The irreversible thermodynamics of curved lipid membranes

The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intra-membrane lipid flow, intra-membrane phase transitions, and protein binding and diffusion is studied. The forms of the entropy production for the irreversible processes are obtained, and the corresponding thermodynamic forces and fluxes are identified. Employing the linear irreversible thermodynamic framework, the governing equations of motion along with appropriate boundary conditions are provided.Comment: 62 pages, 4 figure

Geometry and dynamics of lipid membranes: The Scriven--Love number

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and non-dimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven--Love number, and the well-known F\"oppl--von K\'arm\'an number result from a scaling analysis. The Scriven--Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the F\"oppl--von K\'arm\'an number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven--Love and F\"oppl--von K\'arm\'an numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces---with bending forces playing a negligible role. Calculations of non-negligible Scriven--Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.Comment: 16 pages, 7 figures, 5 table

Optimization of ANN Structure Using Adaptive PSO & GA and Performance Analysis Based on Boolean Identities

In this paper, a novel heuristic structure optimization technique is proposed for Neural Network using Adaptive PSO & GA on Boolean identities to improve the performance of Artificial Neural Network (ANN). The selection of the optimal number of hidden layers and nodes has a significant impact on the performance of a neural network, is decided in an adhoc manner. The optimization of architecture and weights of neural network is a complex task. In this regard the use of evolutionary techniques based on Adaptive Particle Swarm Optimization (APSO) & Adaptive Genetic Algorithm (AGA) is used for selecting an optimal number of hidden layers and nodes of the neural controller, for better performance and low training errors through Boolean identities. The hidden nodes are adapted through the generation until they reach the optimal number. The Boolean operators such as AND, OR, XOR have been used for performance analysis of this technique

Synthesis of thiazole, benzothiazole, oxadiazole, thiadiazole, triazole and thiazolidinone incorporated coumarins

3-Bromoacetylcoumarin-(2)obtained by brominationof 3-acetylcoumarin (1)was condensed with2-amin0-4-phenylthiazole,2-aminothiazole,2-aminobenzothiazole, 2- amino-4-phenyloxadiazole, 2-aminothiadiazole, 3-aminotriazole to form the corresponding heteroaryl aminoacetylcoumarins (3a-f).The reaction of 2 withthiourea furnished 2-amino-4-(coumarinyl-3) thiazole (4) which further reacted with phenyli$othiocyanate forming the unsymmetrical thiourea (5). The thiourea on cyclocondensation withchloroacetic acid gave the thiazolidinone (6)which on further reaction with differen~aromaUcaldehydes resulted inthe formationofthe corresponding arylidene compounds (7). The structures of the products were confirmed from their analytical and spectraldata

Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field

The present study focuses on the cross-stream migration of a neutrally buoyant two-dimensional drop in a Poiseuille flow in a channel under the influence of an electric field. In the absence of an electric field, the important nondimensional parameters describing this problem are the viscosity ratio (λ) between the drop fluid and the surrounding medium, the ratio of drop diameter to channel height (a∗), and the capillary number (Ca). The influence of all these parameters on drop migration is investigated. It is observed that a large drop moves slowly as compared to a smaller drop, but attains a steady shape at the center line of the channel. The increase in value of the capillary number enhances the cross-stream migration rate, while the increase in viscosity ratio reduces the tendency of the drops to move towards the channel center line. The presence of an electric field introduces additional interfacial stresses at the drop interface, which in turn alters the dynamics observed in the absence of an electric field. Extensive computations are carried out to analyze the combined effect of the electric field and the shear flow on the cross-stream migration of the drop. The computational results for a perfect dielectric indicate that the droplet migration enhances in the presence of an electric field. The permittivity ratio (S) and the electric field strength (E) play major roles in drop migration and deformation. Computations using the leaky dielectric model also show that for certain combinations of electrical properties the drop undergoes immense elongation along the direction of the electric field. The conductivity ratio (R) is again a vital parameter in such a system of fluids. It is further observed that for certain conditions the leaky dielectric drops exhibit rotation together with translation

Coalescence dynamics of a hollow droplet falling in a liquid pool

The partial coalescence dynamics of a hollow droplet in a liquid pool is numerically investigated. We study the effect of the ratio of the inner to outer radii (Rr) of the hollow droplet while maintaining a constant volume. It is observed that for small values of the radius ratio, the coalescence dynamics is similar to that of a ‘filled’ droplet, but the partial coalescence is suppressed for large values of Rr. Increasing the value of increases the distance migrated by the inner bubble in the downward direction inside the pool away from the free surface. The location of the bubble after coalescence is found to play an important role in the pinch-off process of the satellite droplet. The influence of the governing dimensionless parameters on the coalescence dynamics has also been investigated

