Supersymmetry,vacuum statistics,and the fundamental theorem of algebra

I give an interpretation of the fundamental theorem of algebra based on supersymmetry and the Witten index. The argument gives a physical explanation of why a real polynomial of degreen need not haven real zeroes, while a complex polynomial of degreen must haven complex zeroes. This paper also addresses in a general and model-independent way the statistics of the perturbative ground states (the states which correspond to classical vacua) in supersymmetric theories with complex and with real superfields.     

A Molecular Circuit Regenerator to Implement Iterative Strand Displacement Operations

The predictable chemistry of Watson–Crick base-pairing imparts a unique structural programmability to DNA, enabling the facile design of molecular reactions that perform computations. However, many of the current architectures limit devices to a single operational cycle. Herein, we introduce the design of the “regenerator”, a device based on coupled enthalpic and entropic reactions that permits the regeneration of molecular circuit components.     

On the mechanoelectrical coupling in the cochlear outer hair cell

Outer hair cell electromotility, a manifestation of the interconnection between the mechanical and electrical processes occurring in outer hair cells, is believed to be an important contribution to the active cochlea. Two modes of mechanoelectrical coupling in the outer hair cell wall are studied: the potential shift caused by mechanical loading under the wall charge preservation conditions and the current (transferred charge) caused by mechanical loading under the voltage-clamp conditions. By using the previously reported elastic moduli of the wall and components of the active force, the potential shift under the charge preservation conditions is derived. This shift is expressed in terms of the wall strains and the active force derivatives with respect to the wall potential. The magnitudes of the potential shift corresponding to the conditions of cell inflation, axial stretch (compression), and the micropipet aspiration are estimated. In the last case, the distribution of the potential shift along the cell wall is also demonstrated. The potential shift can reach -20(-)-40 mV under the conditions of the micropipet aspiration or cell inflation. Such shift is much smaller under the condition of cell stretch (compression). The current and the charge transfer caused by the cell stretch under the voltage-clamp conditions is analyzed, and shows good agreement of predictions with experimental data.     

On Cavitation, Configurational Forces and Implications for Fracture in a Nonlinearly Elastic Material

Experiments on polymers indicate that large tensile stress can induce cavitation, that is, the appearance of voids that were not previously evident in the material. This phenomenon can be viewed as either the growth of pre-existing infinitesimal holes in the material or, alternatively, as the spontaneous creation of new holes in an initially perfect body. In this paper our approach is to adopt both views concurrently within the framework of the variational theory of nonlinear elasticity. We model an elastomer on a macroscale as a void-free material and, on a microscale, as a material containing certain defects that are the only points at which hole formation can occur. Mathematically, this is accomplished by the use of deformations whose point singularities are constrained. One consequence of this viewpoint is that cavitation may then take place at a point that is not energetically optimal. We show that this disparity will generate configurational forces, a type of force identified previously in dislocations in crystals, in phase transitions in solids, in solidification, and in fracture mechanics. As an application of this approach we study the energetically optimal point for a solitary hole to form in a homogeneous and isotropic elastic ball subject to radial boundary displacements. We show, in particular, that the center of the ball is the unique optimal point. Finally, we speculate that the configurational force generated by cavitation at a non-optimal material point may be sufficient to result in the onset of fracture. The analysis utilizes the energy-momentum tensor, the asymptotics of an equilibrium solution with an isolated singularity, and the linear theory of elasticity at the stressed configuration that the body occupies immediately prior to cavitation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Necessary conditions at the boundary for minimizers in finite elasticity

Dedicated to Bernard Coleman on the occasion of his 60^th birthday     

Conductivity in intrinsic quantum well wires: Semimetal-semiconductor transition

The effect of size quantization on the conductivity of semimetallic and semiconducting rectangular quantum well wires (QWW) is studied. A semimental-semiconductor transition is predicted to occur at a critical thickness of the wire. For wires of smaller thickness than the critical thickness, semiconducting behavior will occur with the conductivity decreasing exponentially with decreasing transverse dimensions of the wire. That is due to carrier freeze-out because of the increase in effective bandgap resulting from the size quantization. The effect dominates any thickness dependence of the mobility resulting from scattering interactions.