We study the L1 stability of multi-dimensional discrete-velocity Boltzmann equations. Under suitable smallness assumption on initial data, we show that bounded mild solutions are L1 stable. For a stability estimate, we employ Bonys multi-dimensional analysis for total interactions over characteristic planes. 相似文献
We prove that nonsmooth quasilinear parabolic systems admit a local solution in Lp strongly differentiable with respect to time over a bounded three-dimensional polyhedral space domain. The proof rests essentially on new elliptic regularity results for polyhedral Laplace interface problems for anisotropic materials. These results are based on sharp pointwise estimates for Greens function, which are also of independent interest. To treat the nonlinear problem, we then apply a classical theorem of Sobolevskii for abstract parabolic equations and recently obtained resolvent estimates for elliptic operators and interpolation results. As applications we have in mind primarily reaction-diffusion systems. The treatment of such equations in an Lp context seems to be new and allows (by Gauss theorem) the proper definition of the normal component of currents across the boundary. 相似文献
The electrorheological properties (ER) of some fluids containing particles change extensively under the external electrical
field. This phenomenon is applicable in many industries and equipments, such as clutches and motor driven rotor, which would
transfer the spin to a drive shaft through a thin layer of electrorheological fluid. In this investigation, the effects of
external electrical field on ER properties of non-Newtonian fluids (silicon oil) with the addition of SnO2 and Y2O3 nanoparticles were studied. The ER properties were measured for a wide range of SnO2 and Y2O3 nanoparticle concentrations and DC electrical voltages using concentric cylinder rotary rheometer. Based on the results,
ER properties of nanofluids, e.g., apparent viscosity, shear stress, and yield stress, were enhanced by applying electrical
field and increasing SnO2 and Y2O3 concentrations.
This paper describes a practical method for finding the invariant orbits in J2 relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended
to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space,
which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by
its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the
ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility
between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible
configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo
simulation.
The project supported by the Innovation Foundation of Beihang University for Ph.D. Graduates, and the National Natural Science
Foundation of China (60535010). 相似文献
We consider the N-body problem in with the Newtonian potential 1/r. We prove that for every initial configuration xi and for every minimizing normalized central configuration x0, there exists a collision-free parabolic solution starting from xi and asymptotic to x0. This solution is a minimizer in every time interval. The proof exploits the variational structure of the problem, and it
consists in finding a convergent subsequence in a family of minimizing trajectories. The hardest part is to show that this
solution is parabolic and asymptotic to x0. 相似文献
Nylon-6 is an important engineering polymer that, in its fully spherulitic (bulk) form, has many applications in gears, rollers,
and other long life cycle components. In 1993, Toyota commercialized a nylon-6/clay nanocomposite out of which it produced
the timing belt cover for the Camry. Although these hybrid nanocomposites show significant improvements in their mechanical
response characteristics, including yield strength and heat distortion temperature, little is known about the degradation
of these properties due to environmental pollutants like NOx. Nylon-6 fibers are severely degraded by interaction with NOx and other pollutants, showing a strong synergy between applied load and environmental degradation. While the nanocomposites
show a significant reduction in permeability of gases and water due to the incorporation of lamellar clay, their susceptibility
to nondiffusional mechano-chemical degradation is unknown. The fracture toughness of these nylon-6/clay nanocomposites increases,
not as a function of clay content, but as a function of the volume of nylon-6 polymer chains influenced by the clay lamellae
surfaces. Both the clay and the constrained volume offer the nanocomposites some protection from the deleterious effects of
NOx. The time-to-failure at a given stress intensity factor as a function of clay content and constrained volume is discussed
along with fracture toughness of the materials. 相似文献
Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality are given, respectively. 相似文献
We consider the linearized version of the stationary Navier-Stokes equations on a subdomain of a smooth, compact Riemannian manifold M. The emphasis is on regularity: the boundary of is assumed to be only C1 and even Lipschitz, and the data are selected from appropriate Sobolev-Besov scales. Our approach relies on the method of boundary integral equations, suitably adapted to the variable-coefficient setting we are considering here. Applications to the stationary, nonlinear Navier-Stokes equations in this context are also discussed. 相似文献
This paper presents the numerical study of internal free convection of Al2O3 water nanofluid in vertical annuli. Vertical walls are maintained at constant temperatures and horizontal walls are adiabatic.
