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1.
Discrete nonlinear Schrödinger (DNLS) equation describes a chain of oscillators with nearest-neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to 1/l1+α with fractional α<2 and l as a distance between oscillators. This model is called αDNLS. It exhibits competition between the nonlinearity and a level of correlation between interacting far-distanced oscillators, that is defined by the value of α. We consider transition to chaos in this system as a function of α and nonlinearity. It is shown that decreasing of α with respect to nonlinearity stabilize the system. Connection of the model to the fractional generalization of the NLS (called FNLS) in the long-wave approximation is also discussed and some of the results obtained for αDNLS can be correspondingly extended to the FNLS. 相似文献
2.
The evolution of the scoring performance of Rugby Union players is investigated over the seven rugby world cups (RWC) that took place from 1987 to 2011, and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995. The distribution of the points scored by individual players, Ps, ranked in order of performance were well described by the simplified canonical law Ps∝(r+?)−α, where r is the rank, and ? and α are the parameters of the distribution. The parameter α did not significantly change from 1987 to 2007 (α=0.92±0.03), indicating a negligible effect of professionalism on players’ scoring performance. In contrast, the parameter ? significantly increased from ?=1.32 for 1987 RWC, ?=2.30 for 1999 to 2003 RWC and ?=5.60 for 2007 RWC, suggesting a progressive decrease in the relative performance of the best players. Finally, the sharp decreases observed in both α(α=0.38) and ?(?=0.70) in the 2011 RWC indicate a more even distribution of the performance of individuals among scorers, compared to the more heterogeneous distributions observed from 1987 to 2007, and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players. Note that neither α nor ? significantly correlate with traditional performance indicators such as the number of points scored by the best players, the number of games played by the best players, the number of points scored by the team of the best players or the total number of points scored over each RWC. This indicates that the dynamics of the scoring performance of Rugby Union players is influenced by hidden processes hitherto inaccessible through standard performance metrics; this suggests that players’ scoring performance is connected to ubiquitous phenomena such as anomalous diffusion. 相似文献
3.
A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
4.
M. Teresa Blázquez Marta Anguiano Fernando Arias de Saavedra Antonio M. Lallena Pedro Carpena 《Physica A》2012
The effects associated to the length of stabilograms, a measure of the time dependence of the center of pressure of an individual standing up, are analyzed. The fractal characteristics of 27 signals with a length of 214 points, each one corresponding to a different individual, are studied by using the Detrended Fluctuation Analysis technique. The properties of the complete signals are compared to those of various subsignals extracted from them. No differences have been found between the characteristic exponents found for x and y signals. The relation between the exponents of the position and velocity signals is accomplished by the 214 point signals, while subsignals with up to 212 points do not verify it. Using artificial signals with 214 points, generated for α values given, it has been demonstrated that the exponents obtained from these signals take values larger than expected for α<0.3, while the exponents of the accumulated series are smaller than expected for 0.7<α. For CoP trajectories this indicates that DFA-1 provides feasible exponents for the short τ-end region of the velocity signal and the large τ-end region of the accumulated (position) one. It has been found that the characteristic exponents vary along the series. A slightly larger persistence is found in the last part of the signal for large frequencies in the x direction. 相似文献
5.
A curve α immersed in the three-dimensional sphere S3 is said to be a Bertrand curve if there exists another curve β and a one-to-one correspondence between α and β such that both curves have common principal normal geodesics at corresponding points. The curves α and β are said to be a pair of Bertrand curves in S3. One of our main results is a sort of theorem for Bertrand curves in S3 which formally agrees with the classical one: “Bertrand curves in S3 correspond to curves for which there exist two constants λ≠0 and μ such that λκ+μτ=1”, where κ and τ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S3 as the only twisted curves in S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3 and (1,3)-Bertrand curves in R4. 相似文献
6.
Motivated by speculations about infrared deviations from the standard behavior of local quantum field theories, we explore the possibility that such effects might show up as an anomalous running of coupling constants. The most sensitive probes are presently given by the anomalous magnetic moments of the electron and the muon, that suggest that αem runs 1.00047±0.00018 times faster than predicted by the Standard Model. The running of αem and αs up to the weak scale is confirmed with a precision at the % level. 相似文献
7.
We investigate the geometry of the moduli space of N vortices on line bundles over a closed Riemann surface Σ of genus g>1, in the little explored situation where 1≤N<g. In the regime where the area of the surface is just large enough to accommodate N vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ. For N=1, we show that the metric on the moduli space converges to a natural Bergman metric on Σ. When N>1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics. 相似文献
8.
Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0 1D insulator the charge stiffness D(T) vanishes for T>0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0 and vanishes for U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0 for all finite temperatures T>0. (At T=0 such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model. 相似文献
9.
We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m “ambassador” nodes and l of each ambassador’s descendants where m and l are random variables selected from any choice of distributions pl and qm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m and the number of selected descendants from each ambassador is the constant l, the power-law exponent is (2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l and m. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically. 相似文献
10.
