共查询到20条相似文献,搜索用时 753 毫秒
1.
A nonlinear mathematical model of a system of n rigid bodies undergoing translational vibrations under inertial loading is
constructed. The system includes ball supports as a seismic-isolation mechanism and electromagnetic dampers controlled via
an inertial feedback channel. A system of differential dynamic equations in normal form describing accelerative damping is
derived. The frequencies of small undamped vibrations are calculated. A method for analyzing the dynamic coefficients of rigid
bodies subject to accelerative damping is developed. The double phase–frequency resonance of a two-mass system is studied 相似文献
2.
We consider scalar conservation laws with convex flux and random initial data. The Hopf–Lax formula induces a deterministic
evolution of the law of the initial data. In a recent article, we derived a kinetic theory and Lax equations to describe the
evolution of the law under the assumption that the initial datum is a spectrally negative Markov process. Here we show that:
(i) the Lax equations are Hamiltonian and describe a principle of least action on the Markov group; (ii) the Lax equations
are completely integrable and linearized via a loop-group factorization of operators; (iii) the associated zero-curvature
equations can be solved via inverse scattering. Our results are rigorous for N-dimensional approximations of the Lax equations, and yield formulas for the limit N → ∞. The main observation is that the Lax equations and zero-curvature equations are a Markovian analog of known integrable
systems (geodesic flow on Lie groups and the N-wave model respectively). This allows us to introduce a variety of methods from the theory of integrable systems. 相似文献
3.
This paper presents a multi-frequency analysis of non-linear dynamics in a double circular plate system. The original series
of the amplitude–frequency and phase–frequency graphs as well as eigen forced time functions–frequency graphs are obtained
and analyzed for stationary resonant states. The series of the frequency characteristic of the forced time non-linear harmonics
are presented first. The analyses identify the presence of singularities and triggers of coupled singularities, as well as
resonant jumps. 相似文献
4.
The classical Fokker–Planck equation is a linear parabolic equation which describes the time evolution of the probability
distribution of a stochastic process defined on a Euclidean space. Corresponding to a stochastic process, there often exists
a free energy functional which is defined on the space of probability distributions and is a linear combination of a potential
and an entropy. In recent years, it has been shown that the Fokker–Planck equation is the gradient flow of the free energy
functional defined on the Riemannian manifold of probability distributions whose inner product is generated by a 2-Wasserstein
distance. In this paper, we consider analogous matters for a free energy functional or Markov process defined on a graph with
a finite number of vertices and edges. If N ≧ 2 is the number of vertices of the graph, we show that the corresponding Fokker–Planck equation is a system of N
nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. However, in contrast to stochastic
processes defined on Euclidean spaces, the situation is more subtle for discrete spaces. We have different choices for inner
products on the space of probability distributions resulting in different Fokker–Planck equations for the same process. It
is shown that there is a strong connection but there are also substantial discrepancies between the systems of ordinary differential
equations and the classical Fokker–Planck equation on Euclidean spaces. Furthermore, both systems of ordinary differential
equations are gradient flows for the same free energy functional defined on the Riemannian manifolds of probability distributions
with different metrics. Some examples are also discussed. 相似文献
5.
DNA molecules in the familiar Watson–Crick double helical B form can be treated as though they have rod-like structures obtained
by stacking dominoes one on top of another with each rotated by approximately one-tenth of a full turn with respect to its
immediate predecessor in the stack. These “dominoes” are called base pairs. A recently developed theory of sequence-dependent DNA elasticity (Coleman, Olson, & Swigon, J. Chem. Phys. 118:7127–7140, 2003) takes into account the observation that the step from one base pair to the next can be one of several
distinct types, each having its own mechanical properties that depend on the nucleotide composition of the step. In the present
paper, which is based on that theory, emphasis is placed on the fact that, as each base in a base pair is attached to the
sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson–Crick structure, and
each phosphate group in a backbone chain bears one electronic charge, two such charges are associated with each base pair,
which implies that each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base
pairs but also to long range electrostatic forces that, because they are only partially screened out by positively charged
counter ions, can render the molecule’s equilibrium configurations sensitive to changes in the concentration c of salt in the medium. When these electrostatic forces are taken into account, the equations of mechanical equilibrium for
a DNA molecule with N + 1 base pairs are a system of μN non-linear equations, where μ, the number of kinematical variables describing the relative displacement and orientation of adjacent pairs is in general
6; it reduces to 3 when base-pair steps are assumed to be inextensible and non-shearable. As a consequence of the long-range
electrostatic interactions of base pairs, the μN × μN Jacobian matrix of the equations of equilibrium is full. An efficient numerically stable computational scheme is here presented
for solving those equations and determining the mechanical stability of the calculated equilibrium configurations. That scheme
is employed to compute and analyze bifurcation diagrams in which c is the bifurcation parameter and to show that, for an intrinsically curved molecule, small changes in c can have a strong effect on stable equilibrium configurations. Cases are presented in which several stable configurations
occur at a single value of c.
