New classes of exact solutions of three-dimensional Navier-Stokes equations

New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are obtained. The general physical interpretation and classification of solutions is given.Comment: 11 page

Non-analytical power law correction to the Einstein-Hilbert action: gravitational wave propagation

We analyze the features of the Minkowskian limit of a particular non-analytical f(R) model, whose Taylor expansion in the weak field limit does not hold, as far as gravitational waves (GWs) are concerned. We solve the corresponding Einstein equations and we find an explicit expression of the modified GWs as the sum of two terms, i.e. the standard one and a modified part. As a result, GWs in this model are not transverse, and their polarization is different from that of General Relativity. The velocity of the GW modified part depends crucially on the parameters characterizing the model, and it mostly results much smaller than the speed of light. Moreover, this investigation allows one to further test the viability of this particular f(R) gravity theory as far as interferometric observations of GWs are concerned.Comment: 18 pages, 3 figure

Young's modulus of Graphene: a molecular dynamics study

The Young's modulus of graphene is investigated through the intrinsic thermal vibration in graphene which is `observed' by molecular dynamics, and the results agree quite well with the recent experiment [Science \textbf{321}, 385 (2008)]. This method is further applied to show that the Young's modulus of graphene: 1. increases with increasing size and saturation is reached after a threshold value of the size; 2. increases from 0.95 TPa to 1.1 TPa as temperature increases in the region [100, 500]K; 3. is insensitive to the isotopic disorder in the low disorder region ($< 5$), and decreases gradually after further increasing the disorder percentage.Comment: accepted by PRB, brief report, discussion on Poisson ratio adde

Network growth model with intrinsic vertex fitness

© 2013 American Physical SocietyWe study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions

Nonlinear Schroedinger Equation in the Presence of Uniform Acceleration

We consider a recently proposed nonlinear Schroedinger equation exhibiting soliton-like solutions of the power-law form $e_q^{i(kx-wt)}$, involving the $q$-exponential function which naturally emerges within nonextensive thermostatistics [$e_q^z \equiv [1+(1-q)z]^{1/(1-q)}$, with $e_1^z=e^z$]. Since these basic solutions behave like free particles, obeying $p=\hbar k$, $E=\hbar \omega$ and $E=p^2/2m$ ($1 \le q<2$), it is relevant to investigate how they change under the effect of uniform acceleration, thus providing the first steps towards the application of the aforementioned nonlinear equation to the study of physical scenarios beyond free particle dynamics. We investigate first the behaviour of the power-law solutions under Galilean transformation and discuss the ensuing Doppler-like effects. We consider then constant acceleration, obtaining new solutions that can be equivalently regarded as describing a free particle viewed from an uniformly accelerated reference frame (with acceleration $a$) or a particle moving under a constant force $-ma$. The latter interpretation naturally leads to the evolution equation $i\hbar \frac{\partial}{\partial t}(\frac{\Phi}{\Phi_0}) = - \frac{1}{2-q}\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} [(\frac{\Phi}{\Phi_0})^{2-q}] + V(x)(\frac{\Phi}{\Phi_0})^{q}$ with $V(x)=max$. Remarkably enough, the potential $V$ couples to $\Phi^q$, instead of coupling to $\Phi$, as happens in the familiar linear case ($q=1$).Comment: 4 pages, no figure

Ion-acoustic solitary waves and shocks in a collisional dusty negative ion plasma

We study the effects of ion-dust collisions and ion kinematic viscosities on the linear ion-acoustic instability as well as the nonlinear propagation of small amplitude solitary waves and shocks (SWS) in a negative ion plasma with immobile charged dusts. {The existence of two linear ion modes, namely the `fast' and `slow' waves is shown, and their properties are analyzed in the collisional negative ion plasma.} {Using the standard reductive perturbation technique, we derive a modified Korteweg-de Vries-Burger (KdVB) equation which describes the evolution of small amplitude SWS.} {The profiles of the latter are numerically examined with parameters relevant for laboratory and space plasmas where charged dusts may be positively or negatively charged.} It is found that negative ion plasmas containing positively charged dusts support the propagation of SWS with negative potential. However, the perturbations with both positive and negative potentials may exist when dusts are negatively charged. The results may be useful for the excitation of SWS in laboratory negative ion plasmas as well as for observation in space plasmas where charged dusts may be positively or negatively charged.Comment: 13 pages, 9 figures; To appear in Physical Review

Two electrons on a hypersphere: a quasi-exactly solvable model

We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a $\mathcal{D}$-sphere ($\mathcal{D} \ge 1$), is a polynomial in the interelectronic distance $u$ for a countably infinite set of values of the radius $R$. A selection of these radii, and the associated energies, are reported for ground and excited states on the singlet and triplet manifolds. We conclude that the $\mathcal{D}=3$ model bears the greatest similarity to normal physical systems.Comment: 4 pages, 0 figur

Self-gravitating spheres of anisotropic fluid in geodesic flow

The fluid models mentioned in the title are classified. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order differential equation. Different constraints are imposed on this core of relations, finding new solutions and deriving the classical results for perfect fluids and dust as particular cases. Many uncharged and charged anisotropic solutions, all conformally flat and some uniform density solutions are found. A number of solutions with linear equation among the two pressures are derived, including the case of vanishing tangential pressure.Comment: 21 page

Effective non-Markovian description of a system interacting with a bath

We study a harmonic system coupled to chain of first neighbor interacting oscillators. After deriving the exact dynamics of the system, we prove that one can effectively describe the exact dynamics by considering a suitable shorter chain. We provide the explicit expression for such an effective dynamics and we provide an upper bound on the error one makes considering it instead of the dynamics of the full chain. We eventually prove how error, timescale and number of modes in the truncated chain are related