Stability and instability of steady-state solutions for a hydrodynamic model of semiconductors

1997 ◽  
Vol 127 (4) ◽  
pp. 781-796 ◽  
Author(s):  
Harumi Hattori
Keyword(s):  
Steady State ◽  
Initial Data ◽  
Positive Constant ◽  
Hydrodynamic Model ◽  
Steady State Solution ◽  
Doping Profile ◽  
Asymptotically Stable ◽  
Stability And Instability ◽  
The Stability ◽  
Steady State Solutions

We discuss the stability and instability of steady-state solutions for a hydrodynamic model of semiconductors. We study the case where the doping profile is close to a positive constant and depends on the special variable x. We shall show that a given steady-state solution is asymptotically stable or unstable, depending on whether or not the density of the initial data satisfies P = 0, where P is defined in (3.12).

Dynamic Stability of a Vibrating Hammer

1969 ◽  
Vol 91 (4) ◽  
pp. 1175-1179 ◽  
Author(s):  
C. C. Fu ◽  
B. Paul
Keyword(s):  
Computer Simulation ◽  
Steady State ◽  
Asymptotic Stability ◽  
Drill Bit ◽  
Asymptotically Stable ◽  
Stability Of Motion ◽  
Rock Drill ◽  
The Stability ◽  
Energy Absorbing ◽  
Steady State Solutions

This paper deals with the stability of motion of an elastically suspended vibrating hammer that impacts upon an energy absorbing surface. The energy absorber could represent, for example, a rock drill bit or drill steel, or a spike being driven by the hammer. The problem is intrinsically nonlinear because the instant of impact depends upon the motion of the hammer. “Simple steady-state solutions” are derived, and their asymptotic stability is examined. Regions in which the analytically constructed simple solutions are asymptotically stable are determined in parameter space. Results have been checked by a digital computer simulation.

MODELING BIOLOGICAL CONTROL OF ALGAL BLOOM IN A LAKE CAUSED BY DISCHARGE OF NUTRIENTS

2010 ◽  
Vol 18 (01) ◽  
pp. 161-172 ◽  
Author(s):  
MINI GHOSH
Keyword(s):  
Biological Control ◽  
Steady State ◽  
Algal Bloom ◽  
Agricultural Waste ◽  
Steady State Solution ◽  
Predatory Fish ◽  
Asymptotically Stable ◽  
Half Saturation Constant ◽  
The Stability ◽  
The Mathematical Model

This paper proposes and analyzes a nonlinear model for the biological control of algal bloom in a lake. Algal bloom often occurs in a lake due to excessive flow of nutrients from domestic drainage, industrial and agricultural waste, and this causes the decrease in the concentration of dissolved oxygen in the lake. Hence, it threatens the survival of other species of the ecosystem indirectly, and it is also responsible for the degradation of water quality in the lake because of less oxygen content. In this work we study biological control which means the introduction of predatory fish, i.e. the release of algae-eating fish into the lake to control the rapid growth of algae. We formulate our model by assuming Michaelis-Menten type ratio-dependent prey-predator interaction. The equilibrium of the mathematical model is found and also the stability is discussed in detail. It is observed that the positive equilibria is locally asymptotically stable under certain conditions on the parameters. Also the system is simulated for various sets of parameters and it is found that system may oscillate for some realistic set of parameters. In fact we found that the parameter m, which is the half saturation constant, is very sensitive and with the decrease in this parameter steady state solution of the system changes to stable oscillation. On the practical side, it means that the method of biological control by introducing predatory fish is not always beneficial because outcome of this method depends upon the actual value of the parameter. Here we get the paradox of biological control, which says that it is not possible to have low level of steady state equilibrium of prey population.

Nonlinear Peierls-Boltzmann Equation for Phonons: Structure and Stability of Solutions

1977 ◽  
Vol 32 (8) ◽  
pp. 805-812
Author(s):  
Fr. Kaiser
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Phonon Transport ◽  
Model System ◽  
Steady States ◽  
Different Types ◽  
The Stability ◽  
Steady State Solutions ◽  
Different Order ◽  
Complicated Situation

Abstract Phonon transport in locally disturbed media is considered. The steady state solutions of the Peierls-Boltzmann type equations are studied. In particular, the flux-dependence of local excitations is investigated. It is proven that for a large class of scattering processes only two types of steady states are possible: a hysteresis type and a threshold one. 4 different types of factorization procedures are applied and it is shown that for these cases the steady states remain nearly unchanged. The stability conditions are reformulated in such a way that one can give a geometrical interpretation. The only stable solutions are nodes. The necessary modification of our model system to allow for limit cycles is indicated. Also, a more complicated situation, where the interaction Hamiltonian HI is a superposition of terms of different order, is investigated. The resulting steady state solution is again a hysteresis.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

scholarly journals Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Serdal Pamuk
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Tumor Angiogenesis ◽  
Cell Movement ◽  
Steady State Solution ◽  
Stability Criteria ◽  
Data Perturbation ◽  
Capillary Formation ◽  
The Stability ◽  
Perturbation Approximation

We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation.

The stability of Couette flow of certain anisotropic fluids

1964 ◽  
Vol 60 (4) ◽  
pp. 949-955 ◽  
Author(s):  
F. M. Leslie
Keyword(s):  
Steady State ◽  
Couette Flow ◽  
Steady State Solution ◽  
State Solution ◽  
Rotating Cylinders ◽  
Important Conclusion ◽  
Preferred Direction ◽  
The Stability ◽  
Anisotropic Fluids

AbstractThe stability of the flow between concentric, rotating cylinders is discussed when the gap is small and the cylinders are rotating in the same direction for a class of anisotropic fluids in which the fluid has a preferred direction. An important conclusion of the analysis is that a steady-state solution of the equations has previously been considered unstable on false grounds.

scholarly journals Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay

2000 ◽  
Vol 23 (4) ◽  
pp. 261-270 ◽  
Author(s):  
B. Shi
Keyword(s):  
Steady State ◽  
Difference Equations ◽  
Infinite Delay ◽  
Steady State Solution ◽  
Population Models ◽  
Monotone Iterative ◽  
Positive Steady State ◽  
Infinite Delays ◽  
Steady State Solutions ◽  
Volterra Difference Equations

An open problem given by Kocic and Ladas in 1993 is generalized and considered. A sufficient condition is obtained for each solution to tend to the positive steady-state solution of the systems of nonlinear Volterra difference equations of population models with diffusion and infinite delays by using the method of lower and upper solutions and monotone iterative techniques.

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