Points dissipation

T2] H. R. Thieme (1993), Persistence under relaxed point-dissipativity (with an application to an epidemic model), SIAM Journal on Mathematical Analysis 24 407-35. 

The volt is the SI unit of electric potential. One volt is the difference of potential between two points of an electical conductor when a current of 1 ampere flowing between those points dissipates a power of 1 watt. It is named after the Italian physicist Count Alessandro Giuseppe Anastasio Volta (1745-1827). 

In other words, if we look at any phase-space volume element, the rate of incoming state points should equal the rate of outflow. This requires that be a fiinction of the constants of the motion, and especially Q=Q i). Equilibrium also implies d(/)/dt = 0 for any /. The extension of the above equations to nonequilibriiim ensembles requires a consideration of entropy production, the method of controlling energy dissipation (diennostatting) and the consequent non-Liouville nature of the time evolution [35]. 

Because of tire underlying dissipative nature of tire chemical systems tliat tire ODEs (C3.6.2) represent, tliey have anotlier important property any volume in F will shrink as it evolves. For a given set of initial chemical concentrations tire time evolution under tire chemical rate law will approach arbitrarily close to some final set of points in... 

A typical cascade process. A fast atom or ion collides with surface molecules, sharing its momentum and causing the struck molecules to move faster. The resulting fast-moving particles then strike others, setting up a cascade of collisions until all the initial momentum has been dissipated. The dots ( ) indicate collision points. Ions or atoms (O) leave the surface. 

An alternative point of view assumes that each repeat unit of the polymer chain offers hydrodynamic resistance to the flow such that f-the friction factor per repeat unit-is applicable to each of the n units. This situation is called the free-draining coil. The free-draining coil is the model upon which the Debye viscosity equation is based in Chap. 2. Accordingly, we use Eq. (2.53) to give the contribution of a single polymer chain to the rate of energy dissipation ... 

One-equation models relax the assumption that production and dissipation of turbulence are equal at all points of the flow field. Some effects of the upstream turbulence are incorporated by introducing a transport equation for the turbulence kinetic energy k (20) given by... 

Reoxidation occurs when the metallic iron in hot DRI reacts with oxygen in the air to form either Ee O or Ee202. The reaction continues as long as the DRI remains hot and sufficient oxygen is avadable. Because reoxidation reactions are exothermic and DRI is a good insulator, it is possible that once reoxidation begins inside a pde, the DRI temperature increases and accelerates the reoxidation rate. Although the inner core of the pde may reach temperatures up to the fusion point of iron, the maximum temperature of the outer parts of the pde will be much lower because of heat dissipation. 

Allowing DRI to become wet does not necessatily cause it to overheat. When large pdes of DRI are wetted with rain, the corrosion reactions are limited to the outer surface area of the pde and the resultant heat from the corrosion reactions is dissipated into the atmosphere. However, if water penetrates into the pde from the bottom, or if wet DRI is covered with dry DRI, the heat from corrosion reactions can budd up inside the pde to the point where rapid reoxidation begins. Corrosion occurs significantly faster with salt water than with fresh water. DRI saturated with water can cause steam explosions if it is batch charged into an electric arc furnace. 

Plastic film Melting point, °C Moisture absorption, % Tensile strength, MPa " Ultimate elongation, % Coefficient of thermal expansion, 10-%K Dissipation factor at 1 kH2 Dielectric constant at 1 kHz Dielectric strength, MV/m Cost factor... 

For both the tongue and Elmendorf test methods, it is important to observe the behavior of the specimen as the tear is propagated. In cases where the yams in the test direction are much stronger than the perpendicular yams, it is sometimes difficult or impossible to propagate the tear in the desired direction. In this case, a crosswise tear results. Tear resistance is primarily a function of fabric constmction. Loose, open weaves such as cheesecloth tend to resist tear, whereas tight weaves tend to tear easily. In the open weave, the concentrated force field at the point of tear is dissipated by the compliance of the fabric stmcture to accommodate the stress field, thereby distributing the force over a greater number of yams. 

Elastic Behavior. Elastic deformation is defined as the reversible deformation that occurs when a load is appHed. Most ceramics deform in a linear elastic fashion, ie, the amount of reversible deformation is a linear function of the appHed stress up to a certain stress level. If the appHed stress is increased any further the ceramic fractures catastrophically. This is in contrast to most metals which initially deform elastically and then begin to deform plastically. Plastic deformation allows stresses to be dissipated rather than building to the point where bonds break irreversibly. 

Power dissipation can lead to temperature increases of up to 40°C in the mass. Note that evaporation of liquid as a result of this increase needs to be accounted for in determining liquid requirements for granulation. Liquid should be added through an atomizing nozzle to aid uniform hquid distribution in many cases. In addition, power intensity (kW/kg) has been used with some success to judge granulation end point and for scale-up, primarily due to its relationship to granule deformation [Holm loc. cit.]. Swept volume ratio is a preliminary estimate of expected power intensity. 

In realistic systems, the separation of the modes according to their frequencies and subsequent reduction to one dimension is often impossible with the above-described methods. In this case an accurate multidimensional analysis is needed. Another case in which a multidimensional study is required and which obviously cannot be accounted for within the dissipative tunneling model is that of complex PES with several saddle points and therefore with several MEPs and tunneling paths. 

Most plastics materials may be considered as electrical insulators, i.e., they are able to withstand a potential difference between different points of a given piece of material with the passage of only a small electric current and a low dissipation energy. When assessing a potential insulating material, information on the following properties will be required ... 

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