arXiv subjects

Nir Gavish

Publications and source records attributed to Nir Gavish.

At least 19 recordsLinked to original sources

arXiv2026

An Analytically Tractable Framework for Multi-Strain Epidemics: Resolving Algebraic Complexity to Map Oscillatory Dynamics

Multi-strain epidemiological systems frequently exhibit self-sustained oscillations, yet severe algebraic complexity has long obstructed a complete analytical characterization of these dynamics. Seeking to bypass these barriers, we have identified a broad, analytically tractable class of two-strain models featuring asymmetric cross-immunity that precludes secondary infections for a single strain. This targeted structural simplification allows us to derive explicit expressions for coexistence equilibria and map their stability. We show that the relative transmission advantage of secondary infections fundamentally governs the onset of robust limit-cycle oscillations, extending previous narrow-borderline results. Crucially, numerical simulations reveal a rich macroscopic landscape where small-amplitude local oscillations coexist with large-amplitude, recurrent outbreak cycles. The structural robustness of these phenomena is confirmed by incorporating effects such as waning immunity and isolation and extending the framework beyond the analytically tractable class. These findings provide a clear mechanistic explanation for multi-strain epidemic cycles and offer a highly tractable baseline for future theoretical developments.

q-bio.PE↗

arXiv2026

Modeling the Impact of Immune Boosting on Population-Level Vaccine Effectiveness

We extend the standard susceptible-infected-recovered framework to incorporate natural immune boosting during a short-scale outbreak. By deriving closed-form final size relations, we analytically link total attack rates to boosting dynamics and vaccine coverage. This framework identifies a critical boosting threshold: above it, higher vaccine coverage paradoxically decreases relative vaccine effectiveness. This occurs because successful epidemic suppression deprives vaccinated individuals of the silent pathogen exposures required to maintain their relative immunological advantage. Crucially, the overall population-level impact remains beneficial, consistently reducing absolute disease burden. For highly transmissible variants, asymptotic analysis reveals that relative vaccine effectiveness converges to a positive limit entirely independent of coverage.

q-bio.PE↗

arXiv2025

Optimal regulation in a periodic environment: insights from a simple model

We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for more general problems. In this model one must determine an optimal time-periodic `effort' profile, and the natural setting for the problem is in a space of periodic non-negative measures. We prove that there exists a unique solution for the problem in the space of measures, and then turn to characterizing this solution. Under some regularity conditions on the problem's data, we prove that its solution is an absolutely continuous measure, and provide an explicit formula for the measure's density. On the other hand, when the problem's data is discontinuous, the solution measure can also include atomic components. Complementing our analytical results, we carry out numerical computations to obtain solutions of the problem in various instances, which enable us to examine the interesting ways in which the solution's structure varies as the problem's data is varied.

math.OC↗

arXiv2024

A new oscillatory regime in two-strain epidemic models with partial cross-immunity

Infectious diseases often involve multiple strains that interact through the immune response generated after an infection. This study investigates the conditions under which a two-strain epidemic model with partial cross-immunity can lead to self-sustained oscillations, and reveals a new oscillatory regime in these models. Contrary to previous findings, which suggested that strong cross-immunity and significant asymmetry between strains are necessary for oscillations, our results demonstrate that sustained oscillations can occur even with weak cross-immunity and weak asymmetry. Using asymptotic methods, we provide a detailed mathematical analysis showing that the steady state of coexistence becomes unstable along specific curves in the parameter space, leading to oscillatory solutions for any value of the basic reproduction number greater than one. Numerical simulations support our theoretical findings, highlighting an unexpected oscillatory region in the parameter domain. These results challenge the current understanding of oscillatory dynamics in multi-strain epidemiological models, point to an oversight in previous studies, and suggest broader conditions under which such dynamics can arise.

q-bio.PE↗

arXiv2024

Revisiting the exclusion principle in epidemiology at its ultimate limit

The competitive exclusion principle in epidemiology implies that when competing strains of a pathogen provide complete protection for each other, the strain with the largest reproduction number outcompetes the other strains and drives them to extinction. The introduction of various trade-off mechanisms may facilitate the coexistence of competing strains, especially when their respective basic reproduction numbers are close so that the competition between the strains is weak. Yet, one may expect that a substantial competitive advantage of one of the strains will eventually outbalance trade-off mechanisms driving less competitive strains to extinction. The literature, however, lacks a rigorous validation of this statement. In this work, we challenge the validity of the exclusion principle at an ultimate limit in which one strain has a vast competitive advantage over the other strains. We show that when one strain is significantly more transmissible than the others, and under broad conditions, an epidemic system with two strains has a stable endemic equilibrium in which both strains coexist with comparable prevalence. Thus, the competitive exclusion principle does not unconditionally hold beyond the established case of complete immunity.

