Mixed state pattern

Potato starch exhibits different granular stmcture and composition, as opposed to cereal starches, which are responsible for the variation in functional behavior of these starches. Cereal starches exhibit the t5 ical A type X-ray crystalline pattern, whereas potato starch shows the B-form, andlegumesthe mixed state pattern C . The A, B, and C patterns are the different polymeric forms of starch that differ in the packing of amylopectin double helices. The structure of potato starch is discussed in more detail in Chapter 4. 

It is obvious, for example, that a rev( rsal all of the neuronal values for a given state, Si —Si, leaves the energy unchanged and therefore also represents a local minimum. There are also stable mixed states that are not equal to any of the stored patterns but are linear combinations of an odd number of those patterns [amit85a). For example, it is easy to show that any symmetric combination of three stored patterns is a stable state ... 

Beginning with Kraepelin s (1921) systematic classification of dysphoric mania, considerable attention has been paid to mixed states of bipolar disorder. Kraepelin s model was based on variable symptom patterns expressed in three areas, mood, thought, and motor activity. Once considered to be uncommon, current estimates suggest that the prevalence rate for dysphoric, or mixed mania, is approximately 30 percent (McElroy et al. 1992). Debate continues regarding the status of mixed mania as a distinct affective state versus a form, or stage, of typical mania. However, there is convincing evidence to support the opinion that mixed episodes can be more severe, chronic, and difficult to treat than pure manic or depressive episodes (Clothier,... 

The numerous forms of two-phase flow can be divided into certain basic types, between which transition and mixed states are possible. The basic types of flow pattern in upward two-phase flow in a vertical, unheated tube are shown in Fig. 4.44. 

The mixing-state of supported Rh and Sn was investigated by X-ray diffraction powder patters. TTie X-ray powder pattern of the catalysts was obtained by using Ni filtered Cu-Ka. 

Bromley et al. studied both the (dp) and (dn) reactions. The ground state stripping pattern might be fitted by = 0 and = 2 patterns superimposed. If this is so, and is not a complex angular distribution due to interference, it follows that the ground state spin of F is and is a mixed state. 

Fig. 12.4 Stationary patterns in the CIMA reaction in a CFUR. (a) and (b) hexagons, (c) stripes, (d) mixed state. The bar beside each picture represents 1 mm the reactor is 25 mm in diameter. Reprinted with permission from Macmillan Publishers Ltd Nature [337]. Copyright 1991...

In this section, we have used the rotational invariance to predict the form of the phase equations. Recently, a lot of effort has been devoted to the development of amplitude equations - or order parameter equations - in a rotationally invariant form [15, 85, 86]. According to Gunaratne [86], supplemental terms introduced in the equations to meet this constraint could account for the stabilization of otherwise unstable states, in particular rhombic patterns which have been observed both in experiments [87] and in numerical simulations [29]. This could also explain the stabilization of the mixed states of Equation (16), also observed in experiments [51] and simulations [30]. Nevertheless, alternative interpretations can be proposed in terms of finite size effects in the numerical simulations, and in terms of three-dimensional effects for the experiments. Mixed states observed in our laboratory more likely correspond to projections of two exactly superposed layers, the first one with striped symmetry, and the second one with hexagonal symmetry. More generally, one expects that the strong transverse gradients present in the experiments can produce an hybridization between otherwise flawless structures. 

The general theory of rhombic patterns recently developed by Gunaratne [13,47] has resolved some mysteries around our previous reports of a mixed state , which is now realized to be a type of rhombic patterns [46]. Our experimental results on rhombic pattern formation and selection are in good accord with the theory [13, 47]. Rhombic patterns should occur widely in other nonequilibrium systems, including surface tension driven convection, ferrofluids, Rayleigh-B nard convection, and driven capillary waves, but we know of no other laboratory studies of rhombic patterns. We hope that our work will stimulate a search for rhombic patterns in other systems. 

We previously described the pattern of Figure 6d as a mixed state . A re-examination of our data reveals that the patterns are rhombs with a characteristic angle of 58°. 

Analogous considerations apply to spatially distributed reacting media where diffusion is tire only mechanism for mixing chemical species. Under equilibrium conditions any inhomogeneity in tire system will be removed by diffusion and tire system will relax to a state where chemical concentrations are unifonn tliroughout tire medium. However, under non-equilibrium conditions chemical patterns can fonn. These patterns may be regular, stationary variations of high and low chemical concentrations in space or may take tire fonn of time-dependent stmctures where chemical concentrations vary in botli space and time witli complex or chaotic fonns. 

Conventional TNT-equivalency methods state a proportional relationship between the total quantity of flammable material released or present in the cloud (whether or not mixed within flammability limits) and an equivalent weight of TNT expressing the cloud s explosive power. The value of the proportionality factor—called TNT equivalency, yield factor, or efficiency factor—is directly deduced from damage patterns observed in a large number of major vapor cloud explosion incidents. Over the years, many authorities and companies have developed their own practices for estimating the quantity of flammable material in a cloud, as well as for prescribing values for equivalency, or yield factor. Hence, a survey of the literature reveals a variety of methods. 

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