arXiv subjects

Yariv Kafri

Publications and source records attributed to Yariv Kafri.

67 records · Page 4Linked to original sources

arXiv2008

Dynamics of DNA Melting

The dynamics of loops at the DNA denaturation transition is studied. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The long-time asymptotic behavior of the autocorrelation function is expressed in terms of the entropy exponent, c, of a loop. The validity of the scaling argument is tested using a microscopic model of an isolated loop and a toy model of interacting loops. This suggests a method for measuring the entropy exponent using single-molecule experiments such as florescence correlation spectroscopy.

cond-mat.stat-mech↗

arXiv2008

Non-equilibrium fluctuation theorems in the presence of local heating

We study two non-equilibrium work fluctuation theorems, the Crooks' theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of $<\exp(-βW)>$ to its theoretical mean value, where $W$ is the work done on the test system and $β$ is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.

cond-mat.stat-mech↗

arXiv2007

Steady-State Chemotactic Response in E. coli

The bacterium E. coli maneuvers itself to regions with high chemoattractant concentrations by performing two stereotypical moves: `runs', in which it moves in near straight lines, and `tumbles', in which it does not advance but changes direction randomly. The duration of each move is stochastic and depends upon the chemoattractant concentration experienced in the recent past. We relate this stochastic behavior to the steady-state density of a bacterium population, and we derive the latter as a function of chemoattractant concentration. In contrast to earlier treatments, here we account for the effects of temporal correlations and variable tumbling durations. A range of behaviors obtains, that depends subtly upon several aspects of the system - memory, correlation, and tumbling stochasticity in particular.

q-bio.CB↗

arXiv2007

The insulating phases and superfluid-insulator transition of disordered boson chains

Using a strong disorder real-space renormalization group (RG), we study the phase diagram of a fully disordered chain of interacting bosons. Since this approach does not suffer from run-away flows, it allows a direct study of the insulating phases, which are not accessible in a weak disorder perturbative treatment. We find that the universal properties of the insulating phase are determined by the details and symmetries of the onsite chemical-potential disorder. Three insulating phases are possible: (i) an incompressible Mott glass with a finite superfluid susceptibility, (ii) a random-singlet glass with diverging compressibility and superfluid susceptibility, (iii) a Bose glass with a finite compressibility but diverging superfluid susceptibility. In addition to characterizing the insulating phases, we show that the superfluid-insulator transition is always of the Kosterlitz-Thouless universality class.

cond-mat.dis-nn↗

arXiv2007

Unzipping Vortices in Type-II Superconductors

The unzipping of vortex lines using magnetic-force microscopy from extended defects is studied theoretically. We study both the unzipping isolated vortex from common defects, such as columnar pins and twin-planes, and the unzipping of a vortex from a plane in the presence of other vortices. We show, using analytic and numerical methods, that the universal properties of the unzipping transition of a single vortex depend only on the dimensionality of the defect in the presence and absence of disorder. For the unzipping of a vortex from a plane populated with many vortices is shown to be very sensitive to the properties of the vortices in the two-dimensional plane. In particular such unzipping experiments can be used to measure the ``Luttinger liquid parameter'' of the vortices in the plane. In addition we suggest a method for measuring the line tension of the vortex directly using the experiments.

cond-mat.stat-mech↗

arXiv2006

DNA unzipping and the unbinding of directed polymers in a random media

We consider the unbinding of a directed polymer in a random media from a wall in $d=1+1$ dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these problems are {\em identical} up to an overall normalization factor. Our finding gives an example of a generalization of the stochastic matrix form decomposition to disordered systems; a method which effectively allows to reduce dimensionality of the problem. The equivalence between the two problems, for example, allows us to derive the probability distribution for finding the directed polymer a distance $z$ from the wall. We discuss implications of these results for the related Kardar-Parisi-Zhang equation and the asymmetric exclusion process.

cond-mat.stat-mech↗

arXiv2005

Sequence heterogeneity and the dynamics of molecular motors

The effect of sequence heterogeneity on the dynamics of molecular motors is reviewed and analyzed using a set of recently introduced lattice models. First, we review results for the influence of heterogenous tracks such as a single-strand of DNA or RNA on the dynamics of the motors. We stress how the predicted behavior might be observed experimentally in anomalous drift and diffusion of motors over a wide range of parameters near the stall force and discuss the extreme limit of strongly biased motors with one-way hopping. We then consider the dynamics in an environment containing a variety of different fuels which supply chemical energy for the motor motion, either on a heterogeneous or on a periodic track. The results for motion along a periodic track are relevant to kinesin motors in a solution with a mixture of different nucleotide triphosphate fuel sources.