q-bio.PE↗

arXiv2023

Dynamics of a two-strain epidemic model with waning immunity -- a perturbative approach

Many infectious diseases are comprised of multiple strains with examples including Influenza, tuberculosis, and Dengue virus. The time evolution of such systems is linked to a complex landscape shaped by interactions between competing strains. Possible long-term dynamics include the extinction of less competitive strains, convergence to multi-strain steady-states, or self-sustained oscillations. This work considers a two-strain epidemic model in which the strains can interact indirectly via the immunity response generated following infections, and in which this immune response wanes with time. In particular, we focus on scenarios where the rate of waning immunity is significantly faster than the rate of demographic turnover. The first key result of this study is the explicit computation of the steady states of the nonlinear system of seven equations. Following this result, we take advantage of the separation of time scales in the problem and use perturbation methods to analyze the stability of the fixed points. In particular, we establish the conditions under which the system gives rise to the coexistence of the two strains and whether coexistence is attained via convergence to an endemic steady-state or via self-sustained oscillations. Our study unveils two parameter regimes of distinct qualitative behavior of the system and characterizes the separatrix between them. Within the first regime, the system gives rise to oscillatory coexistence for all feasible conditions. In the second regime, the system's behavior is governed by a solution to a quadratic equation, potentially resulting in the convergence to a multi-strain endemic equilibrium or the persistence of oscillatory coexistence.

q-bio.PE↗

arXiv2022

Optimal vaccination at high reproductive numbers: sharp transitions and counter-intuitive allocations

Optimization of vaccine allocations among different segments of a heterogeneous population is important for enhancing the effectiveness of vaccination campaigns in reducing the burden of epidemics. Intuitively, it would seem that allocations designed to minimize infections should prioritize those with the highest risk of being infected and infecting others. This prescription is well supported by vaccination theory, e.g., when the vaccination campaign aims to reach herd immunity. In this work, we show, however, that for vaccines providing partial protection (leaky vaccines) and for sufficiently high values of the basic reproduction number, intuition is overturned: the optimal allocation for minimizing the number of infections prioritizes the vaccination of those who are least likely to be infected. Furthermore, we show that this phenomenon occurs at a range of basic reproduction numbers relevant for the currently circulating strains of SARS-CoV-19. The work combines numerical investigations, asymptotic analysis for a general model, and complete mathematical analysis in a simple two-group model. The results point to important considerations in managing vaccination campaigns for infections with high transmissibility.

q-bio.QM↗

arXiv2021

Stiffness and coherence length measurements of ultra-thin superconductor, and implications to layered superconductors

Based on the London equation, we use a rotor-free vector potential ${\bf A}$, and current measurements by a SQUID, to determine the superconducting Pearl length $Λ$, and coherence length $ξ$, of ultra-thin, ring shaped, MoSi films, as a function of thickness $d$ and temperature $T$. We find that $ξ$ is a function of $d$ with a jump at $ξ\sim d \sim 5$nm. At base temperature the superconducting stiffness, defined by $1/λ^2=1/(Λd)$, is an increasing function of $T_c$. Similar behavior, known as the Uemura plot, exist in bulk layered superconductors, but with doping as an implicit parameter. We also provide the critical exponents of $Λ(T)$.

cond-mat.supr-con↗

arXiv2020

Bending and pinching of three-phase stripes: From secondary instabilities to morphological deformations in organic photovoltaics

Optimizing the properties of the mosaic morphology of bulk heterojunction (BHJ) organic photovoltaics (OPV) is not only challenging technologically but also intriguing from the mechanistic point of view. Among the recent breakthroughs is the identification and utilization of a three-phase (donor/mixed/acceptor) BHJ, where the (intermediate) mixed-phase can inhibit morphological changes, such as phase separation. Using a mean-field approach, we reveal and distinguish, between generic mechanisms that alter through transverse instabilities the evolution of stripes: the bending (zigzag mode) and the pinching (cross-roll mode) of the donor/acceptor domains. The results are summarized in a parameter plane spanned by the mixing energy and illumination, and show that donor-acceptor mixtures with higher mixing energy are more likely to develop pinching under charge-flux boundary conditions. The latter is notorious as it leads to the formation of disconnected domains and hence to loss of charge flux. We believe that these results provide a qualitative road-map for BHJ optimization, using mixed-phase composition and therefore, an essential step toward long-lasting OPV. More broadly, the results are also of relevance to study the coexistence of multiple-phase domains in material science, such as in ion-intercalated rechargeable batteries.

