In biological contexts as diverse as development, apoptosis, and synthetic microbial consortia, collections of cells or sub-cellular components have been shown to overcome the slow signaling speed of simple diffusion by utilizing diffusive relays, in which the presence of one type of diffusible signaling molecule triggers participation in the emission of the same type of molecule. This collective effect gives rise to fast-traveling diffusive waves. Here, in the context of cell signaling, we show that system dimensionality – the shape of the extracellular medium and the distribution of cells within it – can dramatically affect the wave dynamics, but that these dynamics are insensitive to details of cellular activation. As an example, we show that neutrophil swarming experiments exhibit dynamical signatures consistent with the proposed signaling motif. We further show that cell signaling relays generate much steeper concentration profiles than does simple diffusion, which may facilitate neutrophil chemotaxis.

%B eLife %V 9 %G eng %U https://elifesciences.org/articles/61771#info %N 61771 %0 Journal Article %D 2020 %T Non-genetic variability: survival strategy or nuisance? %A Levien, Ethan %A Jiseon Min %A Kondev, Jane %A Amir, Ariel %X The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context of antibiotic treatments or exponential growth in constant environments, non-genetic variability has shown to have significant effects on population dynamics. Here, we review research that elucidates the relationship between cell-to-cell variability and population dynamics. After summarizing the relevant experimental observations, we discuss models of bet-hedging and phenotypic switching. In the context of these models, we discuss how switching between phenotypes at the single-cell level can help populations survive in uncertain environments. Next, we review more fine-grained models of phenotypic variability where the relationship between single-cell growth rates, generation times and cell sizes is explicitly considered. Variability in these traits can have significant effects on the population dynamics, even in a constant environment. We show how these effects can be highly sensitive to the underlying model assumptions. We close by discussing a number of open questions, such as how environmental and intrinsic variability interact and what the role of non-genetic variability in evolutionary dynamics is. %G eng %U https://arxiv.org/abs/2010.05672 %0 Journal Article %J Physical Review B %D 2020 %T Thermal conductance of one-dimensional disordered harmonic chains %A Biswarup Ash %A Amir, Ariel %A Yohai Bar-Sinai %A Oreg, Yuval %A Imry, Yoseph %X We study heat conduction mediated by longitudinal phonons in one-dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find nontrivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that, suprisingly, the thermal conductance of a system with strong disorder, characterized by a “heavy-tailed” probability distribution, and with large impedance mismatch between the bath and the system, scales normally with the system size, i.e., in a manner consistent with Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior. %B Physical Review B %V 101 %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.101.121403 %N 12 %0 Journal Article %J Physical Review Letters %D 2020 %T Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations %A Levien, Ethan %A Trevor GrandPre %A Amir, Ariel %X In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population’s growth rate. Is there anIn isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler–Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler–Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.

%B Journal of the Royal Society Interface %V 17 %G eng %U https://royalsocietypublishing.org/doi/full/10.1098/rsif.2019.0827?casa_token=xJqU2Cx74DAAAAAA%3AI5ACrQSmiE1W4PKeKhZNbpgKtQ3hhmcrLpwskaFmhqg9RmM5nYYRxrP2oAQIVf5hpwxS6IEnyP6E %N 166 %0 Journal Article %J eLife %D 2019 %T Length regulation of multiple flagella that self-assemble from a shared pool of components %A Thomas G Fai %A Mohapatra, Lishibanya %A Prathitha Kar %A Kondev, Jane %A Amir, Ariel %X The single-celled green algaeMreB is an actin homolog that is essential for coordinating the cell wall synthesis required for the rod shape of many bacteria. Previously we have shown that filaments of MreB bind to the curved membranes of bacteria and translocate in directions determined by principal membrane curvatures to create and reinforce the rod shape (Hussain et al., 2018). Here, in order to understand how MreB filament dynamics affects their cellular distribution, we model how MreB filaments bind and translocate on membranes with different geometries. We find that it is both energetically favorable and robust for filaments to bind and orient along directions of largest membrane curvature. Furthermore, significant localization to different membrane regions results from processive MreB motion in various geometries. These results demonstrate that the *in vivo* localization of MreB observed in many different experiments, including those examining negative Gaussian curvature, can arise from translocation dynamics alone.

