Scale invariant correlations and the distribution of prime numbers

Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.Comment: 13 pages, 8 figures, version to appear in J. Phys.

Confinement Effects on the Kinetics and Thermodynamics of Protein Dimerization

In the cell, protein complexes form relying on specific interactions between their monomers. Excluded volume effects due to molecular crowding would lead to correlations between molecules even without specific interactions. What is the interplay of these effects in the crowded cellular environment? We study dimerization of a model homodimer both when the mondimers are free or tethered to each other. We consider a structured environment: Two monomers first diffuse into a cavity of size $L$ and then fold and bind within the cavity. The folding and binding are simulated using molecular dynamics based on a simplified topology based model. The {\it confinement} in the cell is described by an effective molecular concentration $C \sim L^{-3}$. A two-state coupled folding and binding behavior is found. We show the maximal rate of dimerization occurred at an effective molecular concentration $C^{op}\simeq 1m$M which is a relevant cellular concentration. In contrast, for tethered chains the rate keeps at a plateau when $CC^{op}$. For both the free and tethered cases, the simulated variation of the rate of dimerization and thermodynamic stability with effective molecular concentration agrees well with experimental observations. In addition, a theoretical argument for the effects of confinement on dimerization is also made

Optogenetics and deep brain stimulation neurotechnologies

Brain neural network is composed of densely packed, intricately wired neurons whose activity patterns ultimately give rise to every behavior, thought, or emotion that we experience. Over the past decade, a novel neurotechnique, optogenetics that combines light and genetic methods to control or monitor neural activity patterns, has proven to be revolutionary in understanding the functional role of specific neural circuits. We here briefly describe recent advance in optogenetics and compare optogenetics with deep brain stimulation technology that holds the promise for treating many neurological and psychiatric disorders

Spin swap gate in the presence of qubit inhomogeneity in a double quantum dot

We study theoretically the effects of qubit inhomogeneity on the quantum logic gate of qubit swap, which is an integral part of the operations of a quantum computer. Our focus here is to construct a robust pulse sequence for swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum dot trapped electron spins and the finite-time ramp-up of exchange coupling in a double dot. We first present a geometric explanation of spin swap operation, mapping the two-qubit operation onto a single-qubit rotation. We then show that in this geometric picture a square-pulse-sequence can be easily designed to perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate how finite ramp-up times for the exchange coupling $J$ negatively affect the performance of the swap gate sequence, and show how to correct the problems numerically.Comment: published versio

Mesoscopic modelling of financial markets

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis

Dimensional Crossover in the Effective Second Harmonic Generation of Films of Random Dielectrics

The effective nonlinear response of films of random composites consisting of a binary composite with nonlinear particles randomly embedded in a linear host is theoretically and numerically studied. A theoretical expression for the effective second harmonic generation susceptibility, incorporating the thickness of the film, is obtained by combining a modified effective-medium approximation with the general expression for the effective second harmonic generation susceptibility in a composite. The validity of the thoretical results is tested against results obtained by numerical simulations on random resistor networks. Numerical results are found to be well described by our theory. The result implies that the effective-medium approximation provides a convenient way for the estimation of the nonlinear response in films of random dielectrics.Comment: 9 pages, 2 figures; accepted for publication in Phys. Rev.

Working fluid selection for organic Rankine cycle power generation using hot produced supercritical CO2 from a geothermal reservoir

Geothermal heat mining simulations using supercritical CO2 (sCO2) were performed in this research. Working fluid selection criteria for power generation using sCO2 from a geothermal reservoir are then presented for subcritical, superheated and supercritical organic Rankine cycles (ORCs). Meanwhile, method of working fluid classification for ORC is proposed. To get the most feasible ORC design, this study introduces the concept of “turning point” for isentropic and dry working fluids, as well as minimum turbine inlet temperature for wet working fluids. A thermodynamic model was developed with capabilities to obtain the optimal working fluid mass flow rate, evaporation temperature, superheated temperature, and supercritical pressure, to evaluate the thermal performance of the three ORC approaches using hot produced sCO2. With this model, thirty potential working fluids with critical temperatures in the range from 50 to 225 °C were screened for utilizing hot produced sCO2 considering physical properties, environmental and safety impacts, and thermodynamic performances. Finally, the thermodynamic results were compared for all possible working fluids

Large Magnetoresistance Ratio in Ferromagnetic Single-Electron Transistors in the Strong Tunneling Regime

We study transport through a ferromagnetic single-electron transistor. The resistance is represented as a path integral, so that systems where the tunnel resistances are smaller than the quantum resistance can be investigated. Beyond the low order sequential tunneling and co-tunneling regimes, a large magnetoresistance ratio at sufficiently low temperatures is found. In the opposite limit, when the thermal energy is larger than the charging energy, the magnetoresistance ratio is only slightly enhanced.Comment: updated versio

Path Integral Approach to Strongly Nonlinear Composite

We study strongly nonlinear disordered media using a functional method. We solve exactly the problem of a nonlinear impurity in a linear host and we obtain a Bruggeman-like formula for the effective nonlinear susceptibility. This formula reduces to the usual Bruggeman effective medium approximation in the linear case and has the following features: (i) It reproduces the weak contrast expansion to the second order and (ii) the effective medium exponent near the percolation threshold are $s=1$, $t=1+\kappa$, where $\kappa$ is the nonlinearity exponent. Finally, we give analytical expressions for previously numerically calculated quantities.Comment: 4 pages, 1 figure, to appear in Phys. Rev.