arXiv subjects

Biman Bagchi

Publications and source records attributed to Biman Bagchi.

At least 37 records · Page 2Linked to original sources

arXiv2024

The Hydrophobic Interaction Induced Strengthening of Hydrogen Bond in Water-DMSO Binary Mixture

The lifetime of a hydrogen bond between water and dimethyl sulfoxide (DMSO) is found to be considerably longer than that between two water molecules in the neat water. This is counter-intuitive because the charge on the oxygen in DMSO is considerably less than that in water. Additionally, the strength of the water-dimethyl sulfoxide (w-D) hydrogen bond is found to be strongly composition dependent; the lifetime of the hydrogen bond is ten times larger at 30% over that at very low concentration. Using computer simulations, we perform microscopic structural and dynamic analysis to find that these anomalies arise at least partly from an action-at-a-distance effect where the attraction between the hydrophobic methyl groups results in self-aggregation of DMSO molecules that cages both rotational and linear motions of molecules involved. This is reflected in the observed strong correlation of the lifetime with the local coordination number of the associated methyl groups. The elongated w-D h-bond lifetime causes a slowdown of collective dynamics and affects the lifetime of the w-w h-bond. This nonlinear feedback mechanism explains the strong composition dependence of viscosity and anticipated to play a dominant role in many self-assemblies. Furthermore, the w-D hydrogen bond breaking mechanism changes from low to high DMSO concentration, a phenomenon not anticipated a priori. We introduce a new order parameter-based free energy surface of the bond breaking pathway. A two-dimensional transition state rate theory (TSRT) calculation is performed for the lifetime of the w-D h-bond that is found to be semi-quantitatively accurate

cond-mat.soft↗

arXiv2024

Energy Transfer Mechanism Under Incoherent Light Excitation in noisy Environments: Memory Effects in Efficiency Control

Fluctuations in the energy gap and coupling constants in and between chromophores can play important role in the absorption and energy transfer across a collection of two level systems. In a noisy environment, fluctuations can control efficiency of energy transfer through several factors, including quantum coherence. Several recent studies have investigated the impact of light-induced stationary quantum coherence on the efficiency of transferring optical excitation to a designated "trap" state, crucial for subsequent reactions such as those in photosynthesis. However, these studies have typically employed either a Markovian, or a perturbative approximation for the environment induced fluctuations. In this study, we depart from these approaches to incorporate memory effects by using Kubo's quantum stochastic Liouville equation (QSLE). We introduce the effects of the decay of excitation (to the ground state) and the desired trapping that provides the direction of the motion of the excitation. In the presence of light-induced pumping, we establish a relation between the mean survival time, efficiency, and the correlation decay time of the bath-induced fluctuations. We find a decrease in the steady state coherence during the transition from the non-Markovian regime (characterized by small values of fluctuation strength V and inverse of bath correlation time b) to the Markovian limit (where V and b are both large), resulting in a decrease in efficiency. We recover a connection between transfer flux and the imaginary part of coherences in both equilibrium and excited bath states, in both correlated and We uncover a non-monotonic dependence of efficiency on site energy heterogeneity for both correlated and uncorrelated bath models.

physics.chem-ph↗

arXiv2024

Glassy Dynamics in a Molecular Liquid

A universal dynamical crossover temperature, Tcr, in glassy liquids, associated with the α-\b{eta} bifurcation temperature, TB, has been observed in dielectric spectroscopy and other experiments. Tcr lies significantly above the glass transition temperature. Here, we introduce a new class of glass-forming liquids, binary mixtures of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel-Fulcher-Tammann (VFT) form. As the temperature is lowered, the single peak rotational relaxation spectrum splits into two at a temperature TB significantly above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ~62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

cond-mat.soft↗

arXiv2024

Stokes Law at Molecular Length Scales: Effects of Intermolecular Interactions and Linear Response Theory

The celebrated Stokes Law (SL) of hydrodynamics predicts that the velocity of a particle pulled through a liquid by an external force, Fex, is directly proportional to the force and inversely proportional to the friction ζ acted by the medium on the particle. We investigate the range of validity of Stokes Law at molecular length scales by employing computer simulations to calculate friction by pulling a tagged particle with a constant force. We thus calculate friction for two model interaction potentials, Lennard-Jones, and soft sphere, for several particle sizes, ranging from radius (a) smaller than the solvent particles to three times larger. We next obtain friction from diffusion (D) by using Einstein's relation between diffusion and friction ζ in an unperturbed liquid. We find, to our surprise, a quantitative agreement between the two at a small-to-intermediate pulling force regime for all the sizes studied. The Law does break down at a large pulling force beyond a threshold value. Importantly, the range of validity of Stokes' scheme to obtain friction increases substantially if we turn off the attractive part of the interaction potential. Additionally, we calculate the viscosity (η) of the unperturbed liquid and find a good agreement with the Stokes-Einstein relation ζ=Cηa for the viscosity dependence with a value of C close to 5 π, that is intermediate between the slip and stick boundary condition.