Asymmetric segregation of key proteins at cell division—be it a beneficial or deleterious protein—is ubiquitous in unicellular organisms and often considered as an evolved trait to increase fitness in a stressed environment. Here, we provide a general framework to describe the evolutionary origin of this asymmetric segregation. We compute the population fitness as a function of the protein segregation asymmetry a, and show that the value of a which optimizes the population growth manifests a phase transition between symmetric and asymmetric partitioning phases. Surprisingly, the nature of phase transition is different for the case of beneficial proteins as opposed to deleterious proteins: a smooth (second order) transition from purely symmetric to asymmetric segregation is found in the former, while a sharp transition occurs in the latter. Our study elucidates the optimization problem faced by evolution in the context of protein segregation, and motivates further investigation of asymmetric protein segregation in biological systems.

Many experiments show that the numbers of mRNA and protein are proportional to the cell volume in growing cells. However, models of stochastic gene expression often assume constant transcription rate per gene and constant translation rate per mRNA, which are incompatible with these experiments. Here, we construct a minimal gene expression model to fill this gap. Assuming ribosomes and RNA polymerases are limiting in gene expression, we show that the numbers of proteins and mRNAs both grow exponentially during the cell cycle and that the concentrations of all mRNAs and proteins achieve cellular homeostasis; the competition between genes for the RNA polymerases makes the transcription rate independent of the genome number. Furthermore, by extending the model to situations in which DNA (mRNA) can be saturated by RNA polymerases (ribosomes) and becomes limiting, we predict a transition from exponential to linear growth of cell volume as the protein-to-DNA ratio increases.

%B Nature Communications %V 9 %G eng %U https://www.nature.com/articles/s41467-018-06714-z %N 4496 %0 Journal Article %J Trends in Microbiology %D 2018 %T Learning from Noise: How Observing Stochasticity May Aid Microbiology %A Amir, Ariel %A Nathalie Q. Balaban %X For many decades, the wedding of quantitative data with mathematical modeling has been fruitful, leading to important biological insights. Here, we review some of the ongoing efforts to gain insights into problems in microbiology – and, in particular, cell-cycle progression and its regulation – through observation and quantitative analysis of the natural fluctuations in the system. We first illustrate this idea by reviewing a classic example in microbiology – the Luria–Delbrück experiment – and discussing how, in that case, useful information was obtained by looking beyond theAt low temperatures the dynamical degrees of freedom in amorphous solids are tunneling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a “TLS glass,” described by the random-field Ising model with random 1/r^3 interactions. In this paper we perform a self-consistent mean-field calculation, previously used to study the electron-glass (EG) model [A. Amir *et al.*, Phys. Rev. B **77**, 165207 (2008)]. Similarly to the electron glass, we find a 1/λ distribution of relaxation rates λ, leading to logarithmic slow relaxation. However, with increased interactions the EG model shows slower dynamics whereas the TLS-glass model shows faster dynamics. This suggests that given system-specific properties, glass dynamics can be slowed down or sped up by the interactions.

All organisms control the size of their cells. We focus here on the question of size regulation in bacteria, and suggest that the quantitative laws governing cell size and its dependence on growth rate may arise as byproducts of a regulatory mechanism which evolved to support multiple DNA replication forks. In particular, we show that the increase of bacterial cell size during Lenski’s long-term evolution experiments is a natural outcome of this proposal. This suggests that, in the context of evolution, cell size may be a 'spandrel'

%B eLife %V 6 %P e22186 %G eng %U https://elifesciences.org/content/6/e22186 %0 Journal Article %J Physical Review Letters %D 2017 %T Non-Monotonic Aging and Memory Retention in Disordered Mechanical Systems %A Lahini, Yoav %A Gottesman, Omer %A Amir, Ariel %A Shmuel Rubinstein %XWe observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain long-lasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior.

%B Physical Review Letters %V 118 %P 085501 %G eng %U http://physics.aps.org/articles/v10/18 %0 Journal Article %J Proc. Natl. Acad. Sci. USA %D 2016 %T Interrogating the Escherichia coli cell cycle by cell dimension perturbations %A Hai Zheng %A Ho, Po-Yi %A Meiling Jiang %A Bin Tang %A Weirong Liu %A Dengjin Li %A Xuefeng Yu %A Nancy E. Kleckner %A Amir, Ariel %A Liu, Chenli %XBacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter’s growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ. We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed “adder-per-origin” model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation.

