Large deformation of spherical vesicle studied by perturbation theory and Surface evolver

With tangent angle perturbation approach the axial symmetry deformation of a spherical vesicle in large under the pressure changes is studied by the elasticity theory of Helfrich spontaneous curvature model.Three main results in axial symmetry shape: biconcave shape, peanut shape, and one type of myelin are obtained. These axial symmetry morphology deformations are in agreement with those observed in lipsome experiments by dark-field light microscopy [Hotani, J. Mol. Biol. 178, (1984) 113] and in the red blood cell with two thin filaments (myelin) observed in living state (see, Bessis, Living Blood Cells and Their Ultrastructure, Springer-Verlag, 1973). Furthermore, the biconcave shape and peanut shape can be simulated with the help of a powerful software, Surface Evolver [Brakke, Exp. Math. 1, 141 (1992) 141], in which the spontaneous curvature can be easy taken into account.Comment: 16 pages, 6 EPS figures and 2 PS figure

On classical string configurations

Equations which define classical configurations of strings in $R^3$ are presented in a simple form. General properties as well as particular classes of solutions of these equations are considered.Comment: 10 pages, Latex, no figures, trivial corrections, submitted to Modern Physics Letters

Counting White Blood Cells from a Blood Smear Using Fourier Ptychographic Microscopy

White blood cell (WBC) count is a valuable metric for assisting with diagnosis or prognosis of various diseases such as coronary heart disease, type 2 diabetes, or infection. Counting WBCs can be done either manually or automatically. Automatic methods are capable of counting a large number of cells to give a statistically more accurate reading of the WBC count of a sample, but the specialized equipment tends to be expensive. Manual methods are inexpensive since they only involve a conventional light microscope setup. However, it is more laborious and error-prone because the small field-of-view (FOV) of the microscope necessitates mechanical scanning of a specimen for counting an adequate number of WBCs. Here, we investigate the use of Fourier ptychographic microscopy (FPM) to bypass these issues of the manual methods. With a 2x objective, FPM can provide a FOV of 120 mm^2 with enhanced resolution comparable to that of a 20x objective, which is adequate for non-differentially counting WBCs in just one FOV. A specialist was able to count the WBCs in FPM images with 100% accuracy compared to the count as determined from conventional microscope images. An automatic counting algorithm was also developed to identify WBCs from FPM’s captured images with 95% accuracy, paving the way for a cost-effective WBC counting setup with the advantages of both the automatic and manual counting methods

Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness $\epsilon_{\rm b}$. In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first-order as long as $\epsilon_{\rm b}$ is positive [H. Zhou {\em et al.}, Phys. Rev. Lett. {\bf 97}, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a 2D lattice polymer. The system's phase-diagram at zero force is obtained. Depending on $\epsilon_{\rm b}$ and the temperature $T$, the polymer can be in one of three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous, the globule-coil transition is continuous. At moderate or high values of $\epsilon_{\rm b}$ the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.Comment: 16 page

Numerical observation of non-axisymmetric vesicles in fluid membranes

By means of Surface Evolver (Exp. Math,1,141 1992), a software package of brute-force energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques

Theory on quench-induced pattern formation: Application to the isotropic to smectic-A phase transitions

During catastrophic processes of environmental variations of a thermodynamic system, such as rapid temperature decreasing, many novel and complex patterns often form. To understand such phenomena, a general mechanism is proposed based on the competition between heat transfer and conversion of heat to other energy forms. We apply it to the smectic-A filament growth process during quench-induced isotropic to smectic-A phase transition. Analytical forms for the buckling patterns are derived and we find good agreement with experimental observation [Phys. Rev. {\bf E55} (1997) 1655]. The present work strongly indicates that rapid cooling will lead to structural transitions in the smectic-A filament at the molecular level to optimize heat conversion. The force associated with this pattern formation process is estimated to be in the order of $10^{-1}$ piconewton.Comment: 9 pages in RevTex form, with 3 postscript figures. Accepted by PR

Dynamical description of vesicle growth and shape change

We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity of this prediction is examined in the light of the various assumptions made in its derivation.Comment: 6 page

A generalized integral fluctuation theorem for general jump processes

Using the Feynman-Kac and Cameron-Martin-Girsanov formulas, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Different from the latter approach that was extensively employed in existing literature, our approach can naturally bring out the definition of a time-reversal of a Markovian stochastic system. Additionally, we find the robust GIFT usually does not result into a detailed fluctuation theorem

Interpretation of AIRS Data in Thin Cirrus Atmospheres Based on a Fast Radiative Transfer Model

A thin cirrus cloud thermal infrared radiative transfer model has been developed for application to cloudy satellite data assimilation. This radiation model was constructed by combining the Optical Path Transmittance (OPTRAN) model, developed for the speedy calculation of transmittances in clear atmospheres, and a thin cirrus cloud parameterization using a number of observed ice crystal size and shape distributions. Numerical simulations show that cirrus cloudy radiances in the 800–1130-cm^(-1) thermal infrared window are sufficiently sensitive to variations in cirrus optical depth and ice crystal size as well as in ice crystal shape if appropriate habit distribution models are selected a priori for analysis. The parameterization model has been applied to the Atmospheric Infrared Sounder (AIRS) on board the Aqua satellite to interpret clear and thin cirrus spectra observed in the thermal infrared window. Five clear and 29 thin cirrus cases at nighttime over and near the Atmospheric Radiation Measurement program (ARM) tropical western Pacific (TWP) Manus Island and Nauru Island sites have been chosen for this study. A X^2-minimization program was employed to infer the cirrus optical depth and ice crystal size and shape from the observed AIRS spectra. Independent validation shows that the AIRS-inferred cloud parameters are consistent with those determined from collocated ground-based millimeter-wave cloud radar measurements. The coupled thin cirrus radiative transfer parameterization and OPTRAN, if combined with a reliable thin cirrus detection scheme, can be effectively used to enhance the AIRS data volume for data assimilation in numerical weather prediction models