cond-mat.soft↗

arXiv2024

Friction and Memory Effects in Homogeneous Gas-Liquid Nucleation: Quest for Quantitative Rate Calculation

The task of a first principles theoretical calculation of the rate of gas to liquid nucleation has remained largely incomplete despite the existence of reliable results from unbiased simulation studies at large supersaturation. Although the classical nucleation theory, formulated by Becker-Doring-Zeldovich (BDZ) about a century ago, provides an elegant, widely-used picture of nucleation in a first-order phase transition, the theory finds difficulties in predicting the rate accurately, especially in the case of gas-to-liquid nucleation. Here, we use a multiple-order parameter description to construct the nucleation free energy surface needed to calculate the nucleation rate. A multidimensional non-Markovian rate theory formulation that generalizes Langer's well-known nucleation theory by using Grote-Hynes multidimensional non-Markovian treatment is used to obtain the rate of barrier crossing. We find good agreement of the theory with the rate obtained by direct unbiased molecular dynamics simulations, the latter is feasible at large supersaturation, S. The theory gives the experimentally strong dependence of the rate of nucleation on supersaturation, S. Interestingly, we find a strong influence of frequency-dependent friction at the barrier top. This arises from multiple recrossing of the barrier surface. We find that a Markovian theory, such as Langer's formulation, fails to capture the rate quantitatively. In addition, the multidimensional transition state theory expression performs poorly, revealing the underlying role of friction.

cond-mat.soft↗

arXiv2022

Examination of Boltzmann's H-Function: Dimensionality and Interaction Sensitivity Dependence, and a comment on his H-Theorem

Boltzmann's H-Theorem, formulated 150 years ago in terms of H-function that also bears his name, is one of the most celebrated theorems of science and paved the way for the development of nonequilibrium statistical mechanics. Nevertheless, quantitative studies of the H-function, denoted by H(t), in realistic systems are relatively scarce because of the difficulty of obtaining the time-dependent momentum distribution analytically. Also, the earlier attempts proceeded through the solution of Boltzmann's kinetic equation, which was hard. Here we investigate, by direct molecular dynamics simulations and analytic theory, the time dependence of H(t). We probe the sensitivity of nonequilibrium relaxation to interaction potential and dimensionality by using the H-function H(t). We evaluate H(t) for three different potentials in all three dimensions and find that it exhibits surprisingly strong sensitivity to these factors. The relaxation of H(t) is long in 1D, but short in 3D. We obtain, for the first time, a closed-form analytic expression for H(t) using the solution of the Fokker-Planck equation for the velocity space probability distribution and compare its predictions with the simulation results. Interestingly, H(t) is found to exhibit linear response when vastly different initial nonequilibrium conditions are employed. The oft-quoted relation of H-function with Clausius's entropy theorem is discussed.

cond-mat.stat-mech↗

arXiv2022

Diffusion in the Presence of Correlated Returns in a Two-dimensional Energy Landscape and non-Monotonic Friction Dependence: Examination of Simulation Results by a Random Walk Model

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and simulations of a tagged particle moving on a two-dimensional periodic potential energy surface, both in the presence and absence of noise. Langevin dynamics simulations at multiple temperatures are carried out to obtain the diffusion coefficient of a solute particle. Friction is varied from zero to large values. Diffusive motion emerges in the limit of long times, even in the absence of noise, although the trajectory is found to remain correlated over a long time. This correlation is manifested in correlated returns to the starting minima following a scattering by surrounding maxima. Noise destroys this correlation, induces chaos, and increases diffusion at small friction. Diffusion thus exhibits a non-monotonic friction dependence at the intermediate value of the damping, ultimately converging to our theoretically predicted value. The latter is obtained by using the well-established relation between diffusion and random walk. An excellent agreement is obtained between theory and simulations in the high friction limit, but not so in the intermediate regime. The rate of escape from one cell to another is obtained from the multidimensional rate theory of Langer. We find that enhanced dimensionality plays an important role. In order to quantify the effects of noise on the potential-imposed coherence on the trajectories, we calculate the Lyapunov exponent. At small friction values, the Lyapunov exponent mimics the friction dependence of the rate.