Results are validated by experimental data. Effect of nanofluids on natural convection is investigated as a function of geometrical
and physical parameters and particle fractions for aspect ratio of 1 ≤ H/L ≤ 5, Grashof number of 103 ≤ Gr ≤ 105 and concentration of 0 ≤ ϕ ≤ 0.06. More than 330 different numerical cases are investigated to develop a new correlation for the Nusselt number. This
correlation is presented as a function of Nusselt number of base fluid and particle fraction which is a linear decreasing
function of particle fraction. The developed correlation for annuli is also valid for the natural convection of Al2O3 water nanofluid in a square cavity. Furthermore, the effect of the viscosity and conductivity models on the Nusselt number
of nanofluids in cylindrical cavities are discussed. 相似文献
Several cluster models of oxygen atom adsorption on an Al2O3 surface are constructed on the basis of the density functional method. The performed quantum mechanical computations allow
one to reveal a number of important features of the potential energy surface to describe the heterogeneous catalytic processes
with the use of molecular dynamics methods. The heterogeneous recombination of oxygen atoms is simulated according to the
Eley-Rideal mechanism. It is shown that the potential energy surface should be used with consideration of the internal relaxation
of surface monolayers to correctly describe the process under study. 相似文献
The two-dimensional problem of supercritical carbon dioxide injection into an aquifer is solved. Shocks and rarefaction waves propagating in a sequence from an injection well into the formation are described within the framework of a complete nonisothermal model of flows in a porous medium. In the approximation of isothermal immiscible water and carbon dioxide flow the hydrodynamic stability of the leading displacement front is investigated for various reservoir pressures and temperatures. The parameters of unstable fronts are determined using a sufficient instability condition formulated in analytic form. The approximate analytic results are supported by the direct numerical simulation of CO2 injection using the complete model in which thermal effects and phase transitions are taken into account. 相似文献
This work is focused on numerical simulations of natural convection heat transfer in Al2O3-water nanofluids using computational fluid dynamics approach. Fluent v6.3 is used to simulate water based nanofluid considering
it as a single phase. Thermo-physical properties of the nanofluids are considered in terms of volume fraction and size of
nanoparticles, size of base fluid molecule and temperature. The numerical values of effective thermal conductivity have also
been compared with the experimental values available in the literature. The numerical result simulated shows decrease in heat
transfer with increase in particle volume fraction. Computed result shows similar trend in increase of Nusselt number with
Relayigh number as depicted by experimental results. Streamlines and temperature profiles are plotted to demonstrate the effect. 相似文献
The rheological properties of methylcellulose in N,N-dimethylformamide (MC-DMF) gel are investigated to prepare extruded beads. The temperature scan under dynamic compression for various concentrations of MC in DMF is performed to investigate the rapture of MC gel at a constant frequency of 1 Hz. The morphological studies are performed using a scanning electron microscope (SEM) to analyze the size and shape of dried bead. However, during swelling studies, the MC beads have the capability to swell and retain a large amount of water >?9150% by weight and 9192.6% by volume. The mechanism of swelling is thermodynamically verified, where the enthalpy of hydration of initial layer of MC bead is negative. The newly defined electrostatic penta-pole model explains the anomalous behavior of urea release, where urea is assumed to be electrostatically bounded with the MC molecules.
