Soliton solutions of a BBM(m, n) equation with generalized evolution

We consider a BBM(m, n) equation which is a generalization of the celebrated Benjamin-Bona-Mahony equation with generalized evolution term. By using two solitary wave ansatze in terms of sech^p(x) and tanh^p(x) functions, we find exact analytical bright and dark soliton solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The conditions of existence of solitons are presented. Note that, it is always useful and desirable to construct exact analytical solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.     

On symmetric graphs of valency five

A graph X, with a subgroup G of the automorphism group of X, is said to be (G,s)-transitive, for some s≥1, if G is transitive on s-arcs but not on (s+1)-arcs, and s-transitive if it is -transitive. Let X be a connected (G,s)-transitive graph, and G_v the stabilizer of a vertex v∈V(X) in G. If X has valency 5 and G_v is solvable, Weiss [R.M. Weiss, An application of p-factorization methods to symmetric graphs, Math. Proc. Camb. Phil. Soc. 85 (1979) 43-48] proved that s≤3, and in this paper we prove that G_v is isomorphic to the cyclic group Z₅, the dihedral group D₁₀ or the dihedral group D₂₀ for s=1, the Frobenius group F₂₀ or F₂₀×Z₂ for s=2, or F₂₀×Z₄ for s=3. Furthermore, it is shown that for a connected 1-transitive Cayley graph of valency 5 on a non-abelian simple group G, the automorphism group of is the semidirect product , where R(G) is the right regular representation of G and .     

Physical model for the width distribution of axons

The distribution of widths of axons was recently investigated, and was found to have a distinct peak at an optimized value. The optimized axon width at the peak may arise from the conflicting demands of minimizing energy consumption and assuring signal transmission reliability. The distribution around this optimized value is found to have a distinct non-Gaussian shape, with an exponential “tail”. We propose here a mechanical model whereby this distribution arises from the interplay between the elastic energy of the membrane surrounding the axon core, the osmotic pressure induced by the neurofilaments inside the axon bulk, and active processes that remodel the microtubules and neurofilaments inside the axon. The axon’s radius of curvature can be determined by the cell’s control of the osmotic pressure difference across the membrane, the membrane tension or by changing the composition of the different components of the membrane. We find that the osmotic pressure, determined by the neurofilaments, seems to be the dominant control parameter.     

Non-linear systems under parametric white noise input: Digital simulation and response

Monte Carlo technique is constituted of three steps. Therefore, improving such technique in practice means, improving the procedure used in one of the three following steps: (i) sample paths of the stochastic input process, (ii) calculation of the outputs corresponding to the generated input samples by using methods of classical dynamics and (iii) estimating statistics of the output process from sample outputs related to the previous step. For linear and non-linear systems driven by parametric impulsive inputs such as normal or non-normal white noises, a general integration method requires a considerable reduction of the integration step when the impulse occurs, treating the impulse as a physical one, by means of a window function of finite duration. This makes Monte Carlo simulation very prohibitive from a computational time point of view. While knowing the exact jump value of the response at impulse occurring that is expressed by a numerical series, the aforementioned problem is overcome because there is no need to reduce the integration step saving computational time, reliability being equal as shown by means of a numerical example.     

共轭算子法和非线性动力系统的高阶规范形

规范形理论是研究非线性动力系统退化分含的强有力的方法.在本文里我们利用共轭算子法计算了具有幂零线性部分和不具有Z2-对称性的非线性动力系统的2阶、3阶和4阶规范形,讨论了几种余维3退化分含情况下的普适开析问题及其一些全局特性.     

Pt(110)/Sb电极上甲酸的电催化氧化特征和动力学

研究了Sb在Pt(110)晶面上不可逆吸附电化学特性及甲酸在Sb_ad修饰Pt(110)电极[Pt(110)/Sb]上的电催化氧化特征及其反应动力学.发现当扫描电位的上限E_u≤0.45V时,Sb_ad可稳定地吸附在Pt(110)表面上,从而有效地抑制了甲酸的解离吸附.与未修饰的Pt(110)上的结果相比,在Pt(110)/Sb上甲酸氧化的峰电位负移了0.35V.当θ_Sb=0.126时,Pt(110)/Sb电极对甲酸的电催化活性最高.还研究了Pt(110)/Sb上甲酸氧化反应的动力学,定量解析了不同θ_Sb下甲酸氧化的速度常数kf和传递系数β.     

Effect of doping and temperature on the crystal structure of (V1−xMox)2O3 above and below the metal/insulator transition

The crystal structure of new molybdenum-doped vanadium sesquioxides (V_1−xMo_x)₂O₃ (0?x?0.20) has been studied at low temperature (10 K) and up to room temperature, through neutron and X-ray powder diffraction. The transition from insulating I- to metallic M-type phases, either by doping or thermally driven, is accompanied by an abrupt decrease of all interatomic distances. Within each structural type however, at 10 K, the effect of doping is essentially the same as at room temperature: it increases cation-oxygen distances, and decreases cation-cation distances, making the cationic coordination octahedra more regular. Thermal effects differ for each phase type: all interatomic distances normally increase in the M-type phase (but with different octahedral modifications depending on doping), but they decrease or remain constant in the I-type phase. This produces an unusual negative thermal expansion coefficient up to 5% at low temperature for the doped compounds.     

A fast local search method for minimum energy broadcast in wireless ad hoc networks

Local search methods are often used to reduce the power consumption of broadcast routing in wireless networks. For a classic method, sweep, the best available time complexity result is O(|V|⁴). We present an O(|V|²)-time method, which exhaustively removes unnecessary transmissions yielding a solution comparable to that of sweep.     

Shuttle-run synchronization in mobile ad hoc networks

In this work, we study the collective dynamics of phase oscillators in a mobile ad hoc network whose topology changes dynamically. As the network size or the communication radius of individual oscillators increases, the topology of the ad hoc network first undergoes percolation, forming a giant cluster, and then gradually achieves global connectivity. It is shown that oscillator mobility generally enhances the coherence in such networks. Interestingly, we find a new type of phase synchronization/clustering, in which the phases of the oscillators are distributed in a certain narrow range, while the instantaneous frequencies change signs frequently, leading to shuttle-run-like motion of the oscillators in phase space. We conduct a theoretical analysis to explain the mechanism of this synchronization and obtain the critical transition point.     

Parameter selection in a Peyrard-Bishop-Dauxois model for DNA dynamics

In this Letter we study possible intervals for some parameters existing in the Peyrard-Bishop-Dauxois (PBD) model for the DNA dynamics. These parameters describe longitudinal and helicoidal interactions between nucleotides and a Morse potential approximating transverse interactions. We also estimate a possible interval for a wave number of a carrier component of a modulated solitonic wave. Finally, we compare our statements with experimental value of solitonic velocity in DNA.