Fluctuation theorems and orbital magnetism in nonequilibrium state

We study Langevin dynamics of a driven charged particle in the presence as well as in the absence of magnetic field. We discuss the validity of various work fluctuation theorems using different model potentials and external drives. We also show that one can generate an orbital magnetic moment in a nonequilibrium state which is absent in equilibrium.Comment: Based on a talk by A. M. J at international workshop MESODIS'06 (IIT Kanpur,Dec-2006

Transcriptional Proofreading in Dense RNA Polymerase Traffic

The correction of errors during transcription involves the diffusive backward translocation (backtracking) of RNA polymerases (RNAPs) on the DNA. A trailing RNAP on the same template can interfere with backtracking as it progressively restricts the space that is available for backward translocation and thereby ratchets the backtracked RNAP forward. We analyze the resulting negative impact on proofreading theoretically using a driven lattice gas model of transcription under conditions of dense RNAP traffic. The fraction of errors that are corrected is calculated exactly for the case of a single RNAP; for multi-RNAP transcription, we use simulations and an analytical approximation and find a decrease with increasing traffic density. Moreover, we ask how the parameters of the system have to be set to keep down the impact of the interference of a trailing RNAP. Our analysis uncovers a surprisingly simple picture of the design of the error correction system: its efficiency is essentially determined by the rate for the initial backtracking step, while the value of the cleavage rate ensures that the correction mechanism remains efficient at high transcription rates. Finally, we argue that our analysis can also be applied to cases with transcription-translation coupling where the leading ribosome on the transcript assumes the role of the trailing RNAP

Supersymmetry and Fokker-Planck dynamics in periodic potentials

Recently, the Fokker-Planck dynamics of particles in periodic potentials ±V, have been investigated by using the matrix continued fraction method. It was found that the two periodic potentials, one being bistable and the other metastable give the same diffusion coefficient in the overdamped limit. We show that this result naturally follows from the fact that the considered potentials in the corresponding Schrodinger equation form supersymmetric partners. We show that these differing potentials ±V also exhibit symmetry in current and diffusion coefficients: J+(F)=−J−(−F) and D+(F)=D−(−F) in the presence of a constant applied force F. Moreover, we show numerically that the transport properties in these potentials are related even in the presence of oscillating drive

Split hand/foot malformation with longitudinal deficiency of tibia: novel rehabilitation approach of a rare syndrome

Background: Split hand/foot malformation with longitudinal deficiency of tibia (SHFLD1) is an extremely rare congenital anomaly, even rarer are the descriptions in the literature of suitable techniques of treatment. Most of the literature available are case reports, based on genetic studies. This study highlights on functional management rather than anatomic correction of deformity. A clinician may not come across a patient with such a rare congenital disorder during his entire career.Methods: On retrospective review of hospital record from July 2008 to July 2018, we observed 5 cases of tibial deficiency associated with split hand and or split foot anomalies and diagnosed as SHHLD syndrome. Clinical and radiological analysis was done to plan out surgical and rehabilitation protocol for individual cases.Results: As per Flatt’s grouping of split hand, 3 limbs (37.5%) were group-1 type, 3 limbs (37.5%) of group-2 type and group-3 type was seen in 2 limbs (25%) of a patient with bilateral involvement. With respect to Jone’s radiological classification system, 4 limbs (57%) were of type Ia, 2 limbs (29%) were having type IV deformity and 1 limb (14%) was with type II deformity. One case agreed for amputation was fitted with above knee prosthesis and another one with custom designed bend knee prosthesis. Eldest case was rehabilitated with tricycle and modified orthosis. Surgical correction was tried in one case.Conclusions: Functional rehabilitation instead of anatomic correction should be tried at late presentation. Cleft closure should be done before development of functional adaptability

A charged particle in a magnetic field - Jarzynski Equality

We describe some solvable models which illustrate the Jarzynski theorem and related fluctuation theorems. We consider a charged particle in the presence of magnetic field in a two dimensional harmonic well. In the first case the centre of the harmonic potential is translated with a uniform velocity, while in the other case the particle is subjected to an ac force. We show that Jarzynski identity complements Bohr-van Leeuwen theorem on the absence of diamagnetism in equilibrium classical system.Comment: 5 pages, minor corrections made and journal reference adde

