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1.
A robust SEIR epidemic disease model with a profitless delay and verti- cal transmission is formulated,and the dynamics behaviors of the model under pulse vaccination are analyzed.By use of the discrete dynamical system determined by the stroboscopic map,an‘infection-free’periodic solution is obtained,further,it is shown that the‘infection-free’periodic solution is globally attractive when some parameters of the model are under appropriate conditions.Using the theory on delay functional and impulsive differential equatibn,the sufficient condition with time delay for the perma- nence of the system is obtained,and it is proved that time delays,pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is‘profitless’. 相似文献
2.
We investigated the influence of elastic material compressibility on parameters of an expanding spherical stress wave. The
material compressibility is represented by Poisson’s ratio, ν, in this paper. The stress wave is generated by a pressure produced inside a spherical cavity surrounded by the isotropic
elastic material. The analytical closed form formulae determining the dynamic state of the mechanical parameters (displacement,
particle velocity, strains, stresses, and material density) in the material have been derived. These formulae were obtained
for surge pressure p(t) = p
0 = const inside the cavity. From analysis of these formulae, it is shown that the Poisson’s ratio substantially influences
the course of material parameters in space and time. All parameters intensively decrease in space together with an increase
of the Lagrangian coordinate, r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course
of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” at a different rate. Thus, Poisson’s ratio in the range below about
0.4 causes intense decay of parameter oscillations. On the other hand in the range 0.4 < ν < 0.5, i.e. in quasi-incompressible materials, the “damping” of parameter vibrations is very low. In the limiting case when
ν = 0.5, i.e. in the incompressible material, “damping” vanishes, and the parameters harmonically oscillate around their static
values. The abnormal behaviour of the material occurs in the range 0.4 < ν < 0.5. In this case, an insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration
amplitude and decrease of vibration “damping”.
相似文献
3.
The unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder is considered with combined buoyancy
force effects, for the situation in which the surface temperature T
′
w(x) and C
′
w(x) are subjected to the power-law surface heat and mass flux as K(T
′/r) = −ax
n
and D(C
′/r) = −bx
m
. The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results are
obtained for different values of Prandtl number, Schmidt number ‘n’ and ‘m’. The velocity, temperature and concentration profiles, local and average skin-friction, Nusselt and Sherwood numbers are
shown graphically. The local Nusselt and Sherwood number of the present study are compared with the available result and a
good agreement is found to exist.
Received on 7 July 1998 相似文献
4.
We present an alternative method of producing density stratifications in the laboratory based on the ‘double-tank’ method
proposed by Oster (Sci Am 213:70–76, 1965). We refer to Oster’s method as the ‘forced-drain’ approach, as the volume flow rates between connecting tanks are controlled
by mechanical pumps. We first determine the range of density profiles that may be established with the forced-drain approach
other than the linear stratification predicted by Oster. The dimensionless density stratification is expressed analytically
as a function of three ratios: the volume flow rate ratio n, the ratio of the initial liquid volumes λ and the ratio of the initial densities ψ. We then propose a method which does
not require pumps to control the volume flow rates but instead allows the connecting tanks to drain freely under gravity.
This is referred to as the ‘free-drain’ approach. We derive an expression for the density stratification produced and compare
our predictions with saline stratifications established in the laboratory using the ‘free-drain’ extension of Oster’s method.
To assist in the practical application of our results we plot the region of parameter space that yield concave/convex or linear
density profiles for both forced-drain and free-drain approaches. The free-drain approach allows the experimentalist to produce
a broad range of density profiles by varying the initial liquid depths, cross-sectional and drain opening areas of the tanks.
One advantage over the original Oster approach is that density profiles with an inflexion point can now be established.
相似文献
M. EconomidouEmail: |
G. R. Hunt (Corresponding author)Email: |
5.
Alexandre Freire 《Archive for Rational Mechanics and Analysis》2011,200(2):361-404
We consider the existence problem for ‘Steiner networks’ (trivalent graphs with 2π/3 angles at each junction) in strictly convex domains, with ‘Neumann’ boundary conditions. For each of the three possible
combinatorial possibilities, sufficient conditions on the domain are derived for existence. In addition, in each case explicit
examples of nonexistence are given. 相似文献
6.
