Abstract:
The Flory-Stockmayer theory for the polycondensation of branched polymers, modified for finite systems beyond the gel point, is applied to the connection (synapses) of neurons, which can be considered highly branched “monomeric” units. Initially, the process is a linear growth and tree-like branching between dendrites and axons of nonself-neurons. After the gel point and at the maximum “tree” size, the tree-like model prescribes, on average, one pair of twin synapses per neuron. About 13% of neurons, “unconnected” to the maximum tree, migrate to the surface to form cortical layers. The number of synapses in each neuron may reach 10000, indicating a tremendous amount of flexible, redundant, and neuroplastic loop-forming linkages which can be preserved or pruned by experience and learning. 1. Introduction The molecular weight distribution (MWD) of polycondensation of branched-chain monomers of the type has been derived classically by Flory [1] and generalized by Stockmayer [2]. Here, is the number of functional groups, or “functionality” of group A. Mathematically, this widely quoted distribution function has been treated as power-series distribution and compound distribution that provides a simple concept; that is, single-parameter expressions of number- and weight-average “degrees of polymerization” (DP) are sufficient to generate the entire MWD for branched polymers [3]. Moreover, using a cascade formulation involving functionals and probability generating functions (PGF), this distribution can be extended to finite systems [4]. Here, the previously derived properties of this finite distribution are applied to synapse formation in the brain. A neuron has multiple dendritic processes and an axon, which can also be branched. Neurons are generally three or more orders of magnitude greater in size than molecular units. However, the functionality of a neuron may be 103 times larger than that of typical branched molecules ( ). This large functionality also means there is great accessibility to the connection sites, and the long flexible axons offer a favorable condition for connection between neurons. The “tree-like,” or “ring-free,” assumption in the Flory-Stockmayer theory can be satisfied by the initial linkage of head-to-tail linear chains and followed by a “tree-like branching.” A neuron itself can be considered a small tree. Similarly, the peripheral nervous system (PNS) also resembles a tree made of the nerve bundles, which can be as large as 1.5 meters. The Finite Flory-Stockmayer theory (FFST) deals with numbers of highly branched repeat units and

Abstract:
Using molecular dynamics simulation, we have studied the low-energy sputtering at the energies near the sputtering threshold. Different projectile-target combinations of noble metal atoms (Cu, Ag, Au, Ni, Pd, and Pt) are simulated in the range of incident energy from 0.1 to 200 eV. It is found that the threshold energies for sputtering are different for the cases of M1 < M2 and M1 ≥ M2, where M1 and M2 are atomic mass of projectile and target atoms, respectively. The sputtering yields are found to have a linear dependence on the reduced incident energy, but the dependence behaviors are different for the both cases. The two new formulas are suggested to describe the energy dependences of the both cases by fitting the simulation results with the determined threshold energies. With the study on the energy dependences of sticking probabilities and traces of the projectiles and recoils, we propose two different mechanisms to describe the sputtering behavior of low-energy atoms near the threshold energy for the cases of M1 < M2 and M1 ≥ M2, respectively.

Abstract:
Extracellular guidance cues steer axons towards their targets by eliciting morphological changes in the growth cone. A key part of this process is the asymmetric recruitment of the cytoplasmic scaffolding protein MIG-10 (lamellipodin). MIG-10 is thought to asymmetrically promote outgrowth by inducing actin polymerization. However, the mechanism that links MIG-10 to actin polymerization is not known. We have identified the actin regulatory protein ABI-1 as a partner for MIG-10 that can mediate its outgrowth-promoting activity. The SH3 domain of ABI-1 binds to MIG-10, and loss of function of either of these proteins causes similar axon guidance defects. Like MIG-10, ABI-1 functions in both the attractive UNC-6 (netrin) pathway and the repulsive SLT-1 (slit) pathway. Dosage sensitive genetic interactions indicate that MIG-10 functions with ABI-1 and WVE-1 to mediate axon guidance. Epistasis analysis reveals that ABI-1 and WVE-1 function downstream of MIG-10 to mediate its outgrowth-promoting activity. Moreover, experiments with cultured mammalian cells suggest that the interaction between MIG-10 and ABI-1 mediates a conserved mechanism that promotes formation of lamellipodia. Together, these observations suggest that MIG-10 interacts with ABI-1 and WVE-1 to mediate the UNC-6 and SLT-1 guidance pathways.

