Facilitated movement of inertial Brownian motors driven by a load under an asymmetric potential

Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is increased.Comment: 7 pages, 3 figure

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations

The efficiency of a Brownian particle moving in periodic potential in the presence of asymmetric unbiased fluctuations is investigated. We found that there is a regime where the efficiency can be a peaked function of temperature, which proves that thermal fluctuations facilitate the efficiency of energy transformation, contradicting the earlier findings (H. kamegawa et al. Phys. Rev. Lett. 80 (1998) 5251). It is also found that the mutual interplay between asymmetry of fluctuation and asymmetry of the potential may induce optimized efficiency at finite temperature. The ratchet is not most efficiency when it gives maximum current.Comment: 10 pages, 7 figure

Zigzag edge modes in Z2 topological insulator: reentrance and completely flat spectrum

The spectrum and wave function of helical edge modes in Z_2 topological insulator are derived on a square lattice using Bernevig-Hughes-Zhang (BHZ) model. The BHZ model is characterized by a "mass" term M (k) that is parameterized as M (k) = Delta - B k^2. A topological insulator realizes when the parameters Delta and B fall on the regime, either 0 < Delta /B < 4 or 4 < Delta /B < 8. At Delta /B = 4, which separates the cases of positive and negative (quantized) spin Hall conductivities, the edge modes show a corresponding change that depends on the edge geometry. In the (1,0)-edge, the spectrum of edge mode remains the same against change of Delta /B, although the main location of the mode moves from the zone center for Delta /B < 4, to the zone boundary for Delta /B > 4 of the 1D Brillouin zone. In the (1,1)-edge geometry, the group velocity at the zone center changes sign at Delta /B = 4 where the spectrum becomes independent of the momentum, i.e. flat, over the whole 1D Brillouin zone. Furthermore, for Delta/B < 1.354..., the edge mode starting from the zone center vanishes in an intermediate region of the 1D Brillouin zone, but reenters near the zone boundary, where the energy of the edge mode is marginally below the lowest bulk excitations. On the other hand, the behavior of reentrant mode in real space is indistinguishable from an ordinary edge mode.Comment: 19 pages, 33 figure

Approximation of conformal mappings using conformally equivalent triangular lattices

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be approximated by such discrete conformal maps $f^\epsilon$. In particular, let $T$ be an infinite regular triangulation of the plane with congruent triangles and only acute angles (i.e.\ $<\pi/2$). We scale this tiling by $\epsilon>0$ and approximate a compact subset of the domain of $f$ with a portion of it. For $\epsilon$ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by $\log|f'|$ on the boundary. Furthermore we show that the corresponding discrete conformal maps $f^\epsilon$ converge to $f$ uniformly in $C^1$ with error of order $\epsilon$.Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some proofs extende

Extended conjugated microporous polymers for photocatalytic hydrogen evolution from water

Conjugated microporous polymers (CMPs) have been used as photocatalysts for hydrogen production from water in the presence of a sacrificial electron donor. The relative importance of the linker geometry, the co-monomer linker length, and the degree of planarisation were studied with respect to the photocatalytic hydrogen evolution rate

Sd. Thuwayni's Internal and External Policy: 1273 / 1856-1282 / 1866 (Analysis and Evaluation Study)

The main aim of this paper is to analyze and evaluate the policy of Sd. Thuwayni to consolidate his power over the tribes of Oman and to find solutions for all his problems which emerged after his father's death. The paper discusses the affairs of Oman after the death of Sd. Sa'id b. Sultan in 1856, and sheds some light on the quarrels which faced Sd. Thuwayni with his brothers and others. The great difficult event which occurred in Sd. Thuwayni' s reign was the division of the empire of Oman into the two Sultanates Oman and Zanzibar by the arbitration of the British government in India in 1861. The paper is concluded with the role of foreign policies in Oman and how Sd. Thuwayni accepted them

A Microscopic Mechanism for Muscle's Motion

The SIRM (Stochastic Inclined Rods Model) proposed by H. Matsuura and M. Nakano can explain the muscle's motion perfectly, but the intermolecular potential between myosin head and G-actin is too simple and only repulsive potential is considered. In this paper we study the SIRM with different complex potential and discuss the effect of the spring on the system. The calculation results show that the spring, the effective radius of the G-actin and the intermolecular potential play key roles in the motion. The sliding speed is about $4.7\times10^{-6}m/s$ calculated from the model which well agrees with the experimental data.Comment: 9 pages, 6 figure

The 3Rs of Cell Therapy

The 3Rs for a good education are “reading, 'riting, and 'rithmetic.” The basis for good health care solutions for the emergent field of cell therapy in the future will also involve 3Rs: regulation, reimbursement, and realization of value. The business models in this new field of cell therapy will involve these 3Rs. This article brings forth realities facing this new industry for its approaches to provide curative health care solutions

Exploiting symmetries in SDP-relaxations for polynomial optimization

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimization problems, show how the degree principle for the symmetric group can be computationally exploited and also propose some methods to efficiently compute in the geometric quotient.Comment: (v3) Minor revision. To appear in Math. of Operations Researc