nlin.PS↗

arXiv2020

Stiffnessometer, a magnetic-field-free superconducting stiffness meter and its application

We provide a detailed account for a new method to measure superconducting stiffness $ρ_{s}$, critical current density $j_c$, and coherence length $ξ$, in one apparatus, without subjecting the sample to magnetic field or attaching leads. The method is based on the London equation $\mathbf{j}=-ρ_{s}\mathbf{A}$, where ${\bf j}$ is the current density and ${\bf A}$ is the vector potential. Using a rotor free $\bf{A}$ and a measurement of $\bf{j}$ via the magnetic moment of a superconducting ring, we determine $ρ_{s}$. By increasing $\mathbf{A}$ until the London equation fails we determine $j_c$ and $ξ$. The method is sensitive to very small stiffness, which translates to penetration depth $λ\lesssim 1$~mm. It is also sensitive to low critical current density $j_c \sim 10^3$ Amm$^{-2}$ or long coherence length $ξ\sim 1$~$μ$m. Naturally, the method does not suffer from demagnetization factor complications, the presence of vortices, or out-of-equilibrium conditions. Therefore, the absolute values of the different parameters can be determined. We demonstrate the application of this method to La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.17$.

cond-mat.supr-con↗

arXiv2020

Ginzburg-Landau model of a Stiffnessometer -- a superconducting stiffness meter device

We study the Ginzburg-Landau equations of super-conductivity describing the experimental setup of a Stiffnessometer device. In particular, we consider the nonlinear regime which reveals the impact of the superconductive critical current on the Stiffnessometer signal. As expected, we find that at high flux regimes, superconductivity is destroyed in parts of the superconductive regime. Surprisingly, however, we find that the superconductivity does not gradually decay to zero as flux increases, but rather the branch of solutions undergoes branch folding. We use asymptotic analysis to characterize the solutions at the numerous parameter regimes in which they exist. An immediate application of the work is an extension of the regime in which experimental measurements of the Stiffnessometer device can be interpreted.

cond-mat.supr-con↗

arXiv2020

Large deviations and gradient flows for the Brownian one-dimensional hard-rod system

We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap. We consider a scaling in which the number of particles tends to infinity while the volume fraction of the rods remains constant; in this limit the empirical measure of the rod positions converges almost surely to a deterministic limit evolution. We prove a large-deviation principle on path space for the empirical measure, by exploiting a one-to-one mapping between the hard-rod system and a system of non-interacting particles on a shorter domain. The large-deviation principle naturally identifies a gradient-flow structure for the limit evolution, with clear interpretations for both the driving functional (an `entropy') and the dissipation, which in this case is the Wasserstein dissipation. This study is inspired by recent developments in the continuum modelling of multiple-species interacting particle systems with finite-size effects; for such systems many different modelling choices appear in the literature, raising the question how one can understand such choices in terms of more microscopic models. The results of this paper give a clear answer to this question, albeit for the simpler one-dimensional hard-rod system. For this specific system this result provides a clear understanding of the value and interpretation of different modelling choices, while giving hints for more general systems.

math-ph↗

arXiv2018

Pattern formation aspects of electrically charged tri-stable media with implications to bulk heterojunction in organic photovoltaics

A common thread in designing electrochemically-based renewable energy devices comprises materials that exploit nano-scale morphologies, e.g., supercapacitors, batteries, fuel cells, and bulk heterojunction organic photovoltaics. In these devices, however, Coulomb forces often influence the fine nano-details of the morphological structure of active layers leading to a notorious decrease in performance. By focusing on bulk heterojunction organic photovoltaics as a case model, a self-consistent mean-field framework that combines binary (bi-stable) and ternary (tri-stable) morphologies with electrokinetics is presented and analyzed, i.e., undertaking the coupling between the spatiotemporal evolution of the material and charge dynamics along with charge transfer at the device electrodes. Particularly, it is shown that tri-stable composition may stabilize stripe morphology that is ideal bulk heterojuction. Moreover, since the results rely on generic principles they are expected to be applicable to a broad range of electrically charged amphiphilic-type mixtures, such as emulsions, polyelectrolytes, and ionic liquids.

nlin.PS↗

arXiv2018

The nature of the phase transition in the cuprates as revealed by a magnetic field free stiffness meter

