arXiv subjects

Ayush Saurabh

Publications and source records attributed to Ayush Saurabh.

14 recordsLinked to original sources

arXiv2026

Revisiting the scale dependence of the Reynolds number in correlated fluctuating fluids

For the incompressible Navier--Stokes equation, the Reynolds number ($\mathrm{Re}$) is a dimensionless parameter quantifying the relative importance of inertial over viscous forces. In the low-$\mathrm{Re}$ regime ($\mathrm{Re} \ll 1$), the flow dynamics are commonly approximated by the linear Stokes equation. Here we show that, within the framework of spatially fluctuating hydrodynamics, this linearization breaks down when the thermal noise is spatially correlated, even if $\mathrm{Re} \ll 1$. We perform direct numerical simulations of spatially correlated fluctuating hydrodynamics in both one and two dimensions. In one dimension, the linearized dynamics exhibit significantly slower relaxation of high-wavenumber Fourier modes than the full nonlinear dynamics. In two dimensions, an analogous discrepancy arises in the particle velocity autocorrelation function, which decays more slowly in the correlated linear Stokes case than in the correlated nonlinear Navier--Stokes case. In both settings, spatial correlations inhibit viscous momentum diffusion at small scales, leading to prolonged relaxation under the linear dynamics, whereas nonlinear mode coupling accelerates small-scale relaxation. Thus, the interplay between nonlinear coupling and viscous damping becomes scale dependent, invalidating the use of a single global Reynolds number. Taken together, these findings show that, for spatially correlated fluctuating fluids, the effective Reynolds number must be reinterpreted as a scale-dependent quantity.

physics.flu-dyn↗

arXiv2025

Spatially Correlated Noise Induces Transitions from the Diffusive to Ballistic Regime in Fluids

We investigate the fluctuating incompressible Navier--Stokes equation driven by spatially correlated thermal noise characterized by a single length scale. This formulation is constructed to preserve thermal equilibrium through the fluctuation--dissipation relation (FDR), which enforces the same spatial correlation in the viscous diffusion term and therefore gives rise to nonlocal momentum transport. Numerical simulations of tracer diffusion in fluids governed by this formulation reveal that the mean-squared displacement (MSD) depends monotonically on the correlation length $\ell$ and the correlation strength $β$. Intuitively, increasing $\ell$ enhances MSD and induces the emergence of an early-time ballistic regime, as a larger correlation length slows momentum diffusion. Counterintuitively, decreasing $β$ also increases the MSD, since a weaker correlation strength also retards momentum diffusion, whereas smaller $\ell$ or larger $β$ suppresses the ballistic regime and leads to a diffusive behavior. The emergence or suppression of the ballistic regime stems from how spatial correlations, incorporated through the FDR to maintain equilibrium, alter the effective momentum transport across scales. Interestingly, we further show that the resulting nonlocal diffusion is reminiscent of the slow dynamics in glassy and other disordered systems.

physics.bio-ph↗

arXiv2025

A cautious user's guide in applying HMMs to physical systems

Nature, as far as we know, evolves continuously through space and time. Yet the ubiquitous hidden Markov model (HMM)--originally developed for discrete time and space analysis in natural language processing--remains a central tool in interpreting time series data drawn from from physical systems. This raises a fundamental question: What are the implications of applying a discrete-state, discrete-time framework to analyze data generated by a continuously evolving system? Through synthetic data generated using Langevin dynamics in an effective potential, we explore under what circumstances HMMs yield interpretable results. Our analysis reveals that the discrete-state approximation acts primarily as an abstraction with the inferred states visited in time often more closely reflecting the measurement protocol and modeling choices than features of the underlying physical potential. Crucially, we demonstrate that the states visited over the course of a time series recovered by the HMM can be tuned a priori by adjusting the data acquisition scheme even misleadingly recovering reproducible "intermediate" states using different HMM tools for a system evolving in a single well potential. We conclude with a note of measured caution: while HMMs offer a mathematically elegant framework for time series inference, their use in physical modeling should be guided by an awareness of their limitations. In this light, we outline important generalizations of the HMM to continuous space and time and highlight the importance of a well calibrated measurement noise model.

