Flexural rigidity of a liquid surface

The energy of a mass of liquid is evaluated asymptotically in powers of the range of the intermolecular potential divided by a typical dimension of the liquid. The leading term is the internal energy, proportional to the liquid volume. The second term is the energy of surface tension, proportional to the area of the liquid surface. The third term is proportional to an integral over this surface of the square of the mean curvature of the surface minus one-third of its Gaussian curvature. This new term has exactly the form of the bending energy of a thin elastic plate. Comparing it with the bending energy yields expressions for the flexural rigidity and the Poisson ratio of the liquid surface. This flexural rigidity of the surface leads to new terms in the equation of equilibrium of the liquid surface, in addition to the usual surface tension terms.     

Spinors and multivectors as a unified tool for spacetime geometry and for elementary particle physics

From the definition of spinors as the minimal left (right) modules of multivectors (that is, of vectors and their outer products), we can construct a unified mathematical approach for the study of matter and its interaction fields, which are either defined as fields in the geometrical spacetime or considered as generators of the physical spacetime. It is also shown how matter and interaction fields can be represented either by spinor fields or by multivector fields, both types of fields carrying the same information as the traditional corresponding spinors, vectors, or tensors. Geometry is more transparent in one representation (multivector form), and physics is more obvious in the spinor representation. Our theory provides a unified and totally self-consistent representation of quarks (barions), leptons, and all their known interactions.     

Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

The α transition in Fe1−xMxS materials (M = Mn,Cr): Physical and structural aspects

For Fe_1?xM_xS, the NiAs-type solid solution is limited to x < 0.12, and the materials exhibit a low-temperature FeS-type behavior with an α transition. Fe_1?xM_xS, the low-temperature solid solution is limited to x < 0.08, and for higher Cr concentration a high-temperature FeS-type behavior is observed. Resistivities and magnetic susceptibilities reveal the progressive weakening of the α transition for increasing Mn or Cr concentration.Crystal structure determination of Fe_0.96Mn_0.04S and Fe_0.955Cr_0.045S establish that the superstructure (a√3, 2c) weakening is due to the formation of disordered domains induced by the M substitutions.Physical and structural results are discussed together and lead to an interpretation of the α transition, whether induced by temperature or impurities, as a transition between a nondegenerated polaron gas, at low temperature or for x_Cr < 0.08, and a degenerated polaron gas for T > T_α or for x_Cr > 0.08. The validity of this polaron model is discussed in the case of Fe_1?xM_xS.     

Double exposure, multiple-field particle image velocimetry for turbulent probability density

A particle image velocimeter method is described in which double exposed fields of particles moving in a two-dimensional slice of a steady turbulent flow are photographed repeatedly to build up a statistical ensemble of flow field realizations on a single photographic plate. Each interrogation spot on the plate contains a sample of the probability density function of the two components of velocity that lie in the photographic object plane, assuming paraxial photography. Theory is developed showing how this sample can be measured by two-dimensional spatial correlation analysis, followed by deconvolution to remove the effects of finite particle image size. The probability density measurements are biased inherently against large velocities, but these effects can be minimized and/or corrected.     

Atom-scale ptychographic electron diffractive imaging of boron nitride cones

Ptychographic coherent diffractive imaging (CDI) has been extensively applied using both x rays and electrons. The extension to atomic resolution has been elusive. This Letter demonstrates ptychographic electron diffractive imaging at atomic resolution, permitting identification of structure in a boron nitride helical cone at a resolution of order 1 ?, beyond that of comparative Z-contrast images. A scanning transmission electron microscope is used to create a diverging illumination in a defocused Fresnel CDI geometry, providing a robust strategy leading to a unique solution.     

Electrically controlled optical bandgap in a structurally chiral material

The propagation of light along the axis of non-homogeneity of a structurally chiral medium (SCM) under the influence of a low-frequency (dc) electric field aligned along the same axis is investigated. The Pockels effect is assumed to occur, and the SCM is taken to possess locally a point group symmetry. The frequency-domain Maxwell curl equations are cast in a 4 × 4 matrix representation, and the Oseen transformation is invoked. The band structure is analyzed, as are also the eigenvectors as well as the transfer matrix. Finally, the reflection and transmission of a plane wave due to a SCM of finite thickness is considered. The low-frequency electric field is shown to control the bandgap.