Topological localization in out-of-equilibrium dissipative systems

In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic networks governed by microscopic single particle dynamics as well as collections of driven, interacting particles described by coarse-grained hydrodynamic theory. In both cases, the presence of dissipative couplings to the environment that break time reversal symmetry are crucial to ensuring topologically protection. These examples constitute proof of principle that notions of topological protection, established in the context of electronic and mechanical systems, do indeed extend generically to processes that operate out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.Comment: 11 pages, 4 figures (SI: 8 pages 3 figures

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

Relationship between entrepreneurial optimism and entrepreneurial assets

Abstract. The aim of this study is to explore the relationship between entrepreneurial optimism and entrepreneurial assets, during the opportunity formation process. Entrepreneur is the central component in the entrepreneurship process. Much research has been done on external influences like environments and economics on the entrepreneurial process. However, comparatively less attention is given to the entrepreneur itself and to the intangible strengths and assets possessed by the entrepreneur. The primary aim and goal of our study is to evaluate if the intangible strengths and assets that an entrepreneur possesses, influences entrepreneurial optimism. A secondary goal is to study and test the hypothesis of over optimistic in entrepreneurs. The study draws on literature available for entrepreneurial optimism, opportunity formation and factors influencing optimism to develop a conceptual model. The constructionist approach to opportunity formation is identified and relied upon to examine the various factors that are identified from literature, which influence entrepreneurial optimism. Entrepreneurial assets namely, relevant knowledge, prior experience, educational background and networks are employed to understand if these create and drive entrepreneurial optimism. Qualitative analysis is chosen for the research purpose which is a suitable research method for the perceptional understanding of the optimism phenomenon. Six entrepreneurs were identified, and empirical data obtained from semi structured interview process. Thematic analysis is performed on the empirical data to arrive at important findings. The empirical findings are then compared to the findings from literature review, in order to arrive at the research conclusions and findings. The results of the study indicate that entrepreneurial optimism is created and driven by relevant knowledge, networks, prior work experience and educational background. The results also found prevalence of over optimism among entrepreneurs. It is found that entrepreneurs believe that other entrepreneurs are more overly optimistic in comparison to themselves. It is also found that prior entrepreneurial experience may or may not create optimism depending on the success of past ventures. This study contributes to existing knowledge on entrepreneurial optimism while making important contributions to its relationship with entrepreneurial assets. Altogether the study encourages future studies in the area of entrepreneurship as a research area

The order-disorder transition in model lipid bilayers is a first-order hexatic to liquid phase transition

We characterize the order-disorder transition in a model lipid bilayer using molecular dynamics simulations. We find that the ordered phase is hexatic. In particular, in-plane structures possess a finite concentration of 5-7 disclination pairs that diffuse throughout the plane of the bilayer, and further, in-plane structures exhibit long-range orientational order and short-range translational order. In contrast, the disordered phase is liquid. The transition between the two phases is first order. Specifically, it exhibits hysteresis, and coexistence exhibits an interface with capillary scaling. The location of the interface and its spatial fluctuations are analyzed with a spatial field constructed from a rotational-invariant for local 6-fold orientational order. As a result of finite interfacial tension, there necessarily exist associated forces of assembly between membrane-bound solutes that pre-melt the ordered phase.Comment: Addressed the comments from colleagues, corrected typos, clarified text, updated references. The new draft also contains new results relating to the hexatic phas

Mechanics of torque generation in the bacterial flagellar motor

The bacterial flagellar motor (BFM) is responsible for driving bacterial locomotion and chemotaxis, fundamental processes in pathogenesis and biofilm formation. In the BFM, torque is generated at the interface between transmembrane proteins (stators) and a rotor. It is well-established that the passage of ions down a transmembrane gradient through the stator complex provides the energy needed for torque generation. However, the physics involved in this energy conversion remain poorly understood. Here we propose a mechanically specific model for torque generation in the BFM. In particular, we identify two fundamental forces involved in torque generation: electrostatic and steric. We propose that electrostatic forces serve to position the stator, while steric forces comprise the actual 'power stroke'. Specifically, we predict that ion-induced conformational changes about a proline 'hinge' residue in an $\alpha$-helix of the stator are directly responsible for generating the power stroke. Our model predictions fit well with recent experiments on a single-stator motor. Furthermore, we propose several experiments to elucidate the torque-speed relationship in motors where the number of stators may not be constant. The proposed model provides a mechanical explanation for several fundamental features of the flagellar motor, including: torque-speed and speed-ion motive force relationships, backstepping, variation in step sizes, and the puzzle of swarming experiments