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81.
Rafail V. ABRAMOV 《数学年刊B辑(英文版)》2009,30(5):447-462
The recently developed short-time linear response algorithm, which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation, yields high precision of the response prediction. However, the computation of the short-time linear response formula with the full rank tangent map can be expensive. Here, a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed. The conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established, and two practical situations are examined, where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties. 相似文献
82.
Rafail?V.?AbramovEmail authorView authors OrcID profile 《Journal of Nonlinear Science》2018,28(3):833-845
For the gas near a solid planar wall, we propose a scaling formula for the mean free path of a molecule as a function of the distance from the wall, under the assumption of a uniform distribution of the incident directions of the molecular free flight. We subsequently impose the same scaling onto the viscosity of the gas near the wall and compute the Navier–Stokes solution of the velocity of a shear flow parallel to the wall. Under the simplifying assumption of constant temperature of the gas, the velocity profile becomes an explicit nonlinear function of the distance from the wall and exhibits a Knudsen boundary layer near the wall. To verify the validity of the obtained formula, we perform the Direct Simulation Monte Carlo computations for the shear flow of argon and nitrogen at normal density and temperature. We find excellent agreement between our velocity approximation and the computed DSMC velocity profiles both within the Knudsen boundary layer and away from it. 相似文献
83.
Formica Maria Rosaria Vasil’ovich Kozachenko Yuriy Ostrovsky Eugeny Sirota Leonid 《Lithuanian Mathematical Journal》2020,60(3):330-358
We derive exponential bounds for the tail of the distribution of normalized sums of triangular arrays of random variables, not necessarily independent, under the law of ordinary logarithm.
Furthermore, we provide estimates for partial sums of triangular arrays of independent random variables belonging to suitable grand Lebesgue spaces and having heavy-tailed distributions.
相似文献84.
Rafail V. Abramov 《Journal of statistical physics》2017,166(6):1483-1508
The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic unperturbed dynamical system, we compute the leading order fluctuation-response formulas for two different cases: when the existing stochastic term is perturbed, and when a new, statistically independent, stochastic perturbation is introduced. We numerically investigate the effectiveness of the new response formulas for an appropriately rescaled Lorenz 96 system, in both the deterministic and stochastic unperturbed dynamical regimes. 相似文献
85.
Single-walled carbon nanotubes embedded in oriented polymeric nanofibers by electrospinning 总被引:4,自引:0,他引:4
Salalha W Dror Y Khalfin RL Cohen Y Yarin AL Zussman E 《Langmuir : the ACS journal of surfaces and colloids》2004,20(22):9852-9855
The electrospinning process was used successfully to embed single-walled carbon nanotubes (SWCNTs) in a poly(ethylene oxide) (PEO) matrix, forming composite nanofibers. Initial dispersion of SWCNTs in water was achieved by the use of an amphiphilic alternating copolymer of styrene and sodium maleate. The resulting dispersions were stable, having a dark, smooth, ink-like appearance. For electrospinning, the dispersions were mixed with PEO solution in an ethanol/water mixture. The distribution and conformation of the nanotubes in the nanofibers were studied by transmission electron microscopy (TEM). Oxygen plasma etching was used to expose the nanotubes within the nanofibers to facilitate direct observation. Nanotube alignment within the nanofibers was shown to depend strongly on the quality of the initial dispersions. Well-dispersed and separated nanotubes were embedded in a straight and aligned form, while entangled nonseparated nanotubes were incorporated as dense aggregates. X-ray diffraction demonstrated a high degree of orientation of the PEO crystals in the electrospun nanofibers with embedded SWCNTs. This result is in pronounced distinction to the detrimental effect of incorporation of multiwalled carbon nanotubes on polymer orientation in electrospun nanofibers, as reported previously. 相似文献
86.
The correlation of the local density of states 〈ρɛ(r
1)ρɛ + ω(r
2)〉 in quasi-one-dimensional disordered wires in a magnetic field is calculated under the assumption that |r
1 − r
2| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for
the supersymmetric σ model, which is done exactly by mapping to the three-dimensional Coulomb problem. Both the regimes of
level repulsion and level attraction are obtained, depending on |r
1 − r
2|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional
cases are dissimilar.
The text was submitted by the authors in English. 相似文献
87.
L. A. Ostrovsky 《International Journal of Non》1976,11(6):401-416
Some recent applications of the theory of non-linear waves in smoothly inhomogeneous and weakly dissipative media are discussed in the paper. The possibilities of “linear-ray” approximation when the non-linear self-refraction effects may be neglected in comparison with the non-linear wave distortion along the rays are demonstrated for weak acoustic shocks in stratified atmospheres and ocean, the solitary waves in shallow water of variable depth and the solitons in elastic rods. 相似文献
88.
We consider the conductivity sigma of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class sigma model including a topological term with theta=pi. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e(2)/h. When the effective time-reversal symmetry is broken, the symmetry class becomes unitary, and sigma acquires the value characteristic for the quantum Hall transition. 相似文献
89.
Ostrovsky L Sutin A Il'inskii Y Rudenko O Sarvazyan A 《The Journal of the Acoustical Society of America》2007,121(3):1324-1331
An action of radiation force induced by ultrasonic beam in waterlike media such as biological tissues (where the shear modulus is small as compared to the bulk compressibility) is considered. A new, nondissipative mechanism of generation of shear displacement due to a smooth (nonreflecting) medium inhomogeneity is suggested, and the corresponding medium displacement is evaluated. It is shown that a linear primary acoustic field in nondissipative, isotropic elastic medium cannot excite a nonpotential radiation force and, hence, a shear motion, whereas even smooth inhomogeneity makes this effect possible. An example is considered showing that the generated displacement pulse can be significantly longer than the primary ultrasound pulse. It is noted that, unlike the dissipative effect, the nondissipative action on a localized inhomogeneity (such as a lesion in a tissue) changes its sign along the beam axis, thus stretching or compressing the focus area. 相似文献
90.
Steinberg Y Schroeder A Talmon Y Schmidt J Khalfin RL Cohen Y Devoisselle JM Begu S Avnir D 《Langmuir : the ACS journal of surfaces and colloids》2007,23(24):12024-12031
Liposomes prepared from a mixture of L-alpha-dipalmitoylphosphatidylcholine and the PEGilated phospholipid N-(carbonylmethoxypoly(ethylene glycol 2000))-1,2-distearoyl-sn-glycero-3-phosphoethanolamine were used as templates for the production of silica and alkylated silica approximately 100 nm capsules, "liposils", entrapping aqueous solutions of anionic dyes. Triggered release of this content was successfully affected by either low-frequency ultrasound or by microwave treatments. Cryo-TEM was used to follow the formation process of these particles, which are aggregated in a chain-like manner. A mechanism explaining this phenomenon is suggested. 相似文献