cond-mat.stat-mech↗

arXiv2022

A Stochastic Approach to Maxwell Velocity Distribution via Central Limit Theorem and Boltzmann's Entropy Formula

Maxwell's velocity distribution is known to be universally valid across systems and phases. Here we present a new and general derivation that uses the central limit theorem (CLT) of the probability theory. This essentially uses the idea that repeated intermolecular collisions introduce randomness in the velocity change in the individual components of the velocity vector, leading to, by the CLT, a Gaussian distribution. To complete the derivation, we next show that the mean-square velocity or the standard deviation follows exactly from Boltzmann's formula relating entropy to the density of states, thus avoiding the use of the ideal gas equation of state explicitly. We furthermore prove the Maxwell velocity distribution for a system of harmonic oscillators. This derivation provides a further insight into the origin of Boltzmann's constant in the Maxwell velocity distribution and also in the equipartition theorem. We propose that this derivation provides an approach that explains the universality of Maxwell Gaussian distribution.

cond-mat.stat-mech↗

arXiv2021

Emergence of Dynamical Coherence in a Driven One-dimensional Interacting Rotor Model

In order to understand the dynamics of active matter, we examine a minimalistic model where interacting spins on a one-dimensional lattice are driven by a self-propelled spin at the centre with a fixed rotational velocity $(ω_{0})$. The other spins execute rotational Brownian motion by following the Shore-Zwanzig model of rotational dynamics. The simplicity of the model allows us to inquire about several relevant microscopic quantities. The continuous 'active' torque on the central spin is propagated through nearest neighbour interactions with a uniform coupling parameter, J. We have found a bounded region in the J-$ω_{0}$ plane where the system exhibits 'active matter like behaviour'. Interestingly, in the limits of large J and $ω_{0}$, we observe a 'slipping behaviour'. The site specific average rotational velocity of the spin, as one moves away from the central spin exhibits a nearly exponential decay with distance, allowing the definition of a correlation length $(ξ)$ which grows rapidly with an increase of the coupling (J) between the spins. Site specific average velocity exhibits a change from a single exponential to biexponential decay pattern as the system enters the active region of the phase diagram, accompanied by a non-monotonic behavior of the correlation length. We conclude that a macroscopic coherent state can emerge in the presence of a small concentration of active molecules. We discuss experimental relevance of our results.

cond-mat.stat-mech↗

arXiv2021

Signatures of Surprising Diffusion-Entropy Scaling across Pressure Induced Glass Transition in Water

Because of the negative inclination of the solid-liquid phase separation line in water, ice Ih melts on compression. On further increase in pressure the liquid water transforms into a high density metastable glassy state, characterized by a rapid approach to zero diffusion coefficient and an absence of any crystalline order in the static structure factor. The vitrification is found to occur even at high temperatures (T > 250 K). We study this glass transition process at four temperatures (80 K, 250 K, 300 K and 320 K). The transition pressure increases with increase in temperature, as expected. Interestingly, we find that the total entropy of the system exhibits a sharp crossover near the glass transition pressure where the diffusion of water goes to zero. The diffusion coefficient shows an exponential dependence on the properly defined excess entropy. In an interesting result not reported before, we find a pressure induced realignment of water molecules resulting in two well separated peaks in the O-O-O angle distribution among neighbouring molecules. The difference between the positions of these two peaks undergoes a sharp change at the vitrification pressure suggesting that it can serve as an appropriate order parameter to detect the glass transition point.

cond-mat.soft↗

arXiv2021

Effect of vibronic relaxation in fluorescence resonance energy transfer: An exact analytical solution

Fluorescence resonance energy transfer (FRET) is widely used as a 'spectroscopic ruler' to measure fluctuations in macromolecules because of the strong dependence of the rate on the separation (R) between the donor (D) and acceptor (A). However, the well-known Forster rate expression that predicts an $R^{-6}$ dependence, is limited by several approximations. Notable among them is the neglect of the vibronic relaxation in the reactant (donor) and product (acceptor) manifolds. Vibronic relaxation can play an important role when the energy transfer rate is faster than the vibronic relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibronic states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we attempt to eliminate this lacuna, by allowing relaxation in the vibronic energy levels and adopting a relaxation model to account for vibronic cascading down in the donor manifold. We develop a Green's function based generalized formalism and provide an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibronic relaxation. We find and verify that the neglect of vibronic relaxations can significantly alter the energy transfer rate and overestimates the distance between D and A.

