Karin Berndl

Bio: Karin Berndl is an academic researcher from Ludwig Maximilian University of Munich. The author has contributed to research in topics: De Broglie–Bohm theory & Quantum nonlocality. The author has an hindex of 8, co-authored 14 publications receiving 1509 citations.

Shape transformations of vesicles: Phase diagram for spontaneous- curvature and bilayer-coupling models.

Abstract: Vesicle shapes of low energy are studied for two variants of a continuum model for the bending energy of the bilayer: (i) the spontaneous-curvature model and (ii) the bilayer-coupling model, in which an additional constraint for the area difference of the two monolayers is imposed. We systematically investigate four branches of axisymmetric shapes: (i) the prolate-dumbbell shapes; (ii) the pear-shaped vesicles, which are intimately related to budding; (iii) the oblate-discocyte shapes; and (iv) the stomatocytes. These branches end up at limit shapes where either the membrane self-intersects or two (or more) shapes are connected by an infinitesimally narrow neck. The latter limit shape requires a certain condition between the curvatures of the adjacent shape and the spontaneous curvature. For both models, the phase diagram is determined, which is given by the shape of lowest bending energy for a given volume-to-area ratio and a given spontaneous curvature or area difference, respectively. The transitions between different shapes are continuous for the bilayer-coupling model, while most of the transitions are discontinuous in the spontaneous-curvature model. We introduce trajectories into these phase diagrams that correspond to a change in temperature and osmotic conditions. For the bilayer-coupling model, we find extreme sensitivity to an asymmetry in the monolayer expansivity. Both models lead to different predictions for typical trajectories, such as budding trajectories or oblate-stomatocyte transitions. Our study thus should provide the basis for an experimental test of both variants of the curvature model.

Shape Transformations of Giant Vesicles: Extreme Sensitivity to Bilayer Asymmetry

Abstract: Shape transformations of vesicles of lecithin (DMPC) in water are induced by changing the temperature which effectively changes the volume-to-area ratio. Three different routes are found which include i) symmetric-asymmetric re-entrant transitions from a dumbbell to a pear-shaped state, ii) the expulsion of a smaller vesicle (budding), and iii) discocyte–stomatocyte transitions. All of these shape transformations are explained within a model for the bending energy of the bilayer which assumes i) that the two monolayers do not exchange lipid molecules, and ii) that the adjacent monolayers exhibit a small difference in their thermal expansivities which is easily produced, e.g., by residual impurities.

Nonlocality, Lorentz invariance, and Bohmian quantum theory.

Abstract: We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the nonexistence of absolute time, i.e., of simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum theory: the quantum equilibrium distribution \ensuremath{\rho}=\ensuremath{\Vert}\ensuremath{\psi}${\mathrm{\ensuremath{\Vert}}}^{2}$ cannot simultaneously be realized in all Lorentz frames of reference. \textcopyright{} 1996 The American Physical Society.

On the global existence of Bohmian mechanics

Abstract: We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schrodinger Hamiltonian.

A survey of Bohmian mechanics

Abstract: Bohmian mechanics is the most naively obvious embedding imaginable of Schrodinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that, as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, is a consequence of Bohmian mechanics.

Quantum Theory of Fields

Abstract: To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Polymersomes: tough vesicles made from diblock copolymers.

Abstract: Vesicles were made from amphiphilic diblock copolymers and characterized by micromanipulation. The average molecular weight of the specific polymer studied, polyethyleneoxide-polyethylethylene (EO40-EE37), is several times greater than that of typical phospholipids in natural membranes. Both the membrane bending and area expansion moduli of electroformed polymersomes (polymer-based liposomes) fell within the range of lipid membrane measurements, but the giant polymersomes proved to be almost an order of magnitude tougher and sustained far greater areal strain before rupture. The polymersome membrane was also at least 10 times less permeable to water than common phospholipid bilayers. The results suggest a new class of synthetic thin-shelled capsules based on block copolymer chemistry.

Configurations of fluid membranes and vesicles

Abstract: Vesicles consisting of a bilayer membrane of amphiphilic lipid molecules are remarkably flexible surfaces that show an amazing variety of shapes of different symmetry and topology. Owing to the fluidity of the membrane, shape transitions such as budding can be induced by temperature changes or the action of optical tweezers. Thermally excited shape fluctuations are both strong and slow enough to be visible by video microscopy. Depending on the physical conditions, vesicles adhere to and unbind from each other or a substrate. This article describes the systematic physical theory developed to understand the static and dynamic aspects of membrane and vesicle configurations. The preferred shapes arise from a competition between curvature energy, which derives from the bending elasticity of the membrane, geometrical constraints such as fixed surface area and fixed enclosed volume, and a signature of the bilayer aspect. These shapes of lowest energy are arranged into phase diagrams, which separate regi...

The conformation of membranes

Abstract: Membranes composed of amphiphilic molecules are highly flexible surfaces that determine the architecture of biological systems and provide a basic structural element for complex fluids such as microemulsions. Physical theories have been developed to describe many aspects of their conformational behaviour, such as the preferred shapes and shape transformations of closed vesicles, and the shape fluctuations, random-surface configurations, and adhesion and unbinding of interacting membranes. Understanding of these phenomena has been much improved through fruitful interactions between theory and experiment.

Mechanics of the cell

Abstract: 1. Introduction to the cell Part I. Rods and Ropes: 2. Polymers 3. Two-dimensional networks 4. Three-dimensional networks Part II. Membranes: 5. Biomembranes 6. Membrane undulations Part III. The Whole Cell: 7. The simplest cells 8. Intermembrane forces 9. Dynamic filaments 10. Mechanical designs Appendix A. Animal cells and tissues Appendix B. The cell's molecular building blocks Appendix C. Elementary statistical mechanics Appendix D. Elasticity References Index.