The goal of this paper is to present a flexible multibody formulation for Euler-Bernoulli beams involving large displacements. This method is based on a discretisation of internal and kinetic energies. The beam is represented by its line of centroids and each section is oriented by a frame defined by three Euler angles. We apply a finite element formulation to describe the evolution of these angles along the neutral fibre and describe the internal energy. The kinetic energy is approximated as the one of two rigid bars tangent to the neutral fibre at the ends of the beam. We derive the equations of motion from a Lagrange formulation. These equations are solved using the Newmark method or/and the Newton-Raphson technique. We solve some very classic problems taken from the literature as the curved beam presented by Simo [Simo, J. C., ‘A three-dimensional finite-strain rod model. the three-dimensional dynamic problem. Part I’, Comput. Meths. Appl. Mech. Engrg.
49, 1985, 55–70; Simo, J. C. and Vu-Quoc, L., ‘A three-dimensional finite-strain rod model, Part II: Computationals aspects’, Comput. Meths. Appl. Mech. Engrg.
58, 1988, 79–116] and Lee [Lee, Kisu, ‘Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors’, Commun. Numer. Meth. Engrg.
13, 1997, 987–997] or the rotational rod presented by Avello [Avello, A., Garcia de Jalon, J., and Bayo, E., ‘Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory’, Int. J. Num. Methods in Engineering
32, 1991, 1543–1563] and Simo [Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part I’ Jour. of Appl. Mech.
53, 1986, 849–854; Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part II’, Jour. of Appl. Mech.
53, 1986, 855–863]. 相似文献
7.
The ‘plug’ flow emerging from a long rotating tube into a large stationary reservoir was used in the experimental investigation
of swirling jets with Reynolds numbers, Re = 600, 1,000 and 2,000, and swirl numbers, S = ΩR/U, in the range 0–1.1, to cover flow regimes from the non-rotating jet to vortex breakdown. Here Ω is the nozzle rotation rate,
R is the radius of the nozzle exit, and U is the mean mass axial velocity. The jet was more turbulent and eddies shed faster at larger Re. However the flow criticality and shear layer morphology remained unchanged with Re. After the introduction of sufficient rotation, co-rotating and counter-winding helical waves replaced vortex rings to become
the dominant vortex structure. The winding direction of the vortex lines suggests that Kelvin–Helmholtz and generalized centrifugal
instability dominated the shear layer. A quantitative visualization study has been carried out for cases where the reservoir
was rotating independently with S
a
= Ω
a
R/U = ±0.35, ±0.51 and ±0.70 at Re = 1,000 and 2000, where Ω
a
is the rotation rate of the reservoir. The criterion for breakdown was found to be mainly dependent on the absolute swirl
number of the jet, S. This critical swirl number was slightly different in stationary and counter-swirl surroundings but obviously smaller when
the reservoir co-rotated, i.e. S
c
= 0.88, 0.85 and 0.70, respectively. These results suggest that the flow criticality depends mainly on the velocity distributions
of the vortex core, while instabilities resulting from the swirl difference between the jet and its ambient seem to have only
a secondary effect. 相似文献
8.
The immiscible displacement in a capillary plane channel of a Newtonian liquid by a viscoplastic one that obeys a Papanastasiou’s
constitutive equation is numerically analyzed. An elliptic mesh generation technique, coupled with the Galerkin finite element
method is used to determine the velocity field and the configuration of the interface between the two materials. We investigate
the displacement efficiency and the flow patterns of the problem as functions of the dimensionless parameters that govern
the problem: the capillary number (Ca), the viscosity ratio of the two fluids (N
η
) and the yield number, (τ′0). The numerical results showed that for a fixed viscosity ratio, the fraction of mass attached to the wall is a decreasing
function of τ′0. We constructed maps of streamlines in the Cartesian space defined by τ′0 and Ca for fixed viscosity ratios in order to capture the rough location of bypass and recirculating flow regimes. Higher
yield number values induce bypass flow regimes, especially for high Ca. The dimensionless forms of the momentum conservation
equation and the force balance at the interface were essential for the understanding of the role played by the dimensionless
numbers that govern the problem. 相似文献
9.