%B Proc. Natl. Acad. Sci. USA %G eng %U http://www.pnas.org/content/early/2016/12/08/1617932114.full.pdf %0 Journal Article %J Physical Review Letters %D 2016 %T Glassy Dynamics in Disordered Electronic Systems Reveal Striking Thermal Memory Effects %A A. Eisenbach %A T. Havdala %A J. Delahaye %A T. Grenet %A A. Amir %A A. Frydman %XMemory is one of the unique qualities of a glassy system. The relaxation of a glass to equilibrium contains information on the sample’s excitation history, an effect often refer to as “aging.” We demonstrate that under the right conditions a glass can also possess a different type of memory. We study the conductance relaxation of electron glasses that are fabricated at low temperatures. Remarkably, the dynamics are found to depend not only on the ambient measurement temperature but also on the maximum temperature to which the system was exposed. Hence the system “remembers” its highest temperature. This effect may be qualitatively understood in terms of energy barriers and local minima in configuration space and therefore may be a general property of the glass state.

%B Physical Review Letters %V 117 %P 116601 %G eng %0 Journal Article %J Optica %D 2016 %T Chirped photonic crystals: a natural strategy for broadband reflectance %A Caleb Q. Cook %A Amir, Ariel %XOne-dimensional photonic crystals with slowly varying, i.e. "chirped", lattice period are responsible for broadband light reflectance in many diverse biological contexts, ranging from the shiny coatings of various beetles to the eyes of certain butterflies. We present a quantum scattering analogy for light reflection from these adiabatically chirped photonic crystals (ACPCs) and apply a WKB-type approximation to obtain a closed-form expression for the reflectance. From this expression we infer several design principles, including a differential equation for the chirp pattern required to elicit a given reflectance spectrum and the minimal number of bilayers required to exceed a desired reflectance threshold. Comparison of the number of bilayers found in ACPCs throughout nature and our predicted minimal required number also gives a quantitative measure of the optimality of chirped biological reflectors. Together these results elucidate the design principles of chirped reflectors in nature and their possible application to future optical technologies.

%B Optica %V 3 %P 1436-1439 %G eng %U https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-3-12-1436&id=355669 %0 Journal Article %J American Mathematical Monthly %D 2016 %T Surprises in numerical expressions of physical constants %A Amir, Ariel %A Mikhail Lemeshko %A Tadashi Tokieda %XIn science, as in life, "surprises" can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like pi or e. The inverse problem also arises, whereby the measured value of a physical constant admits a "surprisingly" simple approximation in terms of well-known mathematical constants. Can we estimate the probability for this to be a mere coincidence, rather than an inkling of some theory? We answer the question in the most naive form.

%B American Mathematical Monthly %V 123 %P 609-612 %G eng %N 6 %0 Journal Article %J Phys. Rev. E Stat Nonlin. Soft Matter Phys. %D 2016 %T Stochastic modeling of cell growth with symmetric or asymmetric division %A Andrew Marantan %A Amir, Ariel %XWe consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the "master equation" describing how the resource distribution evolves over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendix, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

%B Phys. Rev. E Stat Nonlin. Soft Matter Phys. %V 94 %P 012405 %G eng %U https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.012405 %0 Journal Article %J Phys. Rev. E (Editor's Choice) %D 2016 %T Non-Hermitian Localization in Biological Networks %A Amir, Ariel %A Naomichi Hatano %A David R. Nelson %XWe explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90∘ rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-Nlimit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the “charges” embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey “Dale's law” (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

%B Phys. Rev. E (Editor's Choice) %V 93 %P 042310 %G eng %U http://arxiv.org/abs/1512.05478 %0 Journal Article %J Am. J. Phys. %D 2015 %T An elementary derivation of first and last return times of 1D random walks %A Sarah Kostinski %A Amir, Ariel %XRandom walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first-return-time distribution of a one-dimensional random walker, which is a heavy-tailed distribution with infinite mean. Using the same method, we find the last-return-time distribution, which follows the arcsine law. Both results have a broad range of applications in physics and other disciplines. The derivation presented here is readily accessible to physics undergraduates and provides an elementary introduction into random walks and their intriguing properties.

