Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to appear in Journal of Evolution Equation

Spontaneous Cdc42 polarization independent of GDI-mediated extraction and actin-based trafficking.

The small Rho-family GTPase Cdc42 is critical for cell polarization and polarizes spontaneously in absence of upstream spatial cues. Spontaneous polarization is thought to require dynamic Cdc42 recycling through Guanine nucleotide Dissociation Inhibitor (GDI)-mediated membrane extraction and vesicle trafficking. Here, we describe a functional fluorescent Cdc42 allele in fission yeast, which demonstrates Cdc42 dynamics and polarization independent of these pathways. Furthermore, an engineered Cdc42 allele targeted to the membrane independently of these recycling pathways by an amphipathic helix is viable and polarizes spontaneously to multiple sites in fission and budding yeasts. We show that Cdc42 is highly mobile at the membrane and accumulates at sites of activity, where it displays slower mobility. By contrast, a near-immobile transmembrane domain-containing Cdc42 allele supports viability and polarized activity, but does not accumulate at sites of activity. We propose that Cdc42 activation, enhanced by positive feedback, leads to its local accumulation by capture of fast-diffusing inactive molecules

Glasslike Arrest in Spinodal Decomposition as a Route to Colloidal Gelation

Colloid-polymer mixtures can undergo spinodal decomposition into colloid-rich and colloid-poor regions. Gelation results when interconnected colloid-rich regions solidify. We show that this occurs when these regions undergo a glass transition, leading to dynamic arrest of the spinodal decomposition. The characteristic length scale of the gel decreases with increasing quench depth, and the nonergodicity parameter exhibits a pronounced dependence on scattering vector. Mode coupling theory gives a good description of the dynamics, provided we use the full static structure as input.Comment: 14 pages, 4 figures; replaced with published versio

A direct numerical simulation method for complex modulus of particle dispersions

We report an extension of the smoothed profile method (SPM)[Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E {\bf 26}, 361(2008)], a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage $G'(\omega)$ and loss $G"(\omega)$ moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of $\Phi=0$, 0.41, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions

Aharonov-Bohm-Type Oscillations of Thermopower in a Quantum Dot Ring Geometry

We investigate Aharonov-Bohm-type oscillations of the thermopower of a quantum dot embedded in a ring for the case when the interaction between electrons can be neglected. The thermopower is shown to be strongly flux dependent, and typically the amplitude of oscillations exceeds the background value. It is also shown to be essentially dependent on the phase of the scattering matrix which is determined by the experimental geometry and is not known in the given experiment. Two procedures to compare theory and experiment are proposed.Comment: Revtex, 5 figures include

Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page