arXiv subjects

Archishman Raju

Publications and source records attributed to Archishman Raju.

14 recordsLinked to original sources

arXiv2026

Multi-particle gates on driven one-dimensional paths: probing deep traps

We study single-file transport of driven overdamped colloidal particles on a periodic path with deep potential wells. In the small trap limit (i.e., trap size smaller than particle size), the particle current transitions from zero to finite as the number of particles on the path exceeds a critical number $n_c$. Beyond this threshold, $n_c$ particles cluster behind the trap, demonstrating collective correlated motion. The remaining `extra' particles circulate, giving a finite current. We study this phenomenon numerically using overdamped Brownian dynamics simulations, and present an experimental realization of this behaviour for micron-scale colloidal particles driven in an optical vortex. Using our experimental observations, we present results characterizing potential wells as deep as several hundred $k_BT$.

cond-mat.soft↗

arXiv2025

Unifying Theories in High-Dimensional Biology: Approaches, Challenges and Opportunities

Across biological subdisciplines, the last decade has seen an explosion of high-dimensional datasets, including datasets for cells, species, immune systems, neurons and behaviour. At the ICTS workshop 'Unifying Theories in High-Dimensional Biophysics' we discussed whether this high dimensionality poses a challenge or opportunity for describing, understanding and predicting biological systems theoretically. We discussed methods, models and frameworks that can help with addressing empirical observations based on these high-dimensional datasets. We summarize the challenges and opportunities that emerged in discussions according to individual participants below.

physics.bio-ph↗

arXiv2025

Evolution of phenocopying in a dynamical model of developmental trajectories

Developmental trajectories are known to be canalized, or robust to both environmental and genetic perturbations. However, even when these trajectories are decanalized by an environmental perturbation outside of the range of conditions to which they are robust, they often produce phenotypes similar to known mutants called phenocopies. This correspondence between the effect of environmental and genetic perturbations has received little theoretical attention. Here, we study an abstract regulatory model which is evolved to follow a specific trajectory. We then study the effect of both small and large perturbations to the trajectory both by changing parameters and by perturbing the state in a timed manner. We find, surprisingly, that the phenomenon of phenocopying emerges in evolved trajectories even though the alternative trajectories are not selected for. Our results suggest that evolution simplifies the structure of high-dimensional phenotypic landscapes which can simultaneously show robustness and phenocopying.

physics.bio-ph↗

arXiv2023

A geometrical perspective on development

Cell fate decisions emerge as a consequence of a complex set of gene regulatory networks. Models of these networks are known to have more parameters than data can determine. Recent work, inspired by Waddington's metaphor of a landscape, has instead tried to understand the geometry of gene regulatory networks. Here, we describe recent results on the appropriate mathematical framework for constructing these landscapes. This allows the construction of minimally parameterized models consistent with cell behavior. We review existing examples where geometrical models have been used to fit experimental data on cell fate and describe how spatial interactions between cells can be understood geometrically.

q-bio.QM↗

arXiv2023

Normal forms, universal scaling functions, and extending the validity of the RG

Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases. We explain how to use normal form theory to write universal scaling functions in systems where the renormalization-group flows cannot be linearized. We use the 2d Ising model to demonstrate how to calculate high-precision implementations of universal scaling functions, and how to extend them into a complete description of the surrounding phases. We discuss prospects and challenges involved into extending these early successes to the many other systems where the RG has successfully described emergent scale invariance, making them invaluable tools for engineers, biologists, and social scientists studying complex systems.

cond-mat.stat-mech↗

arXiv2021

Geometry of Gene Regulatory Dynamics

Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types, that elaborates this complexity, result from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all 3-way cellular decisions realisable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form. Turing systems appear non-potential yet in suitable variables the dynamics are low dimensional, potential, and a time independent embedding recovers the biological variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the Drosophila eye appears as relaxation in a bistable potential. Geometric reasoning provides intuitive dynamic models for development that are well adapted to fit time-lapse data.

q-bio.QM↗

arXiv2019

Weird scaling for 2-D avalanches: Curing the faceting, and scaling in the lower critical dimension

