arXiv subjects

Anuj Kumar

Publications and source records attributed to Anuj Kumar.

At least 55 records · Page 3Linked to original sources

arXiv2024

Almost anomalous dissipation in advection-diffusion of a divergence-free passive vector

We explore the advection-diffusion of a passive vector described by $\partial_t u + U \cdot \nabla u = - \nabla p + νΔu$, where both $U$ and $u$ are divergence-free velocity fields. We approach this equation from an input/output perspective, with $U$ as the input and $u$ as the output. This input/output viewpoint has been widely applied in recent studies on passive scalar equation, in the context of anomalous dissipation, mixing, optimal scalar transport, and nonuniqueness problems. What makes the passive vector equation considerably more challenging compared to the passive scalar equation is the lack of a Lagrangian perspective due to the presence of pressure. In this paper, rather than requiring $U$ and $u$ to be identical (as in the Navier-Stokes equation), we require $U$ and $u$ to be identical only in certain characteristics. We focus on the case where the characteristics in question are anomalous and enhanced dissipation. We study the advection-diffusion of a passive vector in a Couette flow configuration. The main result of this paper is a construction of the velocity field $U$ for which the energy dissipation scales as $(\log ν^{-1})^{-2}$ such that the energy dissipation in velocity field $u$ scales at least as $(\log ν^{-1})^{-2}$. This means that both $U$ and $u$ exhibit near-anomalous dissipation, where the rate of energy dissipation decreases more slowly than any power-law $ν^α$ for any $α> 0$. The result in this paper is not just a mathematical construct; it closely resembles the behavior of turbulent flow in a channel. The $(\log ν^{-1})^{-2}$ decrease of energy dissipation is predicted by phenomenological theories of wall-bounded turbulence, a prediction that has been extensively validated through experiments and numerical simulations.

math.AP↗

arXiv2024

Structural, micro-structural/morphological and magnetic properties of RECrO3 (RE = La, Nd, Sm, Eu and Gd) Orthocromites

We report here the structural, micro-structural/morphological and detailed magnetic properties of RECrO3 (RE = La, Nd, Sm, Eu and Gd) Orthocromites. A series of RECrO3 (RE = La, Nd, Sm, Eu and Gd) Orthocromites polycrystalline samples with uniform particle size were synthesized via standard solid-state reaction method. LaCrO3 (LCO), NdCrO3 (NCO), SmCrO3(SCO), and EuCrO3 (ECO) crystallizes in single phase of orthorhombic structure with Pnma (No.62) space group while GdCrO3 (GCO) found to crystallize in orthorhombic phase with Pbnm space group. SEM images confirms the systematic growth of all studied samples grain growth takes place during the sintering process and images shows the polyhedral shape with varying average grain size ranging from approximately 1.0μm to 3μm confirm the bulk synthesis of studied RECrO3. Lowest average grain size (~ 1.1μm) was observed for LaCrO3 and maximum (~ 2.8μm) for EuCrO3. The shapes of the grain size changes because of crystal lattice distortion induced by various rare earths (La, Nd, Sm, Eu and Gd) at A site. Energy dispersive X-ray Analysis (EDAX) reveals the elements confirmation in different studied RECrO3 samples. Within the detection limit of EDAX no impurity elements were observed in different as synthesized RECrO3 samples. Temperature dependent DC magnetization (M-T) studies showed an antiferromagnetic transition (TN) attributed to Cr3+ spins in all samples at different temperature. At low temperature spin-reorientation (TSR) of rare earth ion was also observed in NCO, SCO at around 50K and the same is observed at around 30K in ECO and the same was missing in GCO because of large moment of Gd3+ ions attributed by ground state spectroscopic term 8S7/2 by external applied magnetic field. The magnetization versus applied magnetic field (M-H) loops exhibited ferromagnetic like behavior at 10K and 100K and paramagnetic at 300K for GCO.

cond-mat.mtrl-sci↗

arXiv2024

Doppelgänger's Watch: A Split Objective Approach to Large Language Models

In this paper, we investigate the problem of "generation supervision" in large language models, and present a novel bicameral architecture to separate supervision signals from their core capability, helpfulness. Doppelgänger, a new module parallel to the underlying language model, supervises the generation of each token, and learns to concurrently predict the supervision score(s) of the sequences up to and including each token. In this work, we present the theoretical findings, and leave the report on experimental results to a forthcoming publication.