相似文献
6.
N. A. Bohai 《Nonlinear Oscillations》2007,10(2):169-175
We obtain sufficient conditions for the existence and uniqueness of continuous N-periodic solutions (N is a positive integer number) for a certain class of systems of nonlinear difference equations with continuous argument and
study their properties.
__________
Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 177–183, April–June, 2007. 相似文献
7.
We obtain conditions for the existence of continuous and N-periodic solutions, where N is a positive integer number, for systems of linear difference equations with continuous argument and investigate the structure
of the set of these solutions.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 351–359, July–September, 2005. 相似文献
8.
The structural theory of short-term damage is generalized to the case where undamaged components of an N-component laminate deform nonlinearly under loads that induce a combined stress state. The basis for this generalization
is the stochastic elasticity equations for an N-component laminate with porous components whose skeleton deforms nonlinearly. The Huber-Mises failure criterion is used to
describe the damage of microvolumes in the composite. The damaged microvolume balance equation is derived for the physically
nonlinear materials of the composite components. Together with the macrostress-macrostrain relationship, they constitute a
closed-form system of equations. This system describes the coupled processes of physically nonlinear deformation and microdamage.
For a two-component laminate, algorithms for calculating the microdamage-macrostrain relationship and plotting stress-strain
curves are proposed. Stress-strain curves are also plotted for the case where microdamages occur in the linearly hardening
component and do not in the linear elastic component under simultaneous normal and tangential loads. The effect of the volume
fraction of reinforcement and tangential load on the curves is examined
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 62–72, April 2007. 相似文献
9.
Christian Hainzl Mathieu Lewin Éric Séré 《Archive for Rational Mechanics and Analysis》2009,192(3):453-499
The Bogoliubov–Dirac–Fock (BDF) model is the mean-field approximation of no-photon quantum electrodynamics. The present paper
is devoted to the study of the minimization of the BDF energy functional under a charge constraint. An associated minimizer, if it exists, will usually represent the ground state of a system of N electrons interacting with the Dirac sea, in an external electrostatic field generated by one or several fixed nuclei. We
prove that such a minimizer exists when a binding (HVZ-type) condition holds. We also derive, study and interpret the equation
satisfied by such a minimizer. Finally, we provide two regimes in which the binding condition is fulfilled, obtaining the
existence of a minimizer in these cases. The first is the weak coupling regime for which the coupling constant α is small whereas αZ and the particle number N are fixed. The second is the non-relativistic regime in which the speed of light tends to infinity (or equivalently α tends to zero) and Z, N are fixed. We also prove that the electronic solution converges in the non-relativistic limit towards a Hartree–Fock ground
state. 相似文献
10.
We consider the problem of the existence of an asymptotically stable toroidal set for a system of linear differential equations
defined on an m-dimensional torus. We establish conditions under which a nonlinear system of differential equations has an invariant toroidal
manifold.
Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 520–529, October–December, 2008. 相似文献
11.
Banavara N. Shashikanth Artan Sheshmani Scott David Kelly Jerrold E. Marsden 《Theoretical and Computational Fluid Dynamics》2008,22(1):37-64
We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid
body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled
without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart
law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving
rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity
and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings
model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure
when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the
Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian
function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure
is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization,
provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency
conditions.
相似文献
12.
In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree–Fock equations of atoms. We show,
for example, that the Hartree–Fock ground state of a closed shell atom is unique provided the atomic number Z is sufficiently
large compared to the number N of electrons. More specifically, a two-electron atom with atomic number
Z\geqq 35{Z\geqq 35} has a unique Hartree–Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This
statement is wrong for some Z > 1, which exhibits a phase segregation. 相似文献
13.
I. H. Stampouloglou E. E. Theotokoglou 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,75(1):1-17
In this study, the generally anisotropic and angularly inhomogeneous wedge under a monomial type of distributed loading of
order n of, the radial coordinate r at its external faces is considered. At first, using variable separable relations in the equilibrium equations, the strain–stress
relations and the strain compatibility equation, a differential system of equations, is constructed. Decoupling this system,
an ordinary differential equation is derived and the stress and displacement fields may be determined. The proposed procedure
is also applied to the elastostatic problem of an isotropic and angularly inhomogeneous wedge. The special cases of loading
of order n=−1 and n=−2, where the self-similarity approach is not valid, are examined and the stress and displacements fields are derived. Applications
are presented for the cases of an angularly inhomogeneous wedge and in the case of a bi-material isotropic wedge. 相似文献
14.