cond-mat.stat-mech↗

arXiv2005

Unzipping flux lines from extended defects in type-II superconductors

With magnetic force microscopy in mind, we study the unbinding transition of individual flux lines from extended defects like columnar pins and twin planes in type II superconductors. In the presence of point disorder, the transition is universal with an exponent which depends only on the dimensionality of the extended defect. We also consider the unbinding transition of a single vortex line from a twin plane occupied by other vortices. We show that the critical properties of this transition depend strongly on the Luttinger liquid parameter which describes the long distance physics of the two-dimensional flux line array.

cond-mat.stat-mech↗

arXiv2004

Vortex pinning by a columnar defect in planar superconductors with point disorder

We study the effect of a single columnar pin on a $(1+1)$ dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, the pinning is most effective right at the temperature of the vortex glass transition. In particular, there is a pronounced maximum in the number of vortices which are prevented from tilting by the columnar defect in a weak transverse magnetic field. Using renormalization group techniques we show that the columnar pin is irrelevant at long length scales both above and below the transition, but due to very different mechanisms. This behavior differs from the disorder-free case, where the pin is relevant in the low temperature phase. Solutions of the renormalization equations in the different regimes allow a discussion of the crossover between the pure and disordered cases. We also compute density oscillations around the columnar pin and the response of these oscillations to a weak transverse magnetic field.

cond-mat.dis-nn↗

arXiv2004

Dynamics of Molecular Motors with Finite Processivity on Heterogeneous Tracks

The dynamics of molecular motors which occasionally detach from a heterogeneous track like DNA or RNA is considered. Motivated by recent single molecule experiments, we study a simple model for a motor moving along a disordered track using chemical energy while an external force opposes its motion. The motors also have finite processivity, i.e., they can leave the track with a position dependent rate. We show that the response of the system to disorder in the hopping off rate depends on the value of the external force. For most values of the external force, strong disorder causes the motors which survive for long times on the track to be localized at preferred positions. However, near the stall force, localization occurs for any amount of disorder. Existence of localized states near the top of the band implies a stretched exponential contribution to the decay of the survival probability. To obtain these results, we study the complex eigenvalue spectrum of the time evolution operator. A similar spectral analysis also provides a very efficient method for studying the dynamics of motors with infinite processivity.

cond-mat.stat-mech↗

arXiv2004

Phase transition of one dimensional bosons with strong disorder

We study one dimensional disordered bosons at large commensurate filling. Using a real space renormalization group approach we find a new random fixed point which controls a phase transition from a superfluid to an incompressible Mott-glass. The transition can be tuned by changing the disorder distribution even with vanishing interactions. We derive the properties of the transition, which suggest that it is in the Kosterlitz-Thouless universality class.

cond-mat.dis-nn↗

arXiv2004

Dynamics of Molecular Motors and Polymer Translocation with Sequence Heterogeneity

The effect of sequence heterogeneity on polynucleotide translocation across a pore and on simple models of molecular motors such as helicases, DNA polymerase/exonuclease and RNA polymerase is studied in detail. Pore translocation of RNA or DNA is biased due to the different chemical environments on the two sides of the membrane, while the molecular motor motion is biased through a coupling to chemical energy. An externally applied force can oppose these biases. For both systems we solve lattice models exactly both with and without disorder. The models incorporate explicitly the coupling to the different chemical environments for polymer translocation and the coupling to the chemical energy (as well as nucleotide pairing energies) for molecular motors. Using the exact solutions and general arguments we show that the heterogeneity leads to anomalous dynamics. Most notably, over a range of forces around the stall force (or stall tension for DNA polymerase/exonuclease systems) the displacement grows sublinearly as t^μwith μ<1. The range over which this behavior can be observed experimentally is estimated for several systems and argued to be detectable for appropriate forces and buffers. Similar sequence heterogeneity effects may arise in the packing of viral DNA.

cond-mat.stat-mech↗

arXiv2000

Why is the DNA Denaturation Transition First Order?

We study a model for the denaturation transition of DNA in which the molecules are considered as composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d=2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.

cond-mat.soft↗