cs.CL↗

arXiv2024

An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods

Mathematical analysis of the analytic hierarchy process (AHP) led to the development of a mathematical function, usually called the inconsistency index, which has the center role in measuring the inconsistency of the judgements in AHP. Inconsistency index is a mathematical function which maps every pairwise comparison matrix (PCM) into a real number. An inconsistency index can be considered more trustworthy when it satisfies a set of suitable properties. Therefore, the research community has been trying to postulate a set of desirable rules (axioms, properties) for inconsistency indices. Subsequently, many axiomatic frameworks for these functions have been suggested independently, however, the literature on the topic is fragmented and missing a broader framework. Therefore, the objective of this article is twofold. Firstly, we provide a comprehensive review of the advancements in the axiomatization of inconsistency indices' properties during the last decade. Secondly, we provide a comparison and discussion of the aforementioned axiomatic structures along with directions of the future research.

cs.LO↗

arXiv2024

Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity

We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of $L^\infty L^2$ weak solutions with vorticity in $L^\infty L^p$ for some $p>1$, surpassing for the first time the critical scaling of the standard convex integration technique. To achieve this, we introduce several new ideas, including: (i) A new family of building blocks built from the Lamb-Chaplygin dipole. (ii) A new method to cancel the error based on time averages and non-periodic, spatially-anisotropic perturbations.

math.AP↗

arXiv2024

Lumos : Empowering Multimodal LLMs with Scene Text Recognition

We introduce Lumos, the first end-to-end multimodal question-answering system with text understanding capabilities. At the core of Lumos is a Scene Text Recognition (STR) component that extracts text from first person point-of-view images, the output of which is used to augment input to a Multimodal Large Language Model (MM-LLM). While building Lumos, we encountered numerous challenges related to STR quality, overall latency, and model inference. In this paper, we delve into those challenges, and discuss the system architecture, design choices, and modeling techniques employed to overcome these obstacles. We also provide a comprehensive evaluation for each component, showcasing high quality and efficiency.

cs.CV↗

arXiv2024

NH3 gas sensing over 2D Phosphorene sheet: A First-Principles Study

First-principles based calculations were executed to investigate the sensing properties of ammonia gas molecules on two-dimensional pristine black phosphorene towards its application as a gas sensor and related applications. We discuss in detail, the interaction of ammonia gas molecules on the phosphorene single sheet through the structural change analysis, electronic band gap, Bader charge transfer, and density-of-states calculations. Our calculations indicate that the phosphorene could be used as a detector of ammonia, where good sensitivity and very short recovery time at room temperature have confirmed the potential use of phosphorene in the detection of ammonia.

cond-mat.mtrl-sci↗

arXiv2024

Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field

Given a divergence-free vector field ${\bf u} \in L^\infty_t W^{1,p}_x(\mathbb R^d)$ and a nonnegative initial datum $ρ_0 \in L^r$, the celebrated DiPerna--Lions theory established the uniqueness of the weak solution in the class of $L^\infty_t L^r_x$ densities for $\frac{1}{p} + \frac{1}{r} \leq 1$. This range was later improved in [BCDL21] to $\frac{1}{p} + \frac{d-1}{dr} \leq 1$. We prove that this range is sharp by providing a counterexample to uniqueness when $\frac{1}{p} + \frac{d-1}{dr} > 1$. To this end, we introduce a novel flow mechanism. It is not based on convex integration, which has provided a non-optimal result in this context, nor on purely self-similar techniques, but shares features of both, such as a local (discrete) self similar nature and an intermittent space-frequency localization.

math.AP↗

arXiv2024

A Posteriori Evaluation of a Physics-Constrained Neural Ordinary Differential Equations Approach Coupled with CFD Solver for Modeling Stiff Chemical Kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system of coupled stiff ordinary differential equations (ODEs). While deep learning techniques have been experimented with to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because deep learning methods optimize for training error without ensuring compatibility with ODE solvers, leading to accumulation of errors over time. Recently, NeuralODE-based techniques have offered a promising solution by effectively modeling chemical kinetics. In this study, we extend the NeuralODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass and the elemental mass are conserved, a critical requirement for reliable downstream integration with CFD solvers. Proof-of-concept studies are performed with physics-constrained neuralODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. Our results demonstrate that this enhancement not only improves the physical consistency with respect to mass conservation criteria but also ensures better robustness. Lastly, a posteriori studies are performed wherein the trained PC-NODE model is coupled with a 3D CFD solver for computing the chemical source terms. PC-NODE is shown to be more accurate relative to the purely data-driven neuralODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