Dynamics of Hot QCD Matter -- Current Status and Developments

The discovery and characterization of hot and dense QCD matter, known as Quark Gluon Plasma (QGP), remains the most international collaborative effort and synergy between theorists and experimentalists in modern nuclear physics to date. The experimentalists around the world not only collect an unprecedented amount of data in heavy-ion collisions, at Relativistic Heavy Ion Collider (RHIC), at Brookhaven National Laboratory (BNL) in New York, USA, and the Large Hadron Collider (LHC), at CERN in Geneva, Switzerland but also analyze these data to unravel the mystery of this new phase of matter that filled a few microseconds old universe, just after the Big Bang. In the meantime, advancements in theoretical works and computing capability extend our wisdom about the hot-dense QCD matter and its dynamics through mathematical equations. The exchange of ideas between experimentalists and theoreticians is crucial for the progress of our knowledge. The motivation of this first conference named "HOT QCD Matter 2022" is to bring the community together to have a discourse on this topic. In this article, there are 36 sections discussing various topics in the field of relativistic heavy-ion collisions and related phenomena that cover a snapshot of the current experimental observations and theoretical progress. This article begins with the theoretical overview of relativistic spin-hydrodynamics in the presence of the external magnetic field, followed by the Lattice QCD results on heavy quarks in QGP, and finally, it ends with an overview of experiment results.Comment: Compilation of the contributions (148 pages) as presented in the `Hot QCD Matter 2022 conference', held from May 12 to 14, 2022, jointly organized by IIT Goa & Goa University, Goa, Indi

Co-Flow Microbial Fuel Cells

Microbial fuel cells (MFCs) are electrochemical devices that use bacteria as a vehicle to oxidize organic and inorganic matter to produce electricity. Previous effort has developed proton exchange membrane (PEM) MFCs, which integrate continuous fluid flow and use the membrane as a physical barrier between anodic and cathodic compartments. Recently, fuel cells have been developed to take advantage of the ability of low Re fluids to flow side by side down a microchannel without convective mixing. The liquid-liquid interface acts as a membrane, through which fast protons are transported, so co-flow devices do not suffer the problem of membrane degradation that their PEM counterparts do. This paper evaluates the design, fabrication, and testing of a microfluidic co-flow MFC using the bacterial strain Shewanella oneidensis MR-1. Technical challenges in the proof of concept experimentation are systematically worked through and the design of other working co-flow devices are adapted to come up with two possible co-flow MFC fabrication procedures

Irreversible Thermodynamics and Hydrodynamics of Biological Membranes

This thesis is concerned with developing a wholistic description of biological membranes: fascinating materials that make up the boundary of the cell, as well as many of the cell’s internal organelles. Our formulation of the theory of such materials relies on two well-known concepts: differential geometry and irreversible thermodynamics. The setting of differential geometry allows us to describe curves and surfaces, which in this case are embedded in the three-dimensional Euclidean space, while irreversible thermodynamics provides a theoretical framework to develop constitutive relations between the various thermodynamic forces and fluxes in a system. Both concepts are well-known, and are reviewed in Part A.We build on these classic results in Part B, and develop the theory of irreversible thermodynamics for arbitrarily curved and deforming lipid membranes. In particular, we treat the membrane as a two-dimensional surface, in which lipids flow in-plane as a two-dimensional fluid while the membrane bends out-of-plane as an elastic shell. We then obtain the fundamental balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the second law of thermodynamics. Finally, we apply the framework of irreversible thermodynamics to determine appropriate constitutive relations, and substitute them into the balance laws to obtain the equations governing membrane dynamics. Our main result is to present the equations of motion and appropriate boundary conditions for three systems of increasing complexity: (i) a compressible, inviscid membrane, (ii) a compressible, viscous membrane, and (iii) an incompressible, viscous membrane.Part C of this thesis focuses on applications of the single-component theory. We begin by specializing the general governing equations to three commonly observed geometries in biological systems: planar sheets, spherical vesicles, and cylindrical tubes. A scaling analysis of the resultant equations reveals membrane dynamics are governed by two dimensionless numbers. The well-known Föppl–von Kármán number, Γ, compares tension forces to the familiar elastic bending forces, while a new dimensionless quantity—which we name the Scriven–Love number, SL—compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to bending forces. Calculations of non-negligible Scriven–Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior, and can never be ignored in lipid membrane tubes. Moreover, a stability analysis indicates membrane tubes are unstable above a critical value of Γ, while SL governs the spatiotemporal evolution of the deforming membrane. We close by investigating a novel hydrodynamic instability in which an initially local disturbance to an unstable tube yields propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of the Föppl–von Kármán number Γ, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions—reminiscent of recent experimental observations on the retraction and atrophy of axons