physics.chem-ph↗

arXiv2020

Origin of Multiple Infection Waves in a Pandemic: Effects of Inherent Susceptibility and External Infectivity Distributions

Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($σ_{inh}$) and external infectivity ($ι_{ext}$), in a given population. While the former is determined by the immunity of an individual towards a disease, the latter depends on the duration of exposure to the infection. We model the spatio-temporal propagation of a pandemic using a generalized SIR (Susceptible-Infected-Removed) model by introducing the susceptibility and infectivity distributions to understand their combined effects, which appear to remain inadequately addressed till date. We consider the coupling between $σ_{inh}$ and $ι_{ext}$ through a new Critical Infection Parameter (CIP) ($γ_c$). We find that the neglect of these distributions, as in the naive SIR model, results in an overestimation of the amount of infection in a population, which leads to incorrect (higher) estimates of the infections required to achieve the herd immunity threshold. Additionally, we include the effects of seeding of infection in a population by long-range migration. We solve the resulting master equations by performing Kinetic Monte Carlo Cellular Automata (KMC-CA) simulations. Importantly, our simulations can reproduce the multiple infection peak scenario of a pandemic. The latent interactions between disease migration and the distributions of susceptibility and infectivity can render the progression a character vastly different from the naive SIR model. In particular, inclusion of these additional features renders the problem a character of a living percolating system where the disease cluster survives by migrating from region to region.

q-bio.PE↗

arXiv2020

Study of Entropy-Diffusion Relation in a Deterministic Hamiltonian System through Microscopic Analysis

Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation between the two does not seem to exist. Here we explore the nature of this entropy-diffusion relation in three deterministic systems where an accurate estimate of both can be carried out. We study three deterministic model systems, (a) the motion of a single point particle with constant energy in a two-dimensional periodic potential energy landscape, (b) the same in regular Lorentz gas where a point particle with constant energy moves between collisions with hard disc scatterers and (c) motion of a point particle among the boxes with small apertures. These models, introduced by Zwanzig, exhibit diffusive motion in the limit where ergodicity is shown to exist. We then explore the diffusion-entropy relation by an accurate calculation of both diffusion and entropy for the aforementioned model systems. We estimate the self-diffusion coefficient of the particle by employing computer simulations and entropy by quadrature using Boltzmann's formula. We observe an interesting crossover in the diffusion-entropy relation in some specific regions which is attributed to the emergence of correlated returns. The crossover could herald a breakdown of the Rosenfeld-like exponential scaling between the two, as observed at low temperatures. Later, we modify the scaling relation to account for the correlated motions and present a detailed analysis of the dynamical entropy obtained via Lyapunov exponent which is rather an important quantity in the study of deterministic systems.

cond-mat.stat-mech↗

arXiv2020

Attainment of Herd Immunity: Mathematical Modelling of Survival Rate

We study the influence of the rate of the attainment of herd immunity (HI), in the absence of an approved vaccine, on the vulnerable population. We essentially ask the question: how hard the evolution towards the desired herd immunity could be on the life of the vulnerables? We employ mathematical modelling (chemical network theory) and cellular automata based computer simulations to study the human cost of an epidemic spread and an effective strategy to introduce HI. Implementation of different strategies to counter the spread of the disease requires a certain degree of quantitative understanding of the time dependence of the outcome. In this paper, our main objective is to gather understanding of the dependence of outcome on the rate of progress of HI. We generalize the celebrated SIR model (Susceptible-Infected-Removed) by compartmentalizing the susceptible population into two categories- (i) vulnerables and (ii) resilients, and study dynamical evolution of the disease progression. We achieve such a classification by employing different rates of recovery of vulnerables vis-a-vis resilients. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population, and the complex dependence on the rate of attainment of herd immunity. Our results quantify the adverse effects on the recovery rates of vulnerables in the course of attaining the herd immunity. We find the important result that a slower attainment of the HI is relatively less fatal. However, a slower progress towards HI could be complicated by many intervening factors.

q-bio.PE↗

arXiv2020

Dynamical Theory and Cellular Automata Simulations of Pandemic Spread: Understanding Different Temporal Patterns of Infections

