Pulled front

U. Ebert and W. van Saarloos. Front propagation into unstable states Universal algebraic convergence towards uniformly translating pulled fronts. Physica D, 146 1-99, 2000. 

It equals the minimum velocity obtained by linearizing around the unstable state, the linear velocity. In this case the front dynamics is determined by the p x, t) 0 region. The front is called a pulled front, since it is pulled by its leading edge. The lower and upper bounds do not coincide for convex kinetic terms, and the front velocity is larger than the linear velocity. In this case, the nonlinear part of the kinetic term plays an important role in determining the value of the front velocity the front dynamics is pushed by its interior part. 

The fact that an infinity of front velocities occurs for pulled fronts gives rise to the problem of velocity selection. In this section we present two methods to tackle this problem. The first method employs the Hamilton-Jacobi theory to analyze the dynamics of the front position. It is equivalent to the marginal stability analysis (MSA) [448] and applies only to pulled fronts propagating into unstable states. However, in contrast to the MSA method, the Hamilton-Jacobi approach can also deal with pulled fronts propagating in heterogeneous media, see Chap. 6. The second method is a variational principle that works both for pulled and pushed fronts propagating into unstable states as well as for those propagating into metastable states. This principle can deal with the problem of velocity selection, if it is possible to find the proper trial function. Otherwise, it provides only lower and upper bounds for the front velocity. 

The sensitivity of fronts to the dynamics of small perturbations about the unstable or metastable states has been studied by Brunet and Derrida [61] for pulled fronts and Kessler et al. [227] for pulled and pushed fronts. The mean-field description of reacting and diffusing systems ceases to be valid for low values of the particle density p, values that correspond to less than one particle. This fact can be incorporated into the RD equation by introducing a cutoff for the reaction term. Such a cutoff strongly affects the front velocity. Throughout this section we consider for simplicity that space and time have been rescaled such that D = r =. ... 

Singular perturbation analysis was employed to study the velocity of pulled fronts, and it was shown that the solvability integrals diverge [103, 104, 448]. Therefore we will use this method only for non-KPP kinetics. We assume 5 = 0(e), weak heterogeneities, i.e., S = as in (6.51) with a = 0(1). Equation (6.51), together with the corresponding boundary conditions, becomes... 

Although a leaf blower is probably way too strong it may still be adequate at its lowest setting. To insure that a correct airflow is being pulled the chemist holds a lit cigarette about a foot in front of the hood s opening and looks to see If the smoke trail is being pulled into the hood. If so, then the hood works just fine. 

When the MWD systems are battery powered and have a downhole recording capability or use an electromagnetic telemetry, logging measurements can be repeated each time the bit is pulled out or run into the borehole. This new capability provides a way to map the progression of the filtrate front in the permeable formations. 

A spearhead or breakdown fluid followed by the cement slurry is circulated downhole with the packer by-pass open. This is done to avoid the squeezing of damaging fluids ahead of the slurry. A small amount of back pressure must be applied on the annulus to prevent the slurry fall caused by U tubing. If no tail pipe has been run, the packer by-pass must be closed 2 or 3 bbl before the slurry reaches the packer. If the cement is to be spotted in front of the perforations, with the packer unset, circulation is stopped as soon as the cement covers the desired zone, the tail pipe pulled out of the cement slurry and the packer set at the desired depth. The depth at which the packer is set must be carefully decided. 

Different tests are used on prototypes. As an example industry has a test where a load may be double that of a heavy person. Its two rear legs are positioned in front of an anchored board. The top of the chair has a rope or chain extending backwards to an oscillating device. The top of the chair will be pulled back to the point of almost failing backward and then released. The loaded chair will bounce on its two front legs. This cycle is repeated thousands of times. The industry test has requirements so if the chair is to be used in commercial environment its number of cycles will be many more than a noncommercial chair. 

Of course, he said, as he pulled up in front of the station and tugged on the hand brake. Then we got out and he lifted my suitcases from the backseat for me. Well, Una my dear, have a good term and we ll see you at Easter. ... 

Arriving for his first day at the old tobacco warehouse that housed Kettering s firm, Dayton Engineering Laboratories Company, Midgley recalled, I was trying to open the door that looked like the front door of the building, but which was locked. As I strained and pulled at it, a rather lanky individual called out to me, Hey, bud, the architects just stuck that door on to look right to fool people. You get in on the side. Follow me. ... 

From the initial state, chains which are close to the growth front are pulled in and rapidly crystallized, adding one layer to it. Chains which are far from the attractive influence of the growth front undergo homogeneous nucleation. 

Liquid seal drums Emergency vent streams are usually passed through a liquid seal, commonly water, before going to the flare stack. The liquid seal drum is usually located downstream of the knockout drum, and some vendors designs include them in the base of the flare stack. A liquid seal drum is used to maintain a positive pressure in the vent header system and upstream system. It also reduces the possibility of flame flashbacks, caused when air is inadvertently introduced into the flare system and the flame front pulls down into the stack it also acts as a mechanical damper on any explosive shock wave in the flare stack. Figure 23-58 is a schematic of a typical flare stack liquid seal drum, designed per API RP 521 criteria. 

To obtain the maximum benefits from the air, we need to breathe from the diaphragm, a muscle situated below the rib cage in the abdominal muscles. Remember, you do not have to pull in the breath atmospheric pressure will take care of that. Simply push out your diaphragm. Your rib cage will expand and air will rush into your lungs. Please do not make the mistake of trying any forcible expansion of the chest. This can cause damage to fine blood vessels in the chest. Let the muscles below your ribs do most of the work. If you do this properly, you will feel an expansion at the small of your back and at your sides, as well as in the front of your body. Always try to ensure that you commence any cycle... 

---