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Register a new userTopological instabilities of spherical vesicles
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Within the framework of the Helfrich elastic theory of membranes and of differential geometry we study the possible instabilities of spherical vesicles towards double bubbles. We find that not only temperature, but also magnetic fields can induce topological transformations between spherical vesicles and double bubbles and provide a phase diagram for the equilibrium shapes.
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We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient $muapprox 1$. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, $Z_{nr}$ , reaches 3, and the dependence of $Z_{nr}$ on the packing fraction $phi$ changes again when $Z_{nr}$ reaches 4. (2) Though the packing fractions $phi_{c1}$ and $phi_{c2}$ at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of $phi_{c1}$ and $phi_{c2}$ for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs comparing to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution.
We calculate the stress tensor for a quasi-spherical vesicle and we thermally average it in order to obtain the actual, mechanical, surface tension $tau$ of the vesicle. Both closed and poked vesicles are considered. We recover our results for $tau$ by differentiating the free-energy with respect to the proper projected area. We show that $tau$ may become negative well before the transition to oblate shapes and that it may reach quite large negative values in the case of small vesicles. This implies that spherical vesicles may have an inner pressure lower than the outer one.
We study the quantum critical phenomena emerging at the transition from triple-Weyl semimetal to band insulator, which is a topological phase transition described by the change of topological invariant. The critical point realizes a new type of semimetal state in which the fermion dispersion is cubic along two directions and quadratic along the third. Our renormalization group analysis reveals that, the Coulomb interaction is marginal at low energies and even arbitrarily weak Coulomb interaction suffices to induce an infrared fixed point. We compute a number of observable quantities, and show that they all exhibit non-Fermi liquid behaviors at the fixed point. When the interplay between the Coulomb and short-range four-fermion interactions is considered, the system becomes unstable below a finite energy scale. The system undergoes a first-order topological transition when the fermion flavor $N$ is small, and enters into a nematic phase if $N$ is large enough. Non-Fermi liquid behaviors are hidden by the instability at low temperatures, but can still be observed at higher temperatures. Experimental detection of the predicted phenomena is discussed.
We present a nanoparticle size-separation device based on a nanofluidic rocking Brownian motor. It features a ratchet-shaped electrostatic particle potential with increasing barrier heights along the particle transport direction. The sharp drop of the particle current with barrier height is exploited to separate a particle suspension into multiple sub-populations. By solving the Fokker--Planck equation, we show that the physics of the separation mechanism is governed by the energy landscape under forward tilt of the ratchet. For a given device geometry and sorting duration, the applied force is thus the only tunable parameter to increase the separation resolution. For the experimental conditions of 3.5 V applied voltage and 20 s sorting, we predict a separation resolution of $sim 2$ nm, supported by experimental data for separating spherical gold particles of nominal 80 and 100 nm diameters.
We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the dynamic free energy concept of the Nonlinear Langevin Equation theory approach. The dynamic free energy at any mean location involves contributions from two adjacent layers where confining forces are not the same. At the most fundamental level of the theory, the caging component of the dynamic free energy varies essentially exponentially with distance from the interface, saturating deep enough into the film with a correlation length of modest size and weak sensitivity to thermodynamic state. This imparts a roughly exponential spatial variation of all the key features of the dynamic free energy required to compute gradients of dynamical quantities including the localization length, jump distance, cage barrier, collective elastic barrier and alpha relaxation time. The spatial gradients are entire of dynamical, not structural nor thermodynamic, origin. The theory is implemented for the hard sphere fluid and diverse interfaces which can be a vapor, a rough pinned particle solid, a vibrating pinned particle solid, or a smooth hard wall. Their basic description at the level of the spatially-heterogeneous dynamic free energy is identical, with the crucial difference arising from the first layer where dynamical constraints can be weakened, softened, or hardly changed depending on the specific interface. Numerical calculations establish the spatial dependence and fluid volume fraction sensitivity of the key dynamical property gradients for five different model interfaces. Comparison of the theoretical predictions for the dynamic localization length and glassy modulus with simulations and experiments for systems with a vapor interface reveals good agreement.
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