Abstract:
Hyperspherical close-coupling method is used to calculate the elastic, positronium formation and excitation cross sections for positron collisions with atomic hydrogen at energies below the H(n=4) threshold for the J=2 partial wave. The resonances below each inelastic threshold are also analyzed. The adiabatic hyperspherical potential curves are used to identify the nature of these resonances.

Abstract:
By using a model Hamiltonian with d-wave superconductivity and competing antiferromagnetic (AF) orders, the local staggered magnetization distribution due to nonmagnetic impurities in cuprate superconductors is investigated. From this, the net magnetic moment induced by a single or double impurities can be obtained. We show that the net moment induced by a single impurity corresponds to a local spin with S_z=0, or 1/2 depending on the strength of the AF interaction and the impurity scattering. When two impurities are placed at the nearest neighboring sites, the net moment is always zero. For two unitary impurities at the next nearest neighboring sites, and at sites separated by a Cu-ion site, the induced net moment has S_z=0, or 1/2, or 1. The consequence of these results on experiments will be discussed.

Abstract:
We introduce a model to describe columnar phases of chiral discotic liquid phases in which the normals to disc-like molecules are constrained to lie parallel to columnar axes. The model includes separate chiral interactions favoring, respectively, relative twist of chiral molecules along the axes of the columns and twist of the two-dimensional columnar lattice. It also includes a coupling between the lattice and the orientation of the discotic molecules. We discuss the instability of the aligned hexagonal lattice phase to the formation of a soliton lattice in which molecules twist within their columns without affecting the lattice and to the formation of a moir\'{e} phase consisting of a periodic array of twist grain boundaries perpendicular to the columns.

Abstract:
We use a set of simplified non-linear Langevin equations to study the hydrodynamic excitations in a nematic liquid crystal. We calculate the one-loop self-energy corrections in the long wavelength limit.

Abstract:
We show that the two branches of collective modes discovered recently in under-doped Cuprates with huge spectral weight are a necessary consequence of the loop-current state. Such a state has been shown in earlier experiments to be consistent with the symmetry of the order parameter competing with superconductivity in four families of Cuprates. We also predict a third branch of excitations and suggest techniques to discover it. Using parameters to fit the observed modes, we show that the direction of the effective moments in the ground state lies in a cone at an angle to the c-axis as observed in experiments.

Abstract:
The collective modes observed in the loop-current ordered state in under-doped cuprates by polarized neutron scattering require that the ground state is a linear combination in each unit-cell of the four basis states which are the possible classical magnetic moment configurations in each unit-cell. The direction of such moments is in the c-axis of the crystals. The basis states are connected by both time-reversal as well as spatial rotations about the center of the unit-cells. Several new features arise in the theory of polarized neutron scattering cross-section in this situation which appear not to have been encountered before. An important consequence of these is that a finite component transverse to the classical magnetic moment directions is detected in the experiments. We show that this transverse component is of purely quantum-mechanical origin and that its direction in the plane normal to the c-axis is not detectable, even in principle, in experiments, at least in the quantum-mechanical model we have adopted. We estimate the direction of the "tilt" in the moment, i.e. the ratio of the transverse component to the c-axis component, using parameters of the ground state obtained by fitting to the observed dispersion of the collective modes in the ordered state. We can obtain reasonable agreement with experiments but only by introducing a parameter for which only an approximate magnitude can be estimated. Approximate calculations of the form-factors are also provided.

Abstract:
The induction of spin density wave (SDW) and charge density wave (CDW) orderings in the mixed state of high $T_c$ superconductors (HTS) is investigated by using the self-consistent Bogoliubov-de Gennes equations based upon an effective model Hamiltonian with competing SDW and d-wave superconductivity interactions. For optimized doping sample, the modulation of the induced SDW and its associated CDW is determined by the vortex lattice and their patterns obey the four-fold symmetry. By deceasing doping level, both SDW and CDW show quasi-one dimensional like behavior, and the CDW has a period just half that of the SDW along one direction. From the calculation of the local density of states (LDOS), we found that the majority of the quasi-particles inside the vortex core are localized. All these results are consistent with several recent experiments on HTS.