q-bio.BM↗

arXiv2025

Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve

Across the scientific realm, we find ourselves subtracting or dividing stochastic signals. For instance, consider a stochastic realization, $x$, generated from the addition or multiplication of two stochastic signals $a$ and $b$, namely $x=a+b$ or $x = ab$. For the $x=a+b$ example, $a$ can be fluorescence background and $b$ the signal of interest whose statistics are to be learned from the measured $x$. Similarly, when writing $x=ab$, $a$ can be thought of as the illumination intensity and $b$ the density of fluorescent molecules of interest. Yet dividing or subtracting stochastic signals amplifies noise, and we ask instead whether, using the statistics of $a$ and the measurement of $x$ as input, we can recover the statistics of $b$. Here, we show how normalizing flows can generate an approximation of the probability distribution over $b$, thereby avoiding subtraction or division altogether. This method is implemented in our software package, NFdeconvolve, available on GitHub with a tutorial linked in the main text.

stat.ML↗

arXiv2024

Re-thinking Richardson-Lucy without Iteration Cutoffs: Physically Motivated Bayesian Deconvolution

Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is achieved by iteratively maximizing a Poisson emission likelihood. However, the RL algorithm is known to prefer sparse solutions and overfit noise, leading to high-frequency artifacts. The structure of these artifacts is sensitive to the number of RL iterations, and this parameter is typically hand-tuned to achieve reasonable perceptual quality of the inferred object. Overfitting can be mitigated by introducing tunable regularizers or other ad hoc iteration cutoffs in the optimization as otherwise incorporating fully realistic models can introduce computational bottlenecks. To resolve these problems, we present Bayesian deconvolution, a rigorous deconvolution framework that combines a physically accurate image formation model avoiding the challenges inherent to the RL approach. Our approach achieves deconvolution while satisfying the following desiderata: I deconvolution is performed in the spatial domain (as opposed to the frequency domain) where all known noise sources are accurately modeled and integrated in the spirit of providing full probability distributions over the density of the putative object recovered; II the probability distribution is estimated without making assumptions on the sparsity or continuity of the underlying object; III unsupervised inference is performed and converges to a stable solution with no user-dependent parameter tuning or iteration cutoff; IV deconvolution produces strictly positive solutions; and V implementation is amenable to fast, parallelizable computation.

cs.CV↗

arXiv2022

Modeling Non-additive Effects in Neighboring Chemically Identical Fluorophores

Quantitative fluorescence analysis is often used to derive chemical properties, including stoichiometries, of biomolecular complexes. One fundamental underlying assumption in the analysis of fluorescence data -- whether it be the determination of protein complex stoichiometry by super-resolution, or step-counting by photobleaching, or the determination of RNA counts in diffraction-limited spots in RNA fluorescence {\it in situ} hybridization (RNA-FISH) experiments -- is that fluorophores behave identically and do not interact. However, recent experiments on fluorophore-labeled DNA-origami structures such as fluorocubes have shed light on the nature of the interactions between identical fluorophores as these are brought closer together, thereby raising questions on the validity of the modeling assumption that fluorophores do not interact. Here, we analyze photon arrival data under pulsed illumination from fluorocubes where distances between dyes range from 2-10 nm. We discuss the implications of non-additivity of brightness on quantitative fluorescence analysis.

physics.chem-ph↗

arXiv2020

Decay of Cosmic Global String Loops

We numerically study the decay of cosmic global string loops due to radiation of Goldstone bosons and massive scalar ($χ$) particles. The length of loops we study range from 200-1000 times the width of the string core. We find that the lifetime of a loop is $\approx 1.4 L$. The energy spectrum of Goldstone boson radiation has a $k^{-1}$ fall off, where $k$ is the wavenumber, and a sharp peak at $k \approx m_χ/2$, where $m_χ$ is the mass of $χ$. The latter is a new feature and implies a peak at high energies (MeV-GeV) in the cosmological distribution of QCD axions.

