Patched

The a priori information involved by this modified Beta law (5) does not consider the local correlation between pixels, however, the image f is mainly constituted from locally constant patches. Therefore, this a priori knowledge can be introduced by means of a piecewise continuous function, the weak membrane [2]. The energy related to this a priori model is ... 

An implicit edge process is involved in the regularization process where A acts as a scale parameter which gives a constraint on the size of the homogeneous patches and p. comes from ho = -y/ p/A where ho is the threshold above which a discontinuity is introduced. We propose, then to combine these two functionals to obtain a satisfactory solution ... 

The limiting compression (or maximum v value) is, theoretically, the one that places the film in equilibrium with the bulk material. Compression beyond this point should force film material into patches of bulk solid or liquid, but in practice one may sometimes compress past this point. Thus in the case of stearic acid, with slow compression collapse occurred at about 15 dyn/cm [81] that is, film material began to go over to a three-dimensional state. With faster rates of compression, the v-a isotherm could be followed up to 50 dyn/cm, or well into a metastable region. The mechanism of collapse may involve folding of the film into a bilayer (note Fig. IV-18). 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

Suppose that a composite surface consists of patches of fli = 20° and 62 = 70°. Compare Eqs. X-27 and X-28 by plotting versus/2 as calculated by each equation. 

C. Point versus Patch Site Energy Distributions... 

The Freundlich equation is defective as a model because of the physically unrealistic/((2) consequences of this are that Henry s law is not approached at low P, nor is a limiting adsorption reached at high P. These difficulties can be patched by supposing that... 

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

Perhaps the most fascinating detail is the surface reconstruction that occurs with CO adsorption (see Refs. 311 and 312 for more general discussions of chemisorption-induced reconstructions of metal surfaces). As shown in Fig. XVI-8, for example, the Pt(lOO) bare surface reconstructs itself to a hexagonal pattern, but on CO adsorption this reconstruction is lifted [306] CO adsorption on Pd( 110) reconstructs the surface to a missing-row pattern [309]. These reconstructions are reversible and as a result, oscillatory behavior can be observed. Returning to the Pt(lOO) case, as CO is adsorbed patches of the simple 1 x 1 structure (the structure of an undistorted (100) face) form. Oxygen adsorbs on any bare 1 x 1 spots, reacts with adjacent CO to remove it as CO2, and at a certain point, the surface reverts to toe hexagonal stmcture. The presumed sequence of events is shown in Fig. XVIII-28. 

Islands occur particularly with adsorbates that aggregate into two-dimensional assemblies on a substrate, leaving bare substrate patches exposed between these islands. Diffraction spots, especially fractional-order spots if the adsorbate fonns a superlattice within these islands, acquire a width that depends inversely on tire average island diameter. If the islands are systematically anisotropic in size, with a long dimension primarily in one surface direction, the diffraction spots are also anisotropic, with a small width in that direction. Knowing the island size and shape gives valuable infonnation regarding the mechanisms of phase transitions, which in turn pemiit one to leam about the adsorbate-adsorbate interactions. 

Figure B3.6.2. Local mterface position in a binary polymer blend. After averaging the interfacial profile over small lateral patches, the interface can be described by a single-valued function u r. (Monge representation). Thennal fluctuations of the local interface position are clearly visible. From Wemer et al [49].

The fixed plate is now a negative , for those patches on which most light fell are black. The process is reversed in printing to make the positive —the printing paper having a covering of silver chloride or bromide or a mixture of the two. This, in turn, is developed and fixed as was the plate or film. 

Fig. 2. Patches divide the simulation space into a regular grid of cubes, each larger than the nonbonded cutoff. Interactions between atoms belonging to neighboring patches are calculated by one of the patches which receives a positions message (p) and returns a force message (f). Shades of gray indicate processors to which patches are assigned.

NAMD was implemented in an object-oriented fashion (Fig. 3). Patches, the encapsulated communication subsystem, the molecular structure, and various output methods were objects. Every patch owned specialized objects... 

Fig. 3. NAMD 1 employs a modular, object-oriented design in which patches communicate via an encapsulated communication subsystem. Every patch owns an integrator and a complete set of force objects for bonded (BondForce), nonbonded (ElectForce), and full electrostatic (DPMTA) calculations.

Fig. 4. In NAMD 2 forces are calculated not by force objects owned by individual patches, but rather by independent compute objects which depend on one or more patches for atomic coordinates. As suggested by shading in this illustration, a compute object need not reside on the same node as the patches upon which it depends.

Fig. 5. Compute objects requiring off-node patches do not engage in off-node communication but rather interact with local proxy patches. When force evaluations are required the home patch sends positions messages (p) to its proxies and receives force messages (f) containing the results of off-node calculations. The proxy patch in this illustration exists on the same node as the compute object but represents the off-node home patch with which it communicates.

Moving responsibility for the force computation away from the patches required a move away from pure message-driven execution to dependency-driven execution in which patches control the data (atomic coordinates) needed for compute objects to execute. A compute object, upon creation, registers this dependency with those patches from which it needs data. The patch then triggers force calculation by notifying its dependent compute objects when the next timestep s data is available. Once a compute object has received notification from all of the patches it depends on, it is placed in a prioritized queue for eventual execution. 

Load balancing can then be achieved in NAMD 2 by moving compute objects and patches between nodes. But what if a compute object and a patch it depends on are on different nodes Compute objects individually communicating with off-node patches would generate a huge amount of redundant communication. Therefore, patches are represented on other nodes by proxy patches, which implement the same interface as home patches for dealing with compute objects and handling dependencies but receive coordinates from and... 

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