Stochastic resonance and heat fluctuations in a driven double-well system

We study a periodically driven (symmetric as well as asymmetric)double-well potential system at finite temperature. We show that mean heat loss by the system to the environment(bath) per period of the applied field is a good quantifier of stochastic resonance. It is found that the heat fluctuations over a single period are always larger than the work fluctuations. The observed distributions of work and heat exhibit pronounced asymmetry near resonance. The heat losses over a large number of periods satisfies the conventional steady-state fluctuation theorem, though different relation exists for this quantity.Comment: modified version, 10 figure

Reorganization of a 2D disordered granular medium due to a small local cyclic perturbation

We measure experimentally the rearrangements due to a small localized cyclic displacement applied to a packing of rigid grains under gravity in a 2D geometry. We analyze the evolution of the response to this perturbation by considering the individual particle displacement and the coarse grained displacement field, as well as the mean packing fraction and coordination number. We find that the displacement response is rather long ranged, and evolves considerably with the number of cycles. We show that a small difference in the preparation method (induced by tapping the container) leads to a significant modification in the response though the packing fraction changes are minute. Not only the initial response but also its further evolution change with preparation, demonstrating that the system still retains a memory of the initial preparation after many cycles. Nevertheless, after a sufficient number of cycles, the displacement response for both preparation methods converges to a nearly radial field with a 1/r decay from the perturbation source. The observed differences between the preparation methods seem to be related to the changes in the coordination number (which is more sensitive to the evolution of the packing than the packing fraction). Specifically, it may be understood as an effect of the breaking of local arches, which affects the lateral transmission of forces.Comment: 13 pages, revised and resubmitted to J. Stat. Mech.: Theory and Exp. (JSTAT

Classical and Thermodynamic work fluctuations

We have studied the nature of classical work ($W_{c}$) and thermodynamic work ($W$) fluctuations in systems driven out of equilibrium both in transient and time periodic steady state. As the observation time of trajectory increases, we show that the number of trajectories which exhibit excursions away from the typical behaviour i.e., $W_{c}<0$, $W<\Delta F$ and dissipated heat $Q<0$ decreases as anticipated for macroscopic time scales. Analytical expressions for such trajectories are obtained. Trajectory for which $W_{c}<0$ may not correspond to $W<\Delta F$ or $Q<0$. The applicability of steady state fluctuation theorems are discussed in our linear as well as nonlinear models.Comment: Based on the talk presented by Mamata Sahoo at the Condensed Matter Days-Aug. 2008 held at Viswavarati University, Kolkata. 19 pages, 8 figure

Synthesis and characterization of flame retardant jute-g-poly (2-ethyl hexylacrylate)/montmorillonite composites

303-310Chemically modified jute fiber (Tossa variety) has been grafted onto 2-ethyl hexylacrylate (2-EHA) to prepare copolymer using <i style="mso-bidi-font-style: normal">in situ developed transition metal complex initiating system; CuSO4/glycine/potassium monopersulfate (KMPS). Then its composites have been prepared by incorporating montmorillonite (MMT) clay. The samples have been characterized by Fourier Transform-Infrared (FTIR) spectroscopy and surface morphology by Scanning Electron Microscopy (SEM). The thermal behavior and tensile strength of the samples have been studied. The fire retardant properties are studied using oxygen consumption cone calorimeter. The biodegradability of the composites has been tested to see if it is ecofriendly by nature and viable for better commercialization

Velocity auto correlation function of a confined Brownian particle

Motivated by the simple models of molecular motor obeying a linear force-velocity relation, we have studied the stochastic dynamics of a Brownian particle in the presence of a linear velocity dependent force, $$f_s(1-\frac{v}{v_0})$$ where $$f_{s}$$ is a constant. The position and velocity auto correlation functions in different situations of the dynamics are calculated exactly. We observed that the velocity auto correlation function shows an exponentially decaying behaviour with time and saturates to a constant value in the time asymptotic limit, for a fixed $$f_s$$. It attains saturation faster with increase in the $$f_{s}$$ value. When the particle is confined in a harmonic well, the spectral density exhibits a symmetric behaviour and the corresponding velocity auto correlation function shows a damped oscillatory behaviour before decaying to zero in the long time limit. With viscous coefficient, a non-systematic variation of the velocity auto correlation function is observed. Further, in the presence of a sinusoidal driving force, the correlation in velocities increases with increase in the amplitude of driving in the transient regime. For the particle confined in a harmonic well, the correlation corresponding to the shift relative to the average position is basically the thermal contribution to the total position correlation. Moreover, in the athermal regime, the total correlation is entirely due to the velocity dependent force