The non-equilibrium random-field Ising model is well studied, yet there are outstanding questions. In two dimensions, power law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of faceting on the square lattice creates avalanches that are lattice dependent at small scales. We propose two methods which we find solve these issues. First, we perform large scale simulations on a Voronoi lattice to mitigate the effects of faceting. Secondly, the invariant arguments of the universal scaling functions necessary to perform scaling collapses can be directly determined using our recent normal form theory of the Renormalization Group. This method has proven useful in cleanly capturing the complex behavior which occurs in both the lower and upper critical dimensions of systems and here captures the 2D NE-RFIM behavior well. The obtained scaling collapses span over a range of a factor of ten in the disorder and a factor of $10^4$ in avalanche cutoff. They are consistent with a critical disorder at zero and with a lower critical dimension for the model equal to two.

cond-mat.dis-nn↗

arXiv2019

Normal form for renormalization groups

The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a case-by-case basis. We use the mathematics of normal form theory to systematically group these into universality families of seemingly unrelated systems united by common scaling variables. We recover and explain the existing literature and predict the nonlinear generalization for the universal homogeneous scaling functions. We show that this procedure leads to a better handling of the singularity even in classic cases and elaborate our framework using several examples.

cond-mat.stat-mech↗

arXiv2018

Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class

A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point but, given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed point can go through a Hopf bifurcation, resulting in a critical limit cycle and a concomitant discrete scale invariance. We further investigate a different renormalization scheme and argue that the basin of attraction of the strong-coupling fixed point/limit cycle may thus stay finite for all dimensions.

cond-mat.stat-mech↗

arXiv2018

Reexamining the renormalization group: Period doubling onset of chaos

We explore fundamental questions about the renormalization group through a detailed re-examination of Feigenbaum's period doubling route to chaos. In the space of one-humped maps, the renormalization group characterizes the behavior near any critical point by the behavior near the fixed point. We show that this fixed point is far from unique, and characterize a submanifold of fixed points of alternative RG transformations. We build on this framework to systematically distinguish and analyze the allowed singular and `gauge' (analytic and redundant) corrections to scaling, explaining numerical results from the literature. Our analysis inspires several conjectures for critical phenomena in statistical mechanics.

cond-mat.stat-mech↗

arXiv2017

Finding stability domains and escape rates in kicked Hamiltonians

We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the resonances, the dynamics typically has a finite region in phase space where it is stable. Inherent noise in the system leads to particle loss from this stable region. The competition of this noise with radiation damping, which increases stability, determines the escape rate. Determining this `aperture' and finding escape rates is therefore an important physical problem. We compare the results of two different perturbation theories and a variational method to estimate this stable region. Including noise, we derive analytical estimates for the steady-state populations (and the resulting beam emittance), for the escape rate in the small damping regime, and compare them with numerical simulations.

cond-mat.stat-mech↗

arXiv2016

Deformation of crystals: Connections with statistical physics

We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, and a variety of depinning transitions are explored. Dislocation dynamics in crystals challenges non equilibrium statistical physics. Statistical physics provides both cautionary tales of subtle memory effects in nonequilibrium systems, and systematic tools designed to address complex scale-invariant behavior on multiple length and time scales.

cond-mat.mtrl-sci↗

arXiv2015

Information Geometry and the Renormalization Group

Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality, for both classical and quantum systems, in an universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.

cond-mat.stat-mech↗

arXiv2015

Pumping single-file colloids: Absence of current reversal

We consider the single-file motion of colloidal particles interacting via short-ranged repulsion and placed in a traveling wave potential, that varies periodically in time and space. Under suitable driving conditions, a directed time-averaged flow of colloids is generated. We obtain analytic results for the model using a perturbative approach to solve the Fokker-Planck equations. The predictions show good agreement with numerical simulations. We find peaks in the time-averaged directed current as a function of driving frequency, wavelength and particle density and discuss possible experimental realizations. Surprisingly, unlike a closely related exclusion dynamics on a lattice, the directed current in the present model does not show current reversal with density. A linear response formula relating current response to equilibrium correlations is also proposed.

cond-mat.stat-mech↗