hep-ph↗

arXiv2019

Decay of Cosmic String Loops Due to Particle Radiation

Constraints on the tension and the abundance of cosmic strings depend crucially on the rate at which they decay into particles and gravitational radiation. We study the decay of cosmic string loops in the Abelian-Higgs model by performing field theory simulations of loop formation and evolution. We find that our set of string loops emit particle radiation primarily due to kink collisions, and that their decay time due to these losses is proportional to $L^p$ with $p \approx 2$ where $L$ is the loop length. In contrast, the decay time to gravitational radiation scales in proportion to $L$, and we conclude that particle emission is the primary energy loss mechanism for loops smaller than a critical length scale, while gravitational losses dominate for larger loops.

hep-ph↗

arXiv2019

Monopole-antimonopole: interaction, scattering and creation

The interaction of a magnetic monopole-antimonopole pair depends on their separation as well as on a second "twist" degree of freedom. This novel interaction leads to a non-trivial bound state solution known as a sphaleron and to scattering in which the monopole-antimonopole bounce off each other and do not annihilate. The twist degree of freedom also plays a role in numerical experiments in which gauge waves collide and create monopole-antimonopole pairs. Similar gauge wavepacket scatterings in the Abelian-Higgs model lead to the production of string loops that may be relevant to superconductors. Ongoing numerical experiments to study the production of electroweak sphalerons that result in changes in the Chern-Simons number, and hence baryon number, are also described but have not yet met with success.

hep-th↗

arXiv2018

String Production in the Abelian Higgs Vacuum

We numerically study string production by evolving classical Abelian-Higgs gauge field wavepackets. Initial conditions are constructed for the propagation of a single wavepacket and for the collision of two wavepackets. We identify regions of parameter space that lead to prompt production of strings from a single wavepacket. The collision of two sub-critical wavepackets can also lead to the production of strings in certain regions of parameter space.

hep-th↗

arXiv2018

Monopole-antimonopole Interaction Potential

We numerically study the interactions of twisted monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of values of the scalar to vector mass ratio. We also recover the sphaleron solution at maximum twist discovered by Taubes, and map out its energy and size as functions of parameters.

hep-th↗

arXiv2014

Strings vs Spins on the Null Orbifold

We study the null orbifold singularity in 2+1 d flat space higher spin theory as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein gravity, we first observe that despite the singular nature of this geometry, the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a resolution of the singularity in higher spin theory: a Kundt spacetime with vanishing scalar curvature invariants. We also point out that the UV divergences previously observed in the 2-to-2 tachyon tree level string amplitude on the null orbifold do not arise in the $α^\prime\to \infty$ limit. We find all the divergences of the amplitude and demonstrate that the ones remaining in the tensionless limit are physical IR-type divergences. We conclude with a discussion on the meaning and limitations of higher spin (cosmological) singularity resolution and its potential connection to string theory.

hep-th↗

arXiv2014

Low Tension Strings on a Cosmological Singularity

It has recently been argued that the singularity of the Milne orbifold can be resolved in higher spin theories. In string theory scattering amplitudes, however, the Milne singularity gives rise to ultraviolet divergences that signal uncontrolled backreaction. Since string theory in the low tension limit is expected to be a higher spin theory (although precise proposals only exist in special cases), we investigate what happens to these scattering amplitudes in the low tension limit. We point out that the known problematic ultraviolet divergences disappear in this limit. In addition we systematically identify all divergences of the simplest 2-to-2 string scattering amplitude on the Milne orbifold, and argue that the divergences that survive in the low tension limit have sensible infrared interpretations.

hep-th↗

arXiv2014

A Stochasticity Threshold in Holography and and the Instability of AdS

We give strong numerical evidence that a self-interacting probe scalar field in AdS, with only a few modes turned on initially, will undergo fast thermalization only if it is above a certain energetic threshold. Below the threshold the energy stays close to constant in a few modes for a very long time instead of cascading quickly. This indicates the existance of a Strong Stochasticity Threshold (SST) in holography. The idea of SST is familiar from certain statistical mechanical systems, and we suggest that it exists also in AdS gravity. This would naturally reconcile the generic non-linear instability of AdS observed by Bizon and Rostworowski, with the Fermi-Pasta-Ulam-Tsingou-like quasi-periodocity noticed recently for some classes of initial conditions. We show that our simple set-up captures many of the relevant features of the full gravity-scalar system.

hep-th↗