Our starting point is a parameterized family of functionals (a ‘theory’) for which we are interested in approximating the
global minima of the energy when one of these parameters goes to zero. The goal is to develop a set of increasingly accurate
asymptotic variational models allowing one to deal with the cases when this parameter is ‘small’ but finite. Since Γ-convergence
may be non-uniform within the ‘theory’, we pose a problem of finding a uniform approximation. To achieve this goal we propose
a method based on rectifying the singular points in the parameter space by using a blow-up argument and then asymptotically
matching the approximations around such points with the regular approximation away from them. We illustrate the main ideas
with physically meaningful examples covering a broad set of subjects from homogenization and dimension reduction to fracture
and phase transitions. In particular, we give considerable attention to the problem of transition from discrete to continuum
when the internal and external scales are not well separated, and one has to deal with the so-called ‘size’ or ‘scale’ effects.
相似文献
10.
Matteo Negri 《Journal of Elasticity》2010,98(2):159-187
On the base of many experimental results, e.g., Ravi-Chandar and Knauss (Int. J. Fract. 26:65–80, 1984), Sharon et al. (Phys. Rev. Lett. 76(12):2117–2120, 1996), Hauch and Marder (Int. J. Fract. 90:133–151, 1998), the object of our analysis is a rate-dependent model for the propagation of a crack in brittle materials. Restricting ourselves
to the quasi-static framework, our goal is a mathematical study of the evolution equation in the geometries of the ‘Single
Edge Notch Tension’ and of the ‘Compact Tension’. Besides existence and uniqueness, emphasis is placed on the regularity of
the evolution making reference also to the ‘velocity gap’. The transition to the rate-independent model of Griffith is obtained
by time rescaling, proving convergence of the rescaled evolutions and of their energies. Further, the discontinuities of the
rate-independent evolution are characterized in terms of unstable points of the free energy. Results are illustrated by a
couple of numerical examples in the above mentioned geometries. 相似文献
11.
The winding or layup procedure for fiber-reinforced composites lends itself to convenient installation of embedded sensors
during fabrication. These permanently installed and protected sensors could be used during the service lifetime of the structure
to monitor real-time conditions and determine when loading or vibration is excessive, and when damage has occurred. Such ‘smart
or intelligent’ structures could be used to provide continuous ‘health monitoring’ of the structure as well as provide input
for active vibration control.
In the present study, two sizes of constantan wire (0.15-mm and 0.025-mm diameter) with a very thin but tough polyimide insulation
were embedded in graphite-epoxy bars and tubes. The 25-mm by 2.5-mm by approximately 300-mm long bars were fabricated from
hand-laid-up panels and subjected to static four-point bending and cantilever bending. The tubes (42-mm diameter by 1.25-m
long) were subjected to static cantilever bending. Output from the constantan wire was monitored with conventional strain-gage
indicators.
Results indicate accurate tensile and compressive measurements of the integrated strain along the length of the constantan
wire when compared with beam formulas and surface mounted strain gages. The constantan strain wire shows promise as an embedded
sensor for ‘smart structures’. 相似文献
12.
Twist maps (θ
1, r
1) = f (θ, r) on the plane are considered which do not exhibit any kind of periodicity in their dependence on θ. Some general results are obtained which typically yield the existence of infinitely many complete and bounded orbits. Examples
that can be treated with this theory include oscillators of the type [(x)\ddot]+V¢(x)=p(t){\ddot{x}+V'(x)=p(t)} under appropriate hypotheses, the bouncing ball system, and the standard map. 相似文献
13.
The resonant-based identification of the in-plane elastic properties of orthotropic materials implies the estimation of four
principal elastic parameters: E
1
, E
2
, G
12
, and ν
12
. The two elastic moduli and the shear modulus can easily be derived from the resonant frequencies of the flexural and torsional
vibration modes, respectively. The identification of the Poisson’s ratio, however, is much more challenging, since most frequencies
are not sufficiently sensitive to it. The present work addresses this problem by determining the test specimen specifications
that create the optimal conditions for the identification of the Poisson’s ratio. Two methods are suggested for the determination
of the Poisson’s ratio of orthotropic materials: the first employs the resonant frequencies of a plate-shaped specimen, while
the second uses the resonant frequencies of a set of beam-shaped specimens. Both methods are experimentally validated using
a stainless steel sheet. 相似文献
14.
