Publications
Art Credit: BLEACH Volume 66
Art Credit: BLEACH Volume 66
Anish Suresh, Dominic Klyve
Abstract: Ducci’s Four-Number Game begins with a square labelled with four positive integers, one on each corner. The game proceeds by labelling the midpoints of each side with the positive difference of the side’s two corners. We formalize this notion using points in N^4 (including 0) to represent each set of numbers, and a map D such that D([a,b,c,d]) = [|a − b|,|b − c|,|c − d|,|d − a|] to represent each turn of the game. This game serves as a fun activity for young kids. Naturally, these children make arithmetic mistakes, which begs the question: how do small mistakes impact the game? Inspired by this question, we introduce a variation to this game by allowing errors or “mutations” in the subtraction step. That is, every fixed number of turns, we use a different map Dn such that D_n([a,b,c,d]) = [|a − b|,|b − c|,|c − d|,|d − a + n|] where the positive integer n is the size of the error and the mutation randomly occurs in one of the four spots. In this paper, we show that if a mutation occurs every two, three, or four iterations, we have two cases. If n is even, any set of initial numbers will reach all 0s, like they would in the original game. If n is odd, no set of initial points reach all 0s. However, if there is a mutation five or more turns, every set of initial points reach all 0s, regardless of the parity of n. On the other hand, if there is a mutation every turn, no set of initial points reach all 0s, irrespective of n.
Type: Article.
Status: Accepted at Rocky Mountain Journal of Mathematics.
Anish Suresh, Tom Banks
Abstract: Holographic space-time, a theory of quantum gravity that generalizes string theory and quantum field theory, predicts black holes in the early matter-dominated era of its models of inflation. Before these black holes can decay, there is a chance that enough of these particles merge to produce radiation visible today in the Cosmic Microwave background. To discover if this is the case, we perform a rudimentary computer simulation. We show that no problematic black holes are formed by mergers in the Holographic Space-time models of inflation. However, we conclude that tiny bound structures containing black holes remnants form in this theory unconditionally. Since black hole decay products are mostly massive standard model particles, and perhaps their superpartners, the fate of these structures is a complicated dynamical problem that requires further study. It suggests the possibility of primordial structures on the order of the horizon size at the beginning of the radiation dominated era. This is about 10^9 L_P in the current model.
Type: Article
Status: Published at SciPost Physics Core.
Anish Suresh, Dominic Klyve
Abstract: In this note, we consider the classical Ducci's Four-Number Game with two additional features: an arithmetic error is committed during an iteration (herein referred to as a mutation), and this error happens randomly with fixed probability p. The random error affects the behavior of the game considerably -- in particular, the number of steps until the values converge increases with p. We perform statistical analyses, including central tendency and probability distribution fitting, to study the number of iterations needed for an arbitrary chosen starting vector to converge in this setting.
Type: Article.
Status: Accepted at Minnesota Journal of Undergraduate Mathematics.
**No link available for this article**
Anish Suresh, Parampreet Singh
Abstract: The dynamics of the classical Bianchi-I model is contained in the Generalized Friedmann Equation. Notably, the anisotropic shear scalar term in this equation dominates the energy density as the Big Bang singularity is approached, indicating the importance of studying anisotropic spacetimes. Loop Quantum Cosmology (LQC) has made significant progress studying the Bianchi-I spacetime through both numerical and analytical means using effective Hamiltonians. However, a Generalized Friedmann Equation has yet to be found in this setting due to the complexity of the effective Hamiltonian and the corresponding Hamilton's equations. In this paper, we find such an equation in the slightly simpler Bianchi-I LRS (Locally Rotation Symmetric) model. Unlike its classical and isotropic counterparts, the Friedmann Equation here consists of five separate solutions. These equations show various branches of the Hubble rate that need to be coupled to accurately describe the universe's behavior.
Type: Article.
Status: Under preparation.
**No link available for this article**
Anish Suresh, Xerxes Arsiwalla
Introduction: Theories of quantum gravity study the universe as a discrete object, due to the addition of quantum mechanics to general relativity. Each such theory has its own set of rules to describe the universe. As an example, consider Loop Quantum Gravity and its ‘patches’ of spacetime with a fixed area in the Ashtekar formalism. The aim of this project is to determine if the various rules of each theory are interconnected in some way; that is, we attempt to model the discrete structures of each theory with causal graphs in Mathematica to determine if the rewriting rules that produce said causal graphs have a pattern to them. This may provide insight on theories of quantum gravity more generally if we find that certain rewriting rules are fundamental in modelling a discrete universe. My work over the period of the Winter School has been on Causal Set Theory specifically.
Type: Wolfram Community Post.
Status: N/A.
Anish Suresh, Parampreet Singh
Abstract: While General Relativity successfully describes the dynamics of the universe, it fails 9 to do so at specific points of space-time known as singularities. One such singularity 10 can be found when traversing backwards in time, resulting in the Big Bang singularity. 11 Loop Quantum Cosmology (LQC) is a theory that uses Quantum Mechanics to resolve 12 these points. Here, the Modified Friedmann Equation, an equation that encapsulates the 13 behavior of the universe, demonstrates that the universe avoids the Big Bang singularity. 14 This was only found for a symmetrical universe, but it can be shown that asymmetrical 15 terms are important to consider. In this thesis report, we derive the Modified Friedmann 16 Equations in the asymmetrical Bianchi I LRS model of LQC. Furthermore, we find all the 17 necessary equations to derive said equation in the more asymmetrical Bianchi I model, 18 which we are currently in the process of doing.
Type: Undergraduate Thesis. Recipient of the Paul L. Leath Prize, awarded by the Physics & Astronomy Department of Rutgers University - New Brunswick.
Status: N/A.
**No link available for this document**
Anish Suresh, Mukund Rangamani
Abstract: The principle of holography, which states that a gravitational theory is closely related to a non-gravitational theory of lower dimension, has revolutionized the search for a theory of quantum gravity. One such example of this is the D0-Brane matrix model, which exhibits signatures of M-theory in specific conditions and is the holographic dual of a 10 dimensional black hole of type IIA string theory. Understanding the properties of this model is difficult to do analytically. In this report, we use the bootstrap method, a numerical technique that utilizes a positivity constraint to narrow down the range of allowed values. We consider many simple systems to provide a comprehensive review of the bootstrap method. We also bootstrap the D0-Brane matrix model and reproduce bounds on observables of that setting.
Type: Summary of my work from the physics REU at UC Davis.
Status: N/A.
**No link available for this summary**
Anish Suresh, Tom Banks
Abstract: We investigate an approximation to the Schwinger-Dyson (SD) equations of the collective Coulomb field of the large N homogeneous electron fluid. The large N approximation transforms the infinite SD hierarchy is into a set of closed, equations for 1 and 2-pt correlators. In this paper, the dynamics of a toy model --- a small, square Euclidean lattice with periodic boundary conditions --- are considered. The Markov Chain Monte Carlo numerical method evaluated the 1 and 2-pt correlation functions on a 2 x 2 and 3 x 3 lattice. The derived equations are checked with the correlator values, and an agreement at N ~ 1000 to order 10^{-3} was found. The agreement can be further strengthened by increasing runs in the Markov Chain Monte Carlo method.
Type: Article.
Status: Submitted to Journal of High Energy Physics.