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Supurna Sinha

Publications and source records attributed to Supurna Sinha.

At least 55 records · Page 3Linked to original sources
arXiv2009

The Universe in a Soap Film

The value of the cosmological constant is one of the major puzzles of modern cosmology: it is tiny but nonzero. Sorkin predicted, from the Causet approach to quantum gravity, that the cosmological constant has quantum fluctuations. The predicted order of magnitude of the fluctuations agrees with the subsequently observed value of the cosmological constant. We had earlier developed an analogy between the cosmological constant of the Universe and the surface tension of fluid membranes. Here we demonstrate by computer simulations that the surface tension of a fluid membrane has statistical fluctuations stemming from its discrete molecular structure. Our analogy enables us to view these numerical experiments as probing a small and fluctuating cosmological constant. Deriving insights from our analogy, we show that a fluctuating cosmological constant is a GENERIC feature of quantum gravity models and is far more general than the specific context in which it was originally proposed. We pursue and refine the idea of a fluctuating cosmological constant and work towards making further testable predictions.

gr-qc↗
arXiv2008

Free Energy of Twisted Semiflexible Polymers

We investigate the role of fluctuations in single molecule measurements of torque-link ($t-lk$) curves. For semiflexible polymers of finite persistence length (i.e. polymers with contour length $L$ comparable to the persistence length $L_P$), the torque versus link curve in the constant torque (isotorque) ensemble is distinct from the one in the constant link (isolink) ensemble. Thus, one encounters the conceptually interesting issue of a ``free energy of transition'' in switching ensembles while making torque-link measurements. We predict the dependence on the semiflexibility parameter $β= L/L_P$ of this extra contribution to the free energy which shows up as an area in the torque-link plane. This can be tested against future torque-link experiments with single biopolymers. We bring out the inequivalence of torque-link curves for a stiff polymer and present explicit analytical expressions for the {\it distinct} torque-link relations in the two ensembles and the free energy difference in switching ensembles in this context. The predictions of our work can be tested against single molecule experiments on torsionally constrained biopolymers.

cond-mat.soft↗
arXiv2007

Elasticity of Stiff Biopolymers

We present a statistical mechanical study of stiff polymers, motivated by experiments on actin filaments and the considerable current interest in polymer networks. We obtain simple, approximate analytical forms for the force-extension relations and compare these with numerical treatments. We note the important role of boundary conditions in determining force-extension relations. The theoretical predictions presented here can be tested against single molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules. Our work is motivated by the buckling of the cytoskeleton of a cell under compression, a phenomenon of interest to biology.

cond-mat.soft↗
arXiv2007

Jamming dynamics in grain mixtures : An extended hydrodynamic approach

We study jamming in granular mixtures from the novel point of view of extended hydrodynamics. Using a hard sphere binary mixture model we predict that a few large grains are expected to get caged more effectively in a matrix of small grains compared to a few small grains in a matrix of larger ones. A similar effect has been experimentally seen in the context of colloidal mixtures.

cond-mat.soft↗
arXiv2006

Short-wavelength collective modes in a binary hard-sphere mixture

We use hard-sphere generalized hydrodynamic equations to discuss the extended hydrodynamic modes of a binary mixture. The theory presented here is analytic and it provides us with a simple description of the collective excitations of a dense binary mixture at molecular length scales. The behavior we predict is in qualitative agreement with molecular-dynamics results for soft-sphere mixtures. This study provides some insight into the role of compositional disorder in forming glassy configurations.

cond-mat.soft↗
arXiv2006

Sound-propagation gap in fluid mixtures

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.

cond-mat.soft↗
arXiv2006

Mode-coupling theory of the stress-tensor autocorrelation function of a dense binary fluid mixture

We present a generalized mode-coupling theory for a dense binary fluid mixture. The theory is used to calculate molecular-scale renormalizations to the stress-tensor autocorrelation function (STAF) and to the long-wavelength zero-frequency shear viscosity. As in the case of a dense simple fluid, we find that the STAF appears to decay as $t^{-3/2}$ over an intermediate range of time. The coefficient of this long-time tail is more than two orders of magnitude larger than that obtained from conventional mode-coupling theory. Our study focuses on the effect of compositional disorder on the decay of the STAF in a dense mixture.

cond-mat.soft↗
arXiv2006

DNA Elasticity : Topology of Self-Avoidance

We present a theoretical treatment of DNA stretching and twisting experiments, in which we discuss global topological subtleties of self avoiding ribbons and provide an underlying justification for the worm like rod chain (WLRC) model proposed by Bouchiat and Mezard. Some theoretical points regarding the WLRC model are clarified: the writhe of open curves and the use of an adjustable cutoff parameter to ``regularise'' the model. Our treatment brings out the precise relation between the worm like chain (WLC), the paraxial worm like chain (PWLC) and the WLRC models. We describe the phenomenon of ``topological untwisting'' and the resulting collapse of link sectors in the WLC model and note that this leads to a free energy profile {\it{periodic}} in the applied link. This periodicity disappears when one takes into account the topology of self avoidance or at large stretch forces (paraxial limit). We note that the difficult nonlocal notion of self avoidance can be replaced (in an approximation) by the simpler local notion of ``south avoidance'' in the WLRC model. This gives an explanation for the efficacy of the approach of Bouchiat and Mezard in explaining the `hat curves' using the WLRC model. We propose a new class of experiments to probe the continuous transition between the periodic and aperiodic behavior of the free energy.