Motivated by optimization problems in structural engineering, we study the critical points of symmetric, ‘reflected', one-parameter
family of potentials U(p, x) = max (f(p,x), f(p, −x)), yielding modest generalizations of classical bifurcations, predicted by elementary catastrophe theory. One such generalization
is the ‘five-branch pitchfork’, where the symmetric optimum persists beyond the critical parameter value. Our theory may help
to explain why symmetrical structures are often optimal. 相似文献
15.
Mallikarjunaiah S. Muddamallappa Dambaru Bhatta Daniel N. Riahi 《Transport in Porous Media》2009,79(2):301-317
In this article, an investigation is conducted to analyze the marginal stability with and without magnetic field in a mushy
layer. During alloy solidification, such mushy layer, which is adjacent to the solidification front and composed of solid
dendrites and liquid, is known to produce vertical chimneys. Here, we carry out numerical investigation for particular range
of parameter values, which cover those of available experimental studies, to determine the convective flow at the onset of
motion. The governing coupled non-linear partial differential equations are non-dimensionalised and solved to get the steady
basic-state solution. The thickness of the mushy layer is determined as a part of the solution. Using multiple shooting technique,
we determine the steady-state solutions in a range of critical Rayleigh number. We analyse the effect of several parameters,
Chandrasekhar number Q, and Robert’s number τ on the problem. It was found that an increase in Q has a stabilizing effect on solidification and the critical Rayleigh number increases on increasing Q. It was also found that for moderate or small values of Robert’s number τ the critical Rayleigh number is mostly insensitive. 相似文献
16.
17.
It is well known that fluid mixing can often be improved by the introduction of ‘baffles’ into the flow – the problem of baffle
placement is examined here for chaotic fluid mixing of a highly viscous fluid. A simple model for a planetary mixer, with
one stirring element, is modified by the introduction of one or more stationary baffles. Regular regions of poor mixing in
the unbaffled flow are shown to be significantly reduced in size if the location of the baffles is chosen so that the flow
necessarily generates ‘topological chaos’. By contrast, the positioning of baffles in superficially similar ways that do not
generate such ‘topological chaos’ fails to provide a similar improvement. 相似文献
18.
19.
Laminar and turbulent computations are presented for annular rectangular-section cavities, on a body of revolution, in a Mach
2.2 flow. Unsteady ‘open cavity flows’ result for all laminar computations for all cavity length-to-depth ratios, L/D (1.33, 10.33, 11.33 and 12.33). The turbulent computations produce ‘closed cavity flows’ for L/D of 11.33 and 12.33. Surface pressure fluctuations at the front corner of the L/D = 1.33 cavity are periodic in some cases depending on the cavity length and depth, the boundary layer at the cavity front
lip and the cavity scale. The turbulent computations are supported by experimental schlieren images, obtained using a spark
light source, and time-averaged surface pressure data. 相似文献
20.
Friction-induced vibration of a two-degree-of-freedom mass-damper-spring system interacting with a decelerating rigid strip
is investigated. The friction law is approximated by an analytical function to facilitate the analyses and numerical integrations.
It is shown that, after a quasi-harmonic transient period, accompanied by viscous energy dissipation, a short period of intensive
‘creep-slip’ vibration occurs, which generates a series of ‘micro-impacts’ on the strip. Because of the impulsive character
of such kind of loading, its Fourier spectrum is rich and quite broadband. Using an averaging technique, the ‘normal form’
equations of motion show that the out-of-phase vibration mode absorbs more energy from the decelerating strip when its natural
frequency satisfies certain resonance conditions. The study is then applied to an automotive disc brake model to gain useful
insight into the generation of squeal. It is shown that the out-of-phase creep-slip vibration (in the longitudinal direction)
of the brake pads generates an impulsive bending moment on the decelerating strip (disc rotor). This impulsive load may be
considered as a possible source for brake squeal. The technique developed in this paper may be extended to other ‘squealing
systems’ including models for geophysical faults (earthquakes). 相似文献