Obtaining accurate approximations for derivatives is important for many scientific applications in such areas as fluid mechanics and chemistry as well as in visualization applications. In this paper we discuss techniques for computing accurate approximations of high-order derivatives for discontinuous Galerkin solutions to hyperbolic equations related to these areas. In previous work, improvement in the accuracy of the numerical solution using discontinuous Galerkin methods was obtained through post-processing by convolution with a suitably defined kernel. This post-processing technique was able to improve the order of accuracy of the approximation to the solution of time-dependent symmetric linear hyperbolic partial differential equations from order k+1 to order 2k+1 over a uniform mesh; this was extended to include one-sided post-processing as well as post-processing over non-uniform meshes. In this paper, we address the issue of improving the accuracy of approximations to derivatives of the solution by using the method introduced by Thomée [19]. It consists in simply taking the αth-derivative of the convolution of the solution with a sufficiently smooth kernel. The order of convergence of the approximation is then independent of the order of the derivative, |α|. We also discuss an efficient way of computing the approximation which does not involve differentiation but the application of simple finite differencing. Our results show that the above-mentioned approximations to the αth-derivative of the exact solution of linear, multidimensional symmetric hyperbolic systems obtained by the discontinuous Galerkin method with polynomials of degree k converge with order 2k+1 regardless of the order |α| of the derivative. 相似文献
11.
The standard Vicsek model (SVM) is a minimal non-equilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noise-driven continuous order–disorder phase transition. In this work, we extend the SVM by introducing a parameter α that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the α-extended model preserves the O(n) symmetry and the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first order), an intriguing manifestation of the richness of the non-equilibrium flocking/swarming phenomenon. 相似文献
12.
We study the oil displacement and production behavior in an isothermal thin layered reservoir model subjected to water flooding. We use the CMG’s (Computer Modelling Group ) numerical simulators to solve mass balance equations. The influences of the viscosity ratio (m≡μoil/μwater) and the inter-well (injector-producer) distance r on the oil production rate C(t) and the breakthrough time tbr are investigated. Two types of reservoir configuration are used, namely one with random porosities and another with a percolation cluster structure. We observe that the breakthrough time follows a power-law of m and r, tbr∝rαmβ, with α=1.8 and β=−0.25 for the random porosity type, and α=1.0 and β=−0.2 for the percolation cluster type. Moreover, our results indicate that the oil production rate is a power law of time. In the percolation cluster type of reservoir, we observe that P(t)∝tγ, with γ=−1.81, where P(t) is the time derivative of C(t). The curves related to different values of m and r may be collapsed suggesting a universal behavior for the oil production rate. 相似文献
13.
We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H and transverse magnetic field Ω. Using the effective-field theory (EFT) with correlation in cluster with N=1 spin we calculate the thermodynamic properties as a function of temperature with values H and Ω fixed. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction, and it is found that for H/Jy∈[0,2] the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=Jx/Jy=1 (isotropic square lattice). 相似文献
14.
By employing the higher (N>5)-dimensional version of the Wu–Yang ansatz we obtain magnetically charged new black hole solutions in the Einstein–Yang–Mills–Lovelock (EYML) theory with second (α2) and third (α3) order parameters. These parameters, where α2 is also known as the Gauss–Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically (r→∞), these parameters contribute to an effective cosmological constant—without cosmological constant—so that the solution behaves de-Sitter (anti de-Sitter) like. 相似文献
15.
In real systems, generous individuals who prefer to contribute can play more important roles on the public than selfish individuals. Inspired by this, a spatial public goods game with weighted and conditional strategies is proposed in this paper. In our model, a player’s contribution behavior is mainly determined by the less cautious neighbors rather than those more cautious ones. The weight effect is adjusted by a non-negative parameter α. Our results show that the number of strategies increases with the weight parameter α for the low multiplication factor r. On the contrary, for the high multiplication factor r, the less cautious cooperators are more likely to appear in the system. 相似文献
16.
Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V are almost the right triangles with α≈90°. We highlight a very suggestive parametrization of V and show that its CP-violating phase ? is nearly equal to α (i.e., ?−α≈1.1°). Both ? and α are stable against the renormalizaton-group evolution from the electroweak scale MZ to a superhigh energy scale MX or vice versa, and thus it is impossible to obtain α=90° at MZ from ?=90° at MX. We conjecture that there might also exist a maximal CP-violating phase φ≈90° in the MNS lepton mixing matrix U. The approximate quark–lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U simply due to the smallness of |Vub| and |Ve3|. 相似文献
17.
18.
The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0<α<1, fractional Laplacian of the order σ, and Gaussian noise correlator. The case of non-linearity φm with odd m≥3 is considered. It is proved that the model is multiplicatively renormalizable. Propagators were found in the momentum and coordinate representation, expressed in terms of Fox’s H functions. 相似文献
19.
We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order q, we first provide a generalized monogamy inequality of multi-qubit entanglement for q=2 or 3. This generalization encapsulates the multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-q entropy for 1≤q≤2 or 3≤q≤4, which also contains the multi-qubit polygamy inequality as a special case. 相似文献