physics.comp-ph↗

arXiv2023

Nonuniqueness of trajectories on a set of full measure for Sobolev vector fields

In this paper, we resolve an important long-standing question of Alberti \cite{alberti2012generalized} that asks if there is a continuous vector field with bounded divergence and of class $W^{1, p}$ for some $p \geq 1$ such that the ODE with this vector field has nonunique trajectories on a set of initial conditions with positive Lebesgue measure? This question belongs to the realm of well-known DiPerna--Lions theory for Sobolev vector fields $W^{1, p}$. In this work, we design a divergence-free vector field in $W^{1, p}$ with $p < d$ such that the set of initial conditions for which trajectories are not unique is a set of full measure. The construction in this paper is quite explicit; we can write down the expression of the vector field at any point in time and space. Moreover, our vector field construction is novel. We build a vector field $\boldsymbol{u}$ and a corresponding flow map $X^{\boldsymbol{u}}$ such that after finite time $T > 0$, the flow map takes the whole domain $\mathbb{T}^d$ to a Cantor set $\mathcal{C}_Φ$, i.e., $X^{\boldsymbol{u}}(T, \mathbb{T}^d) = \mathcal{C}_Φ$ and the Hausdorff dimension of this Cantor set is strictly less than $d$. The flow map $X^{\boldsymbol{u}}$ constructed as such is not a regular Lagrangian flow. The nonuniqueness of trajectories on a full measure set is then deduced from the existence of the regular Lagrangian flow in the DiPerna--Lions theory.

math.AP↗

arXiv2023

Multiple Protein Profiler 1.0 (MPP): A webserver for predicting and visualizing physiochemical properties of proteins at the proteome level

Determining the physicochemical properties of a protein can reveal important insights in their structure, biological functions, stability, and interactions with other molecules. Although tools for computing properties of proteins already existed, we could not find a comprehensive tool that enables the calculations of multiple properties for multiple input proteins on the proteome level at once. Facing this limitation, we have developed Multiple Protein Profiler (MPP) 1.0 as an integrated tool that allows the profiling of 12 individual properties of multiple proteins in a significant manner. MPP provides a tabular and graphic visualization of properties of multiple proteins. The tool is freely accessible at https://mproteinprofiler.microbiologyandimmunology.dal.ca/

q-bio.BM↗

arXiv2023

AnyMAL: An Efficient and Scalable Any-Modality Augmented Language Model

We present Any-Modality Augmented Language Model (AnyMAL), a unified model that reasons over diverse input modality signals (i.e. text, image, video, audio, IMU motion sensor), and generates textual responses. AnyMAL inherits the powerful text-based reasoning abilities of the state-of-the-art LLMs including LLaMA-2 (70B), and converts modality-specific signals to the joint textual space through a pre-trained aligner module. To further strengthen the multimodal LLM's capabilities, we fine-tune the model with a multimodal instruction set manually collected to cover diverse topics and tasks beyond simple QAs. We conduct comprehensive empirical analysis comprising both human and automatic evaluations, and demonstrate state-of-the-art performance on various multimodal tasks.

cs.LG↗

arXiv2023

A Framework for Combustion Chemistry Acceleration with DeepONets

A combustion chemistry acceleration scheme is developed based on deep operator networks (DeepONets). The scheme is based on the identification of combustion reaction dynamics through a modified DeepOnet architecture such that the solutions of thermochemical scalars are projected to new solutions in small and flexible time increments. The approach is designed to efficiently implement chemistry acceleration without the need for computationally expensive integration of stiff chemistry. An additional framework of latent-space dynamics identification with modified DeepOnet is also proposed which enhances the computational efficiency and widens the applicability of the proposed scheme. The scheme is demonstrated on simple chemical kinetics of hydrogen oxidation to more complex chemical kinetics of n-dodecane high- and low-temperature oxidations. The proposed framework accurately learns the chemical kinetics and efficiently reproduces species and temperature temporal profiles corresponding to each application. In addition, a very large speed-up with a great extrapolation capability is also observed with the proposed scheme.

physics.chem-ph↗

arXiv2023

Extended Feature Space-Based Automatic Melanoma Detection System

Melanoma is the deadliest form of skin cancer. Uncontrollable growth of melanocytes leads to melanoma. Melanoma has been growing wildly in the last few decades. In recent years, the detection of melanoma using image processing techniques has become a dominant research field. The Automatic Melanoma Detection System (AMDS) helps to detect melanoma based on image processing techniques by accepting infected skin area images as input. A single lesion image is a source of multiple features. Therefore, It is crucial to select the appropriate features from the image of the lesion in order to increase the accuracy of AMDS. For melanoma detection, all extracted features are not important. Some of the extracted features are complex and require more computation tasks, which impacts the classification accuracy of AMDS. The feature extraction phase of AMDS exhibits more variability, therefore it is important to study the behaviour of AMDS using individual and extended feature extraction approaches. A novel algorithm ExtFvAMDS is proposed for the calculation of Extended Feature Vector Space. The six models proposed in the comparative study revealed that the HSV feature vector space for automatic detection of melanoma using Ensemble Bagged Tree classifier on Med-Node Dataset provided 99% AUC, 95.30% accuracy, 94.23% sensitivity, and 96.96% specificity.