Here we propose and implement a generalized mathematical model to find the time evolution of population in infectious diseases and apply the model to study the recent COVID-19 pandemic. Our model at the core is a non-local generalization of the widely used Kermack-McKendrick(KM) model where the susceptible(S) population evolves into two other categories, namely infectives(I) and removed(R). This is the well-known SIR model in which we further divide both S and I into high and low risk categories. We first formulate a set of non-local dynamical equations for the time evolution of distinct population distributions under this categorization in an attempt to describe the general scenario of infectious disease progression. We then solve the non-linear coupled differential equations-(i) numerically by the method of propagation, and (ii) a more flexible and versatile cellular automata (CA) simulation which provides a coarse-grained description of the generalized non-local model. In order to account for multiple factors such as role of spreaders before containment, we introduce a time dependent rate which appears to be essential to explain the sudden spikes before the plateau observed in many cases (for example like China). We demonstrate how this generalized approach allows us to handle the effects of (i) time-dependence of the rate-constants of spread, (ii) different population density, (iii) the age ratio, (iv) quarantine, (v) lockdown, and (vi) social distancing. Our study allows us to make certain predictions regarding the nature of spread with respect to several external parameters, treated as control variables. Analysis of the model clearly shows that due to the strong heterogeneity in the epidemic process originating from the distribution of initial infectives, the theory must be local in character but at the same time connect to a global perspective.

q-bio.PE↗

arXiv2020

Inherent structure analysis reveals origin of breakdown of Stokes-Einstein relation in aqueous binary mixtures

We show by inherent structure (IS) analysis that the sharp composition dependent breakdown of the Stokes-Einstein relation correlates surprisingly well with an equally sharp non-monotonic variation in the average inherent structure (IS) energy of these mixtures. Further IS analysis reveals the existence of a unique ground state, stabilized by the optimum number of H-bonds at this composition. The surprisingly sharp turnaround behaviour observed in the effective hydrodynamic radius can be traced back to the formation of low energy equilibrium structures at specific compositions.

cond-mat.soft↗

arXiv2019

Understanding Enhanced Mechanical Stability of DNA in the Presence of Intercalated Anticancer Drug: Implications for DNA Associated Processes

Most of the anticancer drugs bind to double-stranded DNA (dsDNA) by intercalative-binding mode. Although experimental studies have become available recently, a molecular-level understanding of the interactions between the drug and dsDNA that lead to the stability of the intercalated drug is lacking. Of particular interest are the modifications of the mechanical properties of dsDNA observed in experiments. The latter could affect many biological functions, such as DNA transcription and replication. Here we probe, via all-atom molecular dynamics (MD) simulations, change in the mechanical properties of intercalated drug-DNA complexes for two intercalators, daunomycin and ethidium. We find that, upon drug intercalation, stretch modulus of DNA increases significantly, whereas its persistence length and bending modulus decrease. Steered MD simulations reveal that it requires higher forces to stretch the intercalated dsDNA complexes than the normal dsDNA. Adopting various pulling protocols to study force-induced DNA melting, we find that the dissociation of dsDNA becomes difficult in the presence of intercalators. The results obtained here provide a plausible mechanism of function of the anticancer drugs, i.e., via altering the mechanical properties of DNA. We also discuss long-time consequences of using these drugs, which require further in vivo investigations.

cond-mat.soft↗

arXiv2019

Ice-water Interface: Correlation between Structure and Dynamics

To comprehend the complexities of the ice-water interface, we perform a study that attempts to correlate the altered dynamics of water to its perturbed structure at, and due to, the interface. The deviation from bulk values of structural and dynamical quantities at the interface are obtained by computer simulations. Water molecules are found to get exchanged between the ice-like and water-like domains of the interface with a time scale of the order of ~10 ps. To investigate the effect of interfaces in general, we study three other systems, namely (i) water between two hydrophobic nano-slabs, (ii) water at protein and (iii) DNA surfaces. In all these systems, we find that the difference from bulk properties become negligible beyond ~1 nm, with structural features converging to bulk values faster than the dynamical properties. Even in the case of the latter, we find that single-particle and collective properties behave differently. The approach to bulk values is rapid except for collective shell-dipole moments. We present a new insightful characterization of the surfaces by establishing a quantitative correlation between tetrahedrality order parameter (q_td) and dynamics by diffusion (D) and angular jumps. In the ice-water system, we find that the variation of qtd, as we move from solid to the liquid phase, correlated well with D. The correlation is found to be present in all the interfaces studied. Our results can be used to explain the experimental outcomes of the likes of dielectric relaxation and solvation dynamics.

cond-mat.soft↗