%B Am. J. Phys. %G eng %0 Journal Article %J Current Biology %D 2015 %T Single-Cell Analysis of Growth in Budding Yeast and Bacteria Reveals a Common Size Regulation Strategy %A Ilya Soifer %A Lydia Robert %A Amir, Ariel %B Current Biology %G eng %U http://www.cell.com/current-biology/abstract/S0960-9822(15)01560-2 %0 Journal Article %J Front Microbiol %D 2015 %T Simultaneous regulation of cell size and chromosome replication in bacteria. %A Ho, Po-Yi %A Amir, Ariel %X Bacteria are able to maintain a narrow distribution of cell sizes by regulating the timing of cell divisions. In rich nutrient conditions, cells divide much faster than their chromosomes replicate. This implies that cells maintain multiple rounds of chromosome replication per cell division by regulating the timing of chromosome replications. Here, we show that both cell size and chromosome replication may be simultaneously regulated by the long-standing initiator accumulation strategy. The strategy proposes that initiators are produced in proportion to the volume increase and is accumulated at each origin of replication, and chromosome replication is initiated when a critical amount per origin has accumulated. We show that this model maps to the incremental model of size control, which was previously shown to reproduce experimentally observed correlations between various events in the cell cycle and explains the exponential dependence of cell size on the growth rate of the cell. Furthermore, we show that this model also leads to the efficient regulation of the timing of initiation and the number of origins consistent with existing experimental results. %B Front Microbiol %V 6 %P 662 %8 2015 %G eng %1 http://www.ncbi.nlm.nih.gov/pubmed/26217311?dopt=Abstract %0 Journal Article %J Physical Review A %D 2014 %T Anomalous symmetry breaking in two-dimensional diffusion of coherent atoms %A Rami Pugatch %A Dipankar Bhattacharyya %A Amir, Ariel %A Yoav Sagi %A Nir Davidson %XThe electromagnetically induced transparency (EIT) spectrum of atoms diffusing in and out of a narrow beam is measured and shown to manifest the two-dimensional δ-function anomaly in a classical setting. In the limit of small-area beams, the EIT line shape is independent of power, and equal to the renormalized local density of states of a free particle Hamiltonian. The measured spectra for different powers and beam sizes collapses to a single universal curve with a characteristic logarithmic Van Hove singularity close to resonance.

%B Physical Review A %V 80 %G eng %N 033807 %0 Journal Article %J Proc Natl Acad Sci U S A %D 2014 %T Bending forces plastically deform growing bacterial cell walls. %A Amir, Ariel %A Babaeipour, Farinaz %A McIntosh, Dustin B %A Nelson, David R. %A Jun, Suckjoon %K Anisotropy %K Bacillus subtilis %K Biomechanical Phenomena %K Cell Wall %K Escherichia coli %K Stress, Mechanical %X Cell walls define a cell's shape in bacteria. The walls are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this paper, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell wall growth. By applying a precisely controllable hydrodynamic force to growing rod-shaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreement with the predictions of the theory of dislocation-mediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell's responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments. %B Proc Natl Acad Sci U S A %V 111 %P 5778-83 %8 2014 Apr 22 %G eng %N 16 %1 http://www.ncbi.nlm.nih.gov/pubmed/24711421?dopt=Abstract %0 Journal Article %J Physical Review Letters %D 2014 %T Cell size regulation in bacteria %A Amir, Ariel %XVarious bacteria such as the canonical gram negative *Escherichia coli* or the well-studied gram positive *Bacillus subtilis* divide symmetrically after they approximately double their volume. Their size at division is not constant, but is typically distributed over a narrow range. Here, we propose an analytically tractable model for cell size control, and calculate the cell size and interdivision time distributions, as well as the correlations between these variables. We suggest ways of extracting the model parameters from experimental data, and show that existing data for *E. coli*supports partial size control, and a particular explanation: a cell attempts to add a constant volume from the time of initiation of DNA replication to the next initiation event. This hypothesis accounts for the experimentally observed correlations between mother and daughter cells as well as the exponential dependence of size on growth rate.