We consider the 3-D evolutionary Navier–Stokes equations with a Navier slip-type boundary condition, see (1.2), and study
the problem of the strong convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations
under the zero-flux boundary condition. We prove here, in the flat boundary case, convergence in Sobolev spaces W
k, p
(Ω), for arbitrarily large k and p (for previous results see Xiao and Xin in Comm Pure Appl Math 60:1027–1055, 2007 and Beir?o da Veiga and Crispo in J Math
Fluid Mech, 2009, doi:). However this problem is still open for non-flat, arbitrarily smooth, boundaries. The main obstacle consists in some boundary
integrals, which vanish on flat portions of the boundary. However, if we drop the convective terms (Stokes problem), the inviscid,
strong limit result holds, as shown below. The cause of this different behavior is quite subtle. As a by-product, we set up
a very elementary approach to the regularity theory, in L
p
-spaces, for solutions to the Navier–Stokes equations under slip type boundary conditions. 相似文献
15.
Peter Kuku?ka 《Journal of Mathematical Fluid Mechanics》2011,13(2):173-189
This paper studies the asymptotic limit for solutions to the equations of magnetohydrodynamics, specifically, the Navier–Stokes–Fourier
system describing the evolution of a compressible, viscous, and heat conducting fluid coupled with the Maxwell equations governing
the behavior of the magnetic field, when Mach number and Alfvén number tends to zero. The introduced system is considered
on a bounded spatial domain in
\mathbbR3{\mathbb{R}^{3}}, supplemented with conservative boundary conditions. Convergence towards the incompressible system of the equations of magnetohydrodynamics
is shown. 相似文献
16.
We consider the question of stability for planar wave solutions that arise in multidimensional conservation laws with only
fourth-order regularization. Such equations arise, for example, in the study of thin films, for which planar waves correspond
to fluid coating a pre-wetted surface. An interesting feature of these equations is that both compressive, and undercompressive,
planar waves arise as solutions (compressive or undercompressive with respect to asymptotic behavior relative to the un-regularized
hyperbolic system), and numerical investigation by Bertozzi, Münch, and Shearer indicates that undercompressive waves can
be nonlinearly stable. Proceeding with pointwise estimates on the Green's function for the linear fourth-order convection–regularization
equation that arises upon linearization of the conservation law about the planar wave solution, we establish that under general
spectral conditions, such as appear to hold for shock fronts arising in our motivating thin films equations, compressive waves
are stable for all dimensions d≧2 and undercompressive waves are stable for dimensions d≧3. (In the special case d=1, compressive waves are stable under a very general spectral condition.) We also consider an alternative spectral criterion
(valid, for example, in the case of constant-coefficient regularization), for which we can establish nonlinear stability for
compressive waves in dimensions d≧3 and undercompressive waves in dimensions d≧5. The case of stability for undercompressive waves in the thin films equations for the critical dimensions d=1 and d=2 remains an interesting open problem. 相似文献
17.
A. Yu. Chebotarev 《Journal of Applied Mechanics and Technical Physics》2008,49(5):705-711
A problem of pulsed control for a three-dimensional magnetohydrodynamic (MHD) model is considered. It is demonstrated that singularities of the solution of MHD equations do not develop with time because they are suppressed by a magnetic field. The existence of an optimal control is
proved. An optimality system with the solution regular in time as a whole is constructed.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 3–10, September–October, 2008. 相似文献
18.
A phase‐field approach to binary alloys is studied. Formal asymptotics of the system of parabolic differential equations leads
to new interface relations as part of a macroscopic model which arises in the limit of vanishing interface thickness. Under
suitable conditions we prove that the phase‐field system has a unique solution which converges to the limiting macroscopic
solution. The concentration and phase are monotonic across the interface for a simplified system. Transition layers in concentration
are induced due to the change in phase and the change in material diffusion across the interface. Excess impurities may be
trapped as a consequence of these layers.
(Accepted October 28, 1996) 相似文献
19.
We obtain a solution of the Chazy system that consists of nine nonlinear algebraic equations. This system gives a necessary
condition for the class of nonlinear third-order differential equations with six singularities to be of P-type.
Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 92–98, January–March, 2009. 相似文献
20.
Ahmed A. Afify 《Transport in Porous Media》2007,66(3):391-401
An analysis is presented to investigate the effects of temperature-dependent viscosity, thermal dispersion, Soret number and
Dufour number on non-Darcy MHD free convective heat and mass transfer of a viscous, incompressible and electrically conducting
fluid past a vertical isothermal surface embedded in a saturated porous medium. The governing partial differential equations
are transferred into a system of ordinary differential equations, which are solved numerically using a fourth order Runge–Kutta
scheme with the shooting method. Comparisons with previously published work by Hong and Tien [Hong, J. T. and Tien, C. L.:
1987, Int. J. Heat Mass Transfer
30, 143–150] and Sparrow et al. [Sparrow, E. M. et al.: 1964, AIAA J. 2 652–659] are performed and good agreement is obtained. Numerical results of the skin friction coefficient, the local Nusselt
number and the local Sherwood number as well as the velocity, temperature and concentration profiles are presented for different
physical parameters. 相似文献