Searcharxiv⌕ Search

arXiv subjects

Rishi Kumar

Publications and source records attributed to Rishi Kumar.

13 recordsLinked to original sources
arXiv2026

On the diffraction spectrum of the set of visible points in lattices and certain cut-and-project sets

Let $k\geq 2$ be a positive integer. It is known that the set of visible lattice points from the origin in $\mathbb{Z}^k$ has a translation bounded pure point diffraction spectrum. We investigate these properties for sets of points simultaneously visible from a finite set of lattice points $ \{\mathbf{x}_1,\dots,\mathbf{x}_n\} \subseteq \mathbb{Z}^k$. We provide explicit formulas for the coefficients of the diffraction spectrum. Additionally, we generalize our procedure to show that the set of visible points from the origin in certain classes of cut-and-project sets has a translation bounded pure point diffraction spectrum.

math.NT↗
arXiv2026

Simultaneous visibility in the algebraic lattice

Let $K$ be a number field with ring of integers $\mathcal{O}$. Two lattice points ${\bf x, y}\in \mathcal{O}^m$ with $m\geq 2$ are said to be visible from one another if $\gcd((x_i-y_i),\ldots, (x_m-y_m))=\mathcal{O}$, where $(x_i-y_i)$ is the ideal generated by $x_i-y_i$. Let $S\subset \mathcal{O}^m$ be a finite set. For $K=\mathbb{Q}$, the asymptotic density of the set of lattice points, visible from all points of $S$, was studied by several authors. For general number fields $K$, however, the asymptotic density has been studied only in the special case $S=\{(0,\ldots,0)\}$. Our main result establishes the corresponding density formula for a number field $K$ whose ring of integers $\mathcal{O}$ is a principal ideal domain, for all finite sets $S$ with $|S|\geq 2$.

math.NT↗
arXiv2025

Analysis of Hematocrit-Plasma Separation in a Trifurcated Microchannel by a Diffusive Flux Model

Platelet-enriched plasma and red blood cells (RBC) are needed in the treatment of blood-related diseases, including anaemia and blood cancer. These essential components must be separated from blood in well-designed experimental setups. If active techniques are used, the blood components are likely to be damaged or contaminated while handling. Passive techniques for component separation are preferred, and their design for effectiveness before manufacturing is the subject of this article. Specifically, the performance of a design consisting of a trifurcated microchannel is examined in the framework of 3D numerical simulation, following similar design ideas in recent experimental studies. The influence of geometrical parameters of the channel, such as width and separation arm angle, inlet extension, flow constriction, and flow parameters, including flow rates, hematocrit concentration, and temperature, is studied. The present study utilizes the diffusive flux model (DFM) to model the shear-driven migration of red blood cells (RBC) in a microchannel along with an appropriate rheology model. The physical mechanism driving separation is the formation of the cell-free layer near the walls, using which the separation efficiency and device effectiveness are quantified. It is found that a microchannel with a smaller width and an extended inlet, along with diluted blood samples of lower hematocrit, is effective for greater separation, while the device performance is less sensitive to the flow rates, flow constriction, and the separator angle.

physics.flu-dyn↗
arXiv2025

On the error bounds for visible points in some cut-and-project sets

We study points in cut-and-project sets which are visible from the origin, continuing a direction of inquiry initiated in [6,14] where the asymptotic density of visible points was investigated. We establish an error bound for the density of visible points in certain cases. We also prove that the set of visible points in irreducible cut-and-project sets with star-shaped windows is never relatively dense.

math.DS↗
arXiv2025

Effects of Geometric Modelling and Blood Rheology in Patient-Specific Arterial Blood Flow Simulations with Speed-Accuracy Trade-Off Analysis

This study investigates the effects of geometric model reduction on blood flow simulations in the patient-specific descending aorta, followed by speed-accuracy trade-off analysis using 3D simulations. We demonstrate how wall shear stresses (WSS) can be reliably estimated for such realistic arteries using significantly faster simulations of highly idealized equivalent geometries, for any blood rheology model. CFD simulations (3D) are performed at two levels of geometry reduction employing realistic pulsatile inflow and pressure outlet boundary conditions and utilizing both Newtonian and non-Newtonian blood rheology models, including the one developed recently by Apostolidis and Beris. The first level of reduction does not retain effects due to local asymmetry but can approximate various flow parameters and patterns, while showing a significant computational speedup. However, further simplification to an idealized smooth geometry loses all information about the vortex structures and flow circulation. The non-Newtonian models retain more accuracy than the Newtonian models in geometry reductions, as quantified by correlations defined in this study. The idealized smooth geometry, combined with area correction, yields WSS estimates that closely approximate those of the actual artery. This study is expected to be applicable in geometric reductions (and speed enhancements) for more complex patient-specific 3D simulations while maintaining accuracy.

physics.flu-dyn↗
arXiv2025

The density conjecture for Juddian points for the quantum Rabi model

We study doubly degenerate (Juddian) eigenvalues for the Quantum Rabi Hamiltonian, a simple model of the interaction between a two-level atom and a single quantized mode of light. We prove a strong form of the density conjecture of Kimoto, Reyes-Bustos, and Wakayama, showing that any fixed value of the splitting between the two atomic levels, there is a dense set of coupling strengths for which the corresponding Rabi Hamiltonian admits Juddian eigenvalues. We also construct infinitely many sets of parameters for which the Rabi Hamiltonian admits two distinct Juddian eigenvalues. The fine structure of the zeros of classical Laguerre polynomials plays a key role in our methods.

math.SP↗
arXiv2024

Exceptional Points for Density Modulo 1

It is well known that almost every dilation of a sequence of real numbers, that diverges to $\infty$, is dense modulo~1. This paper studies the exceptional set of points -- those for which the dilation is not dense. Specifically, we consider the Hausdorff and modified box dimensions of the set of exceptional points. In particular, we show that the dimension of this set may be any number between 0 and 1. Similar results are obtained for two ``natural'' subsets of the set of exceptional points. Furthermore, the paper calculates the dimension of several sets of points, defined by certain constraints on their binary expansion.

math.NT↗
arXiv2024

Exact expressions for the maximal probability that all $k$-wise independent bits are 1

Let $M(n, k, p)$ denote the maximum probability of the event $X_1 = X_2 = \cdots = X_n=1$ under a $k$-wise independent distribution whose marginals are Bernoulli random variables with mean $p$. A long-standing question is to calculate $M(n, k, p)$ for all values of $n,k,p$. This question has been partially addressed by several authors, primarily with the goal of answering asymptotic questions. The present paper focuses on obtaining exact expressions for this probability. To this end, we provide closed-form formulas of $M(n,k,p)$ for $p$ near 0 as well as $p$ near 1.

math.PR↗
arXiv2024

Simultaneous visibility in the integer lattice

Two lattice points are visible from one another if there is no lattice point on the open line segment joining them. Let $S$ be a finite subset of $\mathbb{Z}^k$. The asymptotic density of the set of lattice points, visible from all points of $S$, was studied by several authors. Our main result is an improved upper bound on the error term. We also find the Schnirelmann density of the set of visible points from some sets S. Finally, we discuss these questions from the point of view of ergodic theory.

math.NT↗
arXiv2024

AlabOS: A Python-based Reconfigurable Workflow Management Framework for Autonomous Laboratories

The recent advent of autonomous laboratories, coupled with algorithms for high-throughput screening and active learning, promises to accelerate materials discovery and innovation. As these autonomous systems grow in complexity, the demand for robust and efficient workflow management software becomes increasingly critical. In this paper, we introduce AlabOS, a general-purpose software framework for orchestrating experiments and managing resources, with an emphasis on automated laboratories for materials synthesis and characterization. AlabOS features a reconfigurable experiment workflow model and a resource reservation mechanism, enabling the simultaneous execution of varied workflows composed of modular tasks while eliminating conflicts between tasks. To showcase its capability, we demonstrate the implementation of AlabOS in a prototype autonomous materials laboratory, A-Lab, with around 3,500 samples synthesized over 1.5 years.

cond-mat.mtrl-sci↗
arXiv2021

Dimethylammonium additives alter both vertical and lateral composition in halide perovskite semiconductors

Adding a large A-site cation, such as dimethylammonium (DMA), to the perovskite growth solution has been shown to improve performance and long-term operational stability of halide perovskite solar cells. To better understand the origins of these improvements, we explore the changes in film structure, composition, and optical properties of a formamidinium (FA), Cs, Pb, mixed halide perovskite following addition of DMA to the perovskite growth solution in the ratio DMA0.1FA0.6Cs0.3Pb(I0.8Br0.2)3. Using time-of-flight secondary-ion mass spectrometry (TOF-SIMS) we show that DMA is indeed incorporated into the perovskite, with a higher DMA concentration at the surface. Using a combination of PL microscopy and photo-induced force microscopy-based (PiFM) nanoinfrared (nanoIR), we demonstrate that incorporating DMA into the film leads to increased local heterogeneity in the local bandgap, and clustering of the local formamidinium (CH5N2+) composition. In addition, using nano-X-ray diffraction, we demonstrate that DMA incorporation also alters the local structural composition by changing the local d-spacing distribution and grain size. Our results suggest that compositional variations in the organic cations at the A-site drive the structural heterogeneity observed in case of DMA incorporated films. Our results also suggest that while current-DMA-additive based approaches do have benefits to operational stability and device performance, process optimization to achieve local compositional and structural homogeneity could further boost both of these gains in performance, bringing further gains to solar cells using DMA additives.

physics.app-ph↗
arXiv2018

Method for Hybrid Precision Convolutional Neural Network Representation

This invention addresses fixed-point representations of convolutional neural networks (CNN) in integrated circuits. When quantizing a CNN for a practical implementation there is a trade-off between the precision used for operations between coefficients and data and the accuracy of the system. A homogenous representation may not be sufficient to achieve the best level of performance at a reasonable cost in implementation complexity or power consumption. Parsimonious ways of representing data and coefficients are needed to improve power efficiency and throughput while maintaining accuracy of a CNN.

cs.NE↗