A new method to measure the superconducting stiffness tensor $\overlineρ_s$, without subjecting the sample to magnetic field, is applied to La$_{1.875}$Sr$_{0.125}$CuO$_4$ (LSCO). The method is based on the London equation $\bf{J}=-\overlineρ_s \bf{A}$, where $\bf{J}$ is the current density and $\bf{A}$ is the vector potential. Using rotor free $\bf{A}$ and measuring $\bf{J}$ via the magnetic moment of superconducting rings, we extract $\overlineρ_s$ at $T\rightarrow T_c$. The technique, named Stiffnessometer, is sensitive to very small stiffness, which translates to penetration depth on the order of a few millimeters. We apply this method to two different LSCO rings: one with the current running only in the CuO$_2$ planes, and another where the current must cross planes. We find different transition temperatures for the two rings, namely, there is a temperature range with two dimensional stiffness. The Stiffnessometer results are accompanied by Low Energy $μ$SR measurements on the same sample to determine the stiffness anisotropy at $T < T_c$.

cond-mat.supr-con↗

arXiv2018

Finite domain effects in steady-state solutions of Poisson-Nernst-Planck equations

Steady-state solutions of the Poisson-Nernst-Planck model are studied in the asymptotic limit of large, but finite domains. By using asymptotic matching for integrals, we derive an approximate solution for the steady-state equation with exponentially small error with respect to the domain size. The approximation is used to quantify the extent of finite domain effects over the full parameter space. Surprisingly, already for small applied voltages (several thermal voltages), we found that finite domain effects are significant even for large domains (on the scale of hundreds of Debye lengths). Namely, the solution near the boundary, i.e., the boundary layer (electric double layer) structure, is sensitive to the domain size even when the domain size is many times larger than the characteristic width of the boundary layer. We focus on this intermediate regime between confined domains and `essentially infinite' domains, and study how the domain size effects the solution properties. We conclude by providing an outlook to higher dimensions with applications to ion channels and porous electrodes.

math.AP↗

arXiv2018

Do Bi-Stable Poisson-Nernst-Planck Models Describe Single Channel Gating?

Experiments measuring currents through single protein channels show unstable currents, a phenomena called the gating of a single channel. Channels switch between an 'open' state with a well defined single amplitude of current and 'closed' states with nearly zero current. The existing mean-field theory of ion channels focuses almost solely on the open state. The physical modeling of the dynamical features of ion channels is still in its infancy, and does not describe the transitions between open and closed states, nor the distribution of the duration times of open states. One hypothesis is that gating corresponds to noise-induced fast transitions between multiple steady (equilibrium) states of the underlying system. In this work, we aim to test this hypothesis. Particularly, our study focuses on the (high order) steric Poisson-Nernst-Planck-Cahn-Hilliard model since it has been successful in predicting permeability and selectivity of ionic channels in their open state, and since it gives rise to multiple steady states. We show that this system gives rise to a gating-like behavior, but that important features of this switching behavior are different from the defining features of gating in biological systems. Furthermore, we show that noise prohibits switching in the system of study. The above phenomena are expected to occur in other PNP-type models, strongly suggesting that one has to go beyond over-damped (gradient flow) Nernst-Planck type dynamics to explain the spontaneous gating of single channels.

q-bio.BM↗

arXiv2017

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions

We study the existence and stability of stationary solutions of Poisson-Nernst- Planck equations with steric effects (PNP-steric equations) with two counter-charged species. These equations describe steady current through open ionic channels quite well. The current levels in open ionic channels are known to switch between `open' or `closed' states in a spontaneous stochastic process called gating, suggesting that their governing equations should give rise to multiple stationary solutions that enable such multi-stable behavior. We show that within a range of parameters, steric effects give rise to multiple stationary solutions that are smooth. These solutions, however, are all unstable under PNP-steric dynamics. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, and show that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

math.AP↗

arXiv2017

From solvent free to dilute electrolytes: Essential components for a continuum theory

The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and under-screening, which all impact the emergence of fluid/solid interfaces, and transport in these systems. Since these phenomena are not captured by existing mean field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquids. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing free energy that consists of short and long range interactions, together with a dissipation mechanism via Onsagers' relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as the interactions that are specified in the equilibrium-free energy. The model equations not only provide insights to transport mechanisms beyond the Stokes-Einstein-Smoluchowski relations but also enables to qualitative recovery in the full range (three distinct regions) of non-monotonic electrical screening length that has been recently observed in experiments using organic solvent to dilute ionic liquids.

physics.chem-ph↗