According to the research theory of improved black oil simulator, a practical mathematical model for C02 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance fast, streamline method is employed to solve this model as an alternative to traditional finite difference methods. Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less information need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an effective tool for early stage screening andmiscible oil field.reservoir dynamic management of the CO2 miscible oil field. 相似文献
In this paper, a non-isobaric Marangoni boundary layer flow that can be formed along the interface of immiscible nanofluids
in surface driven flows due to an imposed temperature gradient, is considered. The solution is determined using a similarity
solution for both the momentum and energy equations and assuming developing boundary layer flow along the interface of the
immiscible nanofluids. The resulting system of nonlinear ordinary differential equations is solved numerically using the shooting
method along with the Runge-Kutta-Fehlberg method. Numerical results are obtained for the interface velocity, the surface
temperature gradient as well as the velocity and temperature profiles for some values of the governing parameters, namely
the nanoparticle volume fraction φ (0≤φ≤0.2) and the constant exponent β. Three different types of nanoparticles, namely Cu, Al2O3 and TiO2 are considered by using water-based fluid with Prandtl number Pr =6.2. It was found that nanoparticles with low thermal conductivity,
TiO2, have better enhancement on heat transfer compared to Al2O3 and Cu. The results also indicate that dual solutions exist when β<0.5. The paper complements also the work by Golia and Viviani (Meccanica 21:200–204, 1986) concerning the dual solutions in the case of adverse pressure gradient. 相似文献
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunovs result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium is stable if it is an isolated point in the intersection of a level set of a conserved function with a subset of the phase space that is related to the topology of the symplectic leaf space at that point. This criterion is applied to generalise the energy-momentum method to Hamiltonian systems which are invariant under non-compact symmetry groups for which the coadjoint orbit space is not Hausdorff. We also show that a G-stable relative equilibrium satisfies the stronger condition of being A-stable, where A is a specific group-theoretically defined subset of G which contains the momentum isotropy subgroup of the relative equilibrium. The results are illustrated by an application to the stability of a rigid body in an ideal irrotational fluid.Acknowledgement This work was partially supported by an EPSRC Visiting Fellowship (GR/L57074) and an NSERC individual research grant for GWP, an EPSRC Research Grant (GR/K99893), a Scheme Four grant from the London Mathematical Society, a European Community Marie Curie Fellowship (HPMF-CT-2000-00542) for CW, and by European Community funding for the Research Training Network MASIE (HPRN-CT-2000-00113). We thank the University of Warwick Mathematics Institute for its hospitality during several visits when parts of the paper were written. We are also grateful to TUDOR RATIU for some very helpful remarks. 相似文献
In this paper we present a new approach to the study of linear and nonlinear stability of inviscid multidimensional shock waves under small viscosity perturbation, yielding optimal estimates and eventually an extension to the viscous case of the celebrated theorem of Majda on existence and stability of multidimensional shock waves. More precisely, given a curved Lax shock solution u0 to a hyperbolic system of conservation laws, we construct nearby viscous shock solutions u to a parabolic viscous perturbation of the hyperbolic system which converge to u0 as viscosity 0 and satisfy an appropriate (conormal) version of Majdas stability estimate.The main new feature of the paper is the derivation of maximal and optimal estimates for the linearization of the parabolic problem about a highly singular approximate solution. These estimates are more robust than the singular estimates obtained in our previous work, and permit us to remove an earlier assumption limiting how much the inviscid shock we start with can deviate from flatness.The key to the new approach is to work with the full linearization of the parabolic problem, that is, the linearization with respect to both u and the unknown viscous front, and to allow variation of the front at all stages – not only in the construction of the approximate solution as done in previous work, but also in the final error equation. After reformulating the problem as a transmission problem, we show that the linearized problem can be desingularized and optimal estimates obtained by adding an appropriate extra boundary condition involving the front. The extra condition determines a local evolution rule for the viscous front.Acknowledgement The work of O.G. was partially supported by European network HYKE, HPRN-CT-2002-00282. The work of G.M. was partially supported by European network HYKE, HPRN-CT-2002-00282. The work of M.W. was partially supported by NSF grant DMS-0070684. The work of K.Z. was partially supported by NSF grant DMS-0070765. 相似文献
The efficiency of utilization of CO2 laser energy for vaporization of Al2O3 ceramics is evaluated using a mathematical model for the interaction of laser radiation with materials. It is shown that
the calculated efficiency of radiation-energy utilization is not higher than 15% at a radiation power density of 105W/cm2 on the target. On the experimental facility designed for the synthesis of nanopowders, a vaporization rate of 1 g/h was achieved for Al2O3, which corresponds to a 3% efficiency of radiation-energy utilization. The dependence of the characteristic particle size
of a zirconium oxide nanopowder on helium pressure in the range of 0.01–1.00 atm was studied. Results of experiments on vaporization
of multicomponent materials (LaNiO3 and the Tsarev meteorite) are given.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 172–184, March–April, 2007. 相似文献
We prove the existence of positive radial solutions of the following equation:
and give sufficient conditions on the positive functions K1(r) and K2 (r) for the existence and nonexistence of ground states (G.S.) and Singular ground states (S.G.S.), when
or
. We also give sufficient conditions for the existence of radial S.G.S. and G.S. of equation
when
and
, respectively. We are also able to classify all the S.G.S. of this equation. The proofs use a new Emden–Fowler transform which allow us to use techniques taken from dynamical system theory, in particular the ones developed in Johnson et al. (Nonlinear Anal, T.M.A. 20, 1279–1302 (1993)) for the problems obtained by substituting the ordinary Laplacian Δ for the m-Laplacian Δm in the preceding equations.MSC: 37B55, 35H30, 35J70 相似文献