Characterizing the frequency-dependent response of amorphous systems and glasses can provide important insights into their physics. Here, we study the response of an electron glass, where Coulomb interactions are important and have previously been shown to significantly modify the conductance and lead to memory effects and aging. We propose a model which allows us to take the interactions into account in a self-consistent way, and explore the frequency-dependent conduction at all frequencies. At low frequencies conduction occurs on the percolation backbone, and the model captures the variable-range-hopping behavior. At high frequencies conduction is dominated by localized clusters. Despite the difference in physical mechanisms at low and high frequency, we are able to approximately scale all numerical data onto a single curve, using two parameters: the DC conduction and the DC dielectric constant. The behavior follows the universal scaling that is experimentally observed for a large class of amorphous solids.

%B EPL, %V 107 %G eng %U http://iopscience.iop.org/0295-5075/107/4/47011/pdf/0295-5075_107_4_47011.pdf %N 47011 %0 Journal Article %J American Journal of Physics %D 2013 %T Elucidating the stop bands of structurally colored systems through recursion %A Amir, Ariel %A Peter Vukusic %XInterference phenomena are the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics; namely, specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer and solve it using recursion relations. We present experimental data for various beetles, whose optical structure resembles the proposed model. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursive relations. In order for these to converge, an infinitesimal amount of absorption needs to be present, reminiscent of the regularization procedures commonly used in physics calculations. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concepts of band structure and regularization in the context of experimentally observed phenomena, such as the high reflectance and the iridescent color appearance of structurally colored beetles.

%B American Journal of Physics %V 81 %G eng %N 253 %0 Journal Article %J Physical Review X %D 2013 %T Emergent percolation length and localization in random elastic networks %A Amir, Ariel %A Krich, Jacob %A Vincenzo Vitelli %A Oreg, Yuval %A Imry, Yoseph %XWe study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency, and spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization-delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach, we calculate the speed of sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density and find good agreement of these predictions with numerical results using a recursive Green-function method that was adapted for this problem. The connection of our results to recent experiments on amorphous solids is discussed.

%B Physical Review X %V 3 %G eng %N 021017 %0 Journal Article %J Phys Rev E Stat Nonlin Soft Matter Phys %D 2013 %T Theory of interacting dislocations on cylinders. %A Amir, Ariel %A Paulose, Jayson %A Nelson, David R. %K Bacteria %K Biophysical Processes %K Cell Wall %K Models, Theoretical %K Plant Leaves %K Thermodynamics %X We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are created by a Peach-Koehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind. The thermal nucleation rate of dislocation unbinding is calculated, for an arbitrary mobility tensor and external stress, including the case of a twist-induced Peach-Koehler force along the cylinder axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite their vanishing Gaussian curvature. %B Phys Rev E Stat Nonlin Soft Matter Phys %V 87 %P 042314 %8 2013 Apr %G eng %N 4 %1 http://www.ncbi.nlm.nih.gov/pubmed/23679421?dopt=Abstract %0 Journal Article %J Lectures given by D. R. Nelson at the Les Houches School on ”Soft Interfaces,” July 2-27 %D 2012 %T Defects on cylinders: superfluid helium films and bacterial cell walls %A Nelson, David R. %A Amir, Ariel %B Lectures given by D. R. Nelson at the Les Houches School on ”Soft Interfaces,” July 2-27 %V arxiv:1303.5896 %G eng %0 Journal Article %J Proc Natl Acad Sci U S A %D 2012 %T On relaxations and aging of various glasses. %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %K Electrons %K Glass %K Indium %K Models, Chemical %K Physical Phenomena %K Time Factors %X Slow relaxation occurs in many physical and biological systems. "Creep" is an example from everyday life. When stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: The relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the "waiting time." This ubiquitous phenomenon is called aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, which predicts logarithmic relaxations, and a particular aging dependence on the waiting time. We demonstrate the generality of the approach by comparing our predictions to experimental data on a diverse range of physical phenomena, from conductance in granular metals to disordered insulators and dirty semiconductors, to the low temperature dielectric properties of glasses. %B Proc Natl Acad Sci U S A %V 109 %P 1850-5 %8 2012 Feb 7 %G eng %N 6 %1 http://www.ncbi.nlm.nih.gov/pubmed/22315418?dopt=Abstract %0 Journal Article %J Proc Natl Acad Sci U S A %D 2012 %T Dislocation-mediated growth of bacterial cell walls. %A Amir, Ariel %A Nelson, David R. %K Bacteria %K Cell Wall %K Models, Theoretical %X Recent experiments have illuminated a remarkable growth mechanism of rod-shaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference [Garner EC, et al., (2011) Science 333:222-225], [Domínguez-Escobar J, et al. (2011) Science 333:225-228], [van Teeffelen S, et al. (2011) PNAS 108:15822-15827]. We view these as dislocations in the partially ordered peptidoglycan structure, activated by glycan strand extension machinery, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Generation and motion of these interacting defects lead to surprising effects arising from the cylindrical geometry, with important implications for growth. We also discuss how long range elastic interactions and turgor pressure affect the dynamics of the fraction of actively moving dislocations in the bacterial cell wall. %B Proc Natl Acad Sci U S A %V 109 %P 9833-8 %8 2012 Jun 19 %G eng %N 25 %1 http://www.ncbi.nlm.nih.gov/pubmed/22660931?dopt=Abstract %0 Journal Article %J Annu. Rev. Condens. Matter Phys. %D 2011 %T Electron glass dynamics %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %XExamples of glasses are abundant, yet it remains one of the phases of matter whose understanding is very elusive. In recent years, remarkable experiments have been performed on the dynamical aspects of glasses. Electron glasses offer a particularly good example of the trademarks of glassy behavior, such as aging and slow relaxations. In this work we review the experimental literature on electron glasses, as well as the local mean-field theoretical framework put forward in recent years to understand some of these results. We also present novel theoretical results explaining the periodic aging experiment.