cond-mat.soft↗
arXiv2006

Surface Tension and the Cosmological Constant

The astronomically observed value of the cosmological constant is small but non-zero. This raises two questions together known as the cosmological constant problem a) why is lambda so nearly zero? b) why is lambda not EXACTLY zero? Sorkin has proposed that b) can be naturally explained as a one by square root N fluctuation by invoking discreteness of spacetime at the Planck scale due to quantum gravity. In this paper we shed light on these questions by developing an analogy between the cosmological constant and the surface tension of membranes. The ``cosmological constant problem'' has a natural analogue in the membrane context: the vanishingly small surface tension of fluid membranes provides an example where question a) above arises and is answered. We go on to find a direct analogue of Sorkin's proposal for answering question b) in the membrane context, where the discreteness of spacetime translates into the molecular structure of matter. We propose analogue experiments to probe a small and fluctuating surface tension in fluid membranes. A counterpart of dimensional reduction a la Kaluza-Klein and large extra dimensions also appears in the physics of fluid membranes.

cond-mat.soft↗
arXiv2005

Effect of Fluctuations on the Freezing of a Colloidal Suspension in an External Periodic Potential

We incorporate the effects of fluctuations in a density functional analysis of the freezing of a colloidal liquid in the presence of an external potential generated by interfering laser beams. A mean field treatment, using a density functional theory, predicts that with the increase in the strength of the modulating potential, the freezing transition changes from a first order to a continuous one via a tricritical point for a suitable choice of the modulating wavevectors. We demonstrate here that the continuous nature of the freezing transition at large values of the external potential $V_{e}$ survives the presence of fluctuations. We also show that fluctuations tend to stabilize the liquid phase in the large $V_{e}$ regime.

cond-mat.soft↗
arXiv2005

Euler buckling in red blood cells: An optically driven biological micromotor

We investigate the physics of an optically-driven micromotor of biological origin. A single, live red blood cell, when placed in an optical trap folds into a rod-like shape. If the trapping laser beam is circularly polarized, the folded RBC rotates. A model based on the concept of buckling instabilities captures the folding phenomenon; the rotation of the cell is simply understood using the Poincarè sphere. Our model predicts that (i) at a critical intensity of the trapping beam the RBC shape undergoes large fluctuations and (ii) the torque is proportional to the intensity of the laser beam. These predictions have been tested experimentally. We suggest a possible mechanism for emergence of birefringent properties in the RBC in the folded state.

physics.bio-ph↗
arXiv2005

Four-photon interference: a realizable experiment to demonstrate violation of EPR postulates for perfect correlations

Bell's theorem reveals contradictions between the predictions of quantum mechanics and the EPR postulates for a pair of particles only in situations involving imperfect statistical correlations. However, with three or more particles, contradictions emerge even for perfect correlations. We describe an experiment which can be realized in the laboratory, using four-photon entangled states generated by parametric down-conversion, to demonstrate this contradiction at the level of perfect correlations.

physics.optics↗
arXiv2005

Brownian motion and magnetism

We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an arbitrary system of spinless bosons in a magnetic field. The work presented here is expected to shed light on polymer entanglement, depolarized light scattering, and magnetic behavior of spinless bosons.

cond-mat.stat-mech↗
arXiv2005

Brownian motion at absolute zero

We derive a general quantum formula giving the mean-square displacement of a diffusing particle as a function of time. Near {\bf 0 K} we find a universal logarithmic behavior (valid for times longer than the relaxation time), and deviations from classical behavior can also be significant at larger values of time and temperature. Our derivation depends neither on the specific composition of the heat bath nor on the strength of the coupling between the bath and the particle. An experimental regime of microseconds and microdegrees Kelvin would elicit the pure logarithmic diffusion.

cond-mat.stat-mech↗
arXiv2005

Dynamic structure factors of a dense mixture

We compute the dynamic structure factors of a dense binary liquid mixture. These describe dynamics on molecular length scales, where structural relaxation is important. We find that the presence of a few large particles in a dense fluid of small particles slows down the dynamics considerably. We also observe a deep narrowing of the spectrum for a disordered mixture composed of a nearly equal packing of the two species. In contrast, a few small particles diffuse easily in the background of a dense fluid of large particles. We expect our results to describe neutron scattering from a dense mixture.

cond-mat.soft↗
arXiv2005

Decoherence at absolute zero

We present an analytical study of the loss of quantum coherence at absolute zero. Our model consists of a harmonic oscillator coupled to an environment of harmonic oscillators at absolute zero. We find that for an Ohmic bath, the offdiagonal elements of the density matrix in the position representation decay as a power law in time at late times. This slow loss of coherence in the quantum domain is qualitatively different from the exponential decay observed in studies of high temperature environments.

quant-ph↗
arXiv2004

Inequivalence of Statistical Ensembles in Single Molecule Measurements

We study the role of fluctuations in single molecule experimental measurements of force-extension curves. We use the Worm Like Chain (WLC) model to bring out the connection between the Helmholtz ensemble characterized by the Free Energy and the Gibbs ensemble characterized by the Free Energy . We consider the rigid rod limit of the WLC model as an instructive special case to bring out the issue of ensemble inequivalence. We point out the need for taking into account the free energy of transition when one goes from one ensemble to another. We also comment on the ``phase transition'' noticed in an isometric setup for semiflexible polymers and propose a realization of its thermodynamic limit. We present general arguments which rule out non-monotonic force-extension curves in some ensembles and note that these do not apply to the isometric ensemble.

cond-mat.soft↗