Collapsed phases

If tire mean Aq is positive tlien tire majority of tire residues are hydrophilic. A description of tire collapsed