%B Annu. Rev. Condens. Matter Phys. %V 2 %G eng %N 235-62 %0 Journal Article %J Phys Rev Lett %D 2011 %T Huge (but finite) time scales in slow relaxations: beyond simple aging. %A Amir, Ariel %A Borini, Stefano %A Oreg, Yuval %A Imry, Yoseph %K Electric Conductivity %K Porosity %K Silicon %K Time Factors %X Experiments performed in the last years demonstrated slow relaxations and aging in the conductance of a large variety of materials. Here, we present experimental and theoretical results for conductance relaxation and aging for the case-study example of porous silicon. The relaxations are experimentally observed even at room temperature over time scales of hours, and when a strong electric field is applied for a time tw, the ensuing relaxation depends on tw. We derive a theoretical curve and show that all experimental data collapse onto it with a single time scale as a fitting parameter. This time scale is found to be of the order of thousands of seconds at room temperature. The generic theory suggested is not fine-tuned to porous silicon, and thus we believe the results should be universal, and the presented method should be applicable for many other systems manifesting memory and other glassy effects. %B Phys Rev Lett %V 107 %P 186407 %8 2011 Oct 28 %G eng %N 18 %1 http://www.ncbi.nlm.nih.gov/pubmed/22107656?dopt=Abstract %0 Journal Article %J Phys Rev Lett %D 2010 %T Localization, anomalous diffusion, and slow relaxations: a random distance matrix approach. %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %X We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum), for low densities, and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results. %B Phys Rev Lett %V 105 %P 070601 %8 2010 Aug 13 %G eng %N 7 %1 http://www.ncbi.nlm.nih.gov/pubmed/20868026?dopt=Abstract %0 Book Section %B 50 Years of Anderson Localization %D 2010 %T The localization transition at finite temperatures: electric and thermal transport %A Imry, Yoseph %A Amir, Ariel %E E. Abrahams %XThe Anderson localization transition is considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.

%B 50 Years of Anderson Localization %I World Scientific %C Singapore %G eng %U http://arxiv.org/abs/1004.0966 %0 Conference Proceedings %B TIDS conference %D 2009 %T 1/f noise and slow relaxations in glasses %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %XRecently we have shown that slow relaxations in the electron glass system can be understood in terms of the spectrum of a matrix describing the relaxation of the system close to a metastable state. The model focused on the electron glass system, but its generality was demonstrated on various other examples. Here, we study the noise spectrum in the same framework. We obtain a remarkable relation between the spectrum of relaxation rates λ described by the distribution function P(λ)∼1/λ and the 1/f noise in the fluctuating occupancies of the localized electronic sites. This noise can be observed using local capacitance measurements. We confirm our analytic results using numerics, and also show how the Onsager symmetry is fulfilled in the system.

