLE FLOWS

Abstract: The talk will explore nonlinear wave phenomena in hyperbolic systems of conservation laws, with a focus on the two-dimensional Riemann problem and transonic flow problem in non-ideal gas models such as the Noble-Abel and van der Waals gases. I will discuss the structure and interaction of elementary waves in 2-D Riemann problems, the impact of real gas effects on wave patterns, and the behavior of sonic-supersonic transitions in steady compressible flows. A significant part of the talk will be devoted to magnetohydrodynamics (MHD) flow with van der Waals gas, where I construct special solutions (e.g., circulatory and spiral flows) and analyze the existence and regularity of sonic-supersonic solutions via hodograph and characteristic decomposition methods. The results provide new insights into flow structures influenced by real gas dynamics and magnetic fields, with implications for theoretical and applied fluid dynamics.

Combinatorics Seminar
Spreaker: Samir Mondal (University of Regina)
Host: Krishnan Sivasubramanian
Title: P-matrix Powers
Time, day and date: 11:00:00 AM – 12:00:00 PM, Tuesday, July 22
Venue: Ramanuajan Hall
Abstract: A P-matrix is a matrix all of whose principal minors are positive. We demonstrate that the fractional powers of a P-matrix are also P-matrices. This insight allows us to affirmatively address a longstanding conjecture raised in [D. Hershkowitz and C.R. Johnson, Spectra of matrices with P-matrix powers, Linear Algebra Appl., 80:159–171, 1986]: It is shown that if Ak is a P-matrix for all positive integers k, then the eigenvalues of A are positive. [In order to study (fractional and integer) powers of a matrix, we will make use of some classical aspects of the theory of matrix functions. Definition 0.1 Let f(z) be a complex function defined and analytic on a domain containing all the eigenvalues of a matrix A ∈ Mn (C). The function of A induced by f, denoted by f[A], is defined by the Cauchy integral formula

,

where Γ is any simple closed curve surrounding all eigenvalues of A and contained in the given domain. If time permits, we will explore this topic in a bit more detail.]