THE VALUE DISTRIBUTION OF GAUSS MAPS OF IMMERSED HARMONIC SURFACES WITH RAMIFICATION

Motivated by the result of Chen-Liu-Ru[1],we investigate the value distribution properties for the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(n) with ramification,which can be seen as a generalization of the results in the case of the minimal surfaces.In addition,we give an estimate of the Gauss curvature for the K-quasiconfomal harmonic surfaces whose generalized Gauss map is ramified over a set of hyperplanes.

Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation

Lipid vesicles appear ubiquitously in biological systems.Understanding how the mechanical and intermolecular interactions deform vesicle membranes is a fundamental question in biophysics.In this article we develop a fast algorithm to compute the surface configurations of lipid vesicles by introducing surface harmonic functions to approximate themembrane surface.This parameterization allows an analytical computation of themembrane curvature energy and its gradient for the efficient minimization of the curvature energy using a nonlinear conjugate gradient method.Our approach drastically reduces the degrees of freedom for approximating the membrane surfaces compared to the previously developed finite element and finite difference methods.Vesicle deformations with a reduced volume larger than 0.65 can be well approximated by using as small as 49 surface harmonic functions.The method thus has a great potential to reduce the computational expense of tracking multiple vesicles which deform for their interaction with external fields.

Towards critical and supercritical electromagnetic fields

The availability of ever stronger,laser-generated electromagnetic fields underpins continuing progress in the study and application of nonlinear phenomena in basic physical systems,ranging from molecules and atoms to relativistic plasmas and quantum electrodynamics.This raises the question:how far will we be able to go with future lasers?One exciting prospect is the attainment of field strengths approaching the Schwinger critical field Ecr in the laboratory frame,such that the field invariant E^(2)−c^(2)B^(2)>E_(cr)^(2) is reached.The feasibility of doing so has been questioned,on the basis that cascade generation of dense electron–positron plasma would inevitably lead to absorption or screening of the incident light.Here we discuss the potential for future lasers to overcome such obstacles,by combining the concept of multiple colliding laser pulses with that of frequency upshifting via a tailored laser–plasma interaction.This compresses the electromagnetic field energy into a region of nanometre size and attosecond duration,which increases the field magnitude at fixed power but also suppresses pair cascades.Our results indicate that laser facilities with peak power of tens of PW could be capable of reaching Ecr.Such a scenario opens up prospects for the experimental investigation of phenomena previously considered to occur only in the most extreme environments in the universe.

Comparative Study on Methods for Computing Soil Heat Storage and Energy Balance in Arid and Semi-Arid Areas

Observations collected in the Badan Jaran desert hinterland and edge during 19-23 August 2009 and in the Jinta Oasis during 12-16 June 2005 are used to assess three methods for calculating the heat storage of the5-20-cm soil layer.The methods evaluated include the harmonic method,the conduction-convection method,and the temperature integral method.Soil heat storage calculated using the harmonic method provides the closest match with measured values.The conduction-convection method underestimates nighttime soil heat storage.The temperature integral method best captures fluctuations in soil heat storage on sub-diurnal timescales,but overestimates the amplitude and peak values of the diurnal cycle.The relative performance of each method varies with the underlying land surface.The land surface energy balance is evaluated using observations of soil heat flux at 5-cm depth and estimates of ground heat flux adjusted to account for soil heat storage.The energy balance closure rate increases and energy balance is improved when the ground heat flux is adjusted to account for soil heat storage.The results achieved using the harmonic and temperature integral methods are superior to those achieved using the conduction-convection method.