%B TIDS conference %C Berlin %V 18 %P 836 %G eng %N 12 %0 Journal Article %J Phys Rev E Stat Nonlin Soft Matter Phys %D 2009 %T Classical diffusion of a quantum particle in a noisy environment. %A Amir, Ariel %A Lahini, Yoav %A Perets, Hagai B %X We study the spreading of a quantum-mechanical wave packet in a tight-binding model with a noisy potential and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite correlation time of the noisy environment and treat the system by utilizing the separation of fast (dephasing) and slow (diffusion) processes. We show that classical diffusive behavior emerges at long times and we calculate analytically the dependence of the classical diffusion coefficient on the noise magnitude and correlation time. This method provides a general solution to this problem for arbitrary conditions of the noisy environment. The calculation can be done in any dimension, but we demonstrate it in one dimension for clarity of representation. The results are relevant to a large variety of physical systems, from electronic transport in solid-state physics to light transmission in optical devices, diffusion of excitons, and quantum computation. %B Phys Rev E Stat Nonlin Soft Matter Phys %V 79 %P 050105 %8 2009 May %G eng %N 5 Pt 1 %1 http://www.ncbi.nlm.nih.gov/pubmed/19518400?dopt=Abstract %0 Journal Article %J Phys Rev Lett %D 2009 %T Slow relaxations and aging in the electron glass. %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %X Glassy systems are ubiquitous in nature. They are characterized by slow relaxations to equilibrium without a typical time scale, aging, and memory effects. Understanding this has been a long-standing problem in physics. We study the aging of the electron glass, a system showing remarkable slow relaxations of the conductance. We find that the appropriate broad distribution of relaxation rates leads to a universal relaxation of the form log(1 + t_{w}/t) for the common aging protocol, where t_{w} is the length of time the perturbation driving the system out of equilibrium was on, and t the time of measurement. These results agree well with several experiments performed on different glassy systems, and examining different physical observables, for times ranging from seconds to several hours. The suggested theoretical framework appears to offer a paradigm for aging in a broad class of glassy materials. %B Phys Rev Lett %V 103 %P 126403 %8 2009 Sep 18 %G eng %N 12 %1 http://www.ncbi.nlm.nih.gov/pubmed/19792451?dopt=Abstract %0 Journal Article %J Physical Review B %D 2009 %T Variable range hopping in the Coulomb glass %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %XWe use a local mean-field (Hartree-like) approach to study the conductance of a strongly localized electron system in two dimensions. We find a crossover between a regime where Coulomb interactions modify the conductance significantly to a regime where they are negligible. We show that under rather general conditions the conduction obeys a scaling relation which we verify using numerical simulations. The use of a local mean-field approach gives a clear physical picture, and removes the ambiguity of the use of single-particle tunneling density of states (DOS) in the calculation of the conductance. Furthermore, the theory contains interaction-induced correlations between the on site energy of the localized states and distances, as well as finite temperature corrections of the DOS.

%B Physical Review B %V 80 %G eng %N 245214 %0 Journal Article %J Physical Review A %D 2008 %T Decays in quantum hierarchical models %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %XWe study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudocontinuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudocontinuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random, several cases are identified. For a pseudocontinuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudocontinuum space. They last for a long time compared to the nonrandom case.

%B Physical Review A %V 77 %G eng %N 050101(R) %0 Journal Article %J Physical Review B %D 2008 %T Mean-field model for electron-glass dynamics %A Amir, Ariel %A Oreg, Yuval %A Imry, Yoseph %XWe study a microscopic mean-field model for the dynamics of the electron glass near a local equilibrium state. Phonon-induced tunneling processes are responsible for generating transitions between localized electronic sites, which eventually lead to the thermalization of the system. We find that the decay of an excited state to a locally stable state is far from being exponential in time and does not have a characteristic time scale. Working in a mean-field approximation, we write rate equations for the average occupation numbers ⟨ni⟩ and describe the return to the locally stable state by using the eigenvalues of a rate matrix A describing the linearized time evolution of the occupation numbers. By analyzing the probability distribution P(λ) of the eigenvalues of A, we find that, under certain physically reasonable assumptions, it takes the form P(λ)∼1/∣λ∣, leading naturally to a logarithmic decay in time. While our derivation of the matrix A is specific for the chosen model, we expect that other glassy systems, with different microscopic characteristics, will be described by random rate matrices belonging to the same universality class of A. Namely, the rate matrix has elements with a very broad distribution, as in the case of exponentials of a variable with nearly uniform distribution.

%B Physical Review B %V 77 %G eng %N 165207