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The rapidly advancing field of Fluid Mechanics has recently employed Deep Learning to solve various problems within that field. In that same spirit we try to perform Direct Numerical Simulation(DNS) which is one of the tasks in Computational Fluid Dynamics, using three fundamental architectures in the field of Deep Learning that were each used to solve various high dimensional problems. We train these three models in an autoencoder manner, for this the dataset is treated like sequential frames given to the model as input. We observe that recently introduced architecture called Transformer significantly outperforms its counterparts on the selected dataset.Furthermore, we conclude that using Transformers for doing DNS in the field of CFD is an interesting research area worth exploring., Comment: 5 figures, 8 pages

In Bosonic, Heterotic and Type II theories, by employing soft theorems and string techniques, we analyze the gyromagnetic ratios of massive high spin particles coupled to Abelian gauge fields arising from the compactification of the metric and Kalb-Ramond fields. We derive a universal form for such couplings showing that mixed symmetry states of the leading Regge-trajectory, described by a Young-tableau with two rows, have a gyromagnetic ratio associated with each row., Comment: 15 pages, 2 figures, Contribution to Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" 29 August - 9 October 2021 Corfu, Greece

The practical implementation of free-space quantum information tasks requires entanglement to be sustained over long distances and in the presence of turbulent and noisy environments. The transverse position-momentum entanglement of photon pairs produced by parametric down-conversion has found several uses in quantum information science, however, it is not suitable for applications involving long-distance propagation as the entanglement decays very rapidly when photons propagate away from their source. Entanglement is lost after a few centimetres of propagation, and the effect becomes even more pronounced in turbulent environments. In contrast, in this article, we show that entanglement in the angle-orbital angular momentum (OAM) bases exhibits a remarkably different behaviour. As with the position-momentum case, initially, the angle-OAM entanglement decays with propagation, but as the photons continue to travel further from the source, the photons regain their strongly correlated behaviour, and the entanglement returns. We theoretically and experimentally demonstrate this behaviour and show that entanglement returns even in the presence of strong turbulence. The only effect of turbulence is to increase the propagation distance for revival, but once revived, the two photons remain entangled up to an arbitrary propagation distance. This work highlights the role that OAM-angle entanglement will play in applications where quantum information is shared over long distances.

We analyze Bosonic, Heterotic, and Type II string theories compactified on a generic torus having constant moduli. By computing the hamiltonian giving the interaction between massive string excitations and $U(1)$ gauge fields arising from the graviton and Kalb-Ramond field upon compactification, we derive a general formula for such couplings that turns out to be universal in all these theories. We also confirm our result by explicitly evaluating the relevant string three-point amplitudes. From this expression, we determine the gyromagnetic ratio $g$ of massive string states coupled to both gauge-fields. For a generic mixed symmetry state, there is one gyromagnetic coupling associated with each row of the corresponding Young Tableau diagram. For all the states having zero Kaluza Klein or Winding charges, the value of $g$ turns out to be $1$. We also explicitly consider totally symmetric and mixed symmetry states (having two rows in the Young diagram) associated with the first Regge-trajectory and obtain their corresponding $g$ value., Comment: 27+23 pages, 2 figures

We analyze the single subleading soft graviton theorem in $(d+1)$ dimensions under compactification on $S^1$. This produces the single soft theorems for the graviton, vector and scalar fields in $d$ dimension. For the compactification of $11$-dimensional supergravity theory, this gives the soft factorization properties of the single graviton, dilaton and RR 1-form fields in type IIA string theory in ten dimensions. For the case of the soft vector field, we also explicitly check the result obtained from compactification by computing the amplitudes with external massive spin two and massless finite energy states interacting with soft vector field. The former are the Kaluza-Klein excitations of the $d+1$ dimensional metric. Describing the interaction of the KK-modes with the vector field at each level by the minimally coupled Fierz-Pauli Lagrangian, we find agreement with the results obtained from the compactification if the gyromagnetic ratio in the minimally coupled Fierz-Pauli Lagrangian is taken to be $g=1$., Comment: 22 pages + appendix

We construct Lorentz invariant and gauge invariant 1PI effective action for closed and open superstrings and demonstrate that it satisfies the classical BV master equation. We also construct the quantum master action for this theory satisfying the quantum BV master equation and generalize the construction to unoriented theories. The extra free field needed for the construction of closed superstring field theory plays a crucial role in coupling the closed strings to D-branes and orientifold planes., Comment: LaTeX, 47 pages; v2: some typos corrected