cs.LG↗

arXiv2022

An Indian Roads Dataset for Supported and Suspended Traffic Lights Detection

Autonomous vehicles are growing rapidly, in well-developed nations like America, Europe, and China. Tech giants like Google, Tesla, Audi, BMW, and Mercedes are building highly efficient self-driving vehicles. However, the technology is still not mainstream for developing nations like India, Thailand, Africa, etc., In this paper, we present a thorough comparison of the existing datasets based on well-developed nations as well as Indian roads. We then developed a new dataset "Indian Roads Dataset" (IRD) having more than 8000 annotations extracted from 3000+ images shot using a 64 (megapixel) camera. All the annotations are manually labelled adhering to the strict rules of annotations. Real-time video sequences have been captured from two different cities in India namely New Delhi and Chandigarh during the day and night-light conditions. Our dataset exceeds previous Indian traffic light datasets in size, annotations, and variance. We prove the amelioration of our dataset by providing an extensive comparison with existing Indian datasets. Various dataset criteria like size, capturing device, a number of cities, and variations of traffic light orientations are considered. The dataset can be downloaded from here https://sites.google.com/view/ird-dataset/home

cs.CV↗

arXiv2022

Three dimensional branching pipe flows for optimal scalar transport between walls

We consider the problem of "wall-to-wall optimal transport" in which we attempt to maximize the transport of a passive temperature field between hot and cold plates. Specifically, we optimize the choice of the divergence-free velocity field in the advection-diffusion equation subject to an enstrophy constraint (which can be understood as a constraint on the power required to generate the flow). Previous work established an a priori upper bound on the transport, scaling as the 1/3-power of the flow's enstrophy. Recently, Tobasco & Doering (Phys. Rev. Lett. vol.118, 2017, p.264502}) and Doering & Tobasco (Comm. Pure Appl. Math. vol.72, 2019, p.2385--2448}) constructed self-similar two-dimensional steady branching flows saturating this bound up to a logarithmic correction. This logarithmic correction appears to arise due to a topological obstruction inherent to two-dimensional steady branching flows. We present a construction of three-dimensional "branching pipe flows" that eliminates the possibility of this logarithmic correction and therefore identifies the optimal scaling as a clean 1/3-power law. Our flows resemble previous numerical studies of the three-dimensional wall-to-wall problem by Motoki, Kawahara & Shimizu (J. Fluid Mech. vol.851, 2018, p.R4}). We also discuss the implications of our result to the heat transfer problem in Rayleigh--Bénard convection and the problem of anomalous dissipation in a passive scalar.

math.AP↗

arXiv2022

Optimal bounds in Taylor--Couette flow

This paper is concerned with the optimal upper bound on mean quantities (torque, dissipation and the Nusselt number) obtained in the framework of the background method for the Taylor--Couette flow with a stationary outer cylinder. Along the way, we perform the energy stability analysis of the laminar flow, and demonstrate that below radius ratio 0.0556, the marginally stable perturbations are not the axisymmetric Taylor vortices but rather a fully three-dimensional flow. The main result of the paper is an analytical expression of the optimal bound as a function of the radius ratio. To obtain this bound, we begin by deriving a suboptimal analytical bound using analysis techniques. We use a definition of the background flow with two boundary layers, whose relative thicknesses are optimized to obtain the bound. In the limit of high Reynolds number, the dependence of this suboptimal bound on the radius ratio (the geometrical scaling) turns out to be the same as that of numerically computed optimal bounds in three different cases: (1) where the perturbed flow only satisfies the homogeneous boundary conditions but need not be incompressible, (2) the perturbed flow is three dimensional and incompressible, (3) the perturbed flow is two dimensional and incompressible. We compare the geometrical scaling with the observations from the turbulent Taylor--Couette flow, and find that the analytical result indeed agrees well with the available DNS data. In this paper, we also dismiss the applicability of the background method to certain flow problems and therefore establish the limitation of this method.

physics.flu-dyn↗

arXiv2021

Analytical bounds on the heat transport in internally heated convection

We obtain an analytical bound on the mean vertical convective heat flux $\langle w T \rangle$ between two parallel boundaries driven by uniform internal heating. We consider two configurations, one with both boundaries held at the same constant temperature, and the other one with a top boundary held at constant temperature and a perfectly insulating bottom boundary. For the first configuration, Arslan et al. (J. Fluid Mech. 919:A15, 2021) recently provided numerical evidence that Rayleigh-number-dependent corrections to the only known rigorous bound $\langle w T \rangle \leq 1/2$ may be provable if the classical background method is augmented with a minimum principle stating that the fluid's temperature is no smaller than that of the top boundary. Here, we confirm this fact rigorously for both configurations by proving bounds on $\langle wT \rangle$ that approach $1/2$ exponentially from below as the Rayleigh number is increased. The key to obtaining these bounds are inner boundary layers in the background fields with a particular inverse-power scaling, which can be controlled in the spectral constraint using Hardy and Rellich inequalities. These allow for qualitative improvements in the analysis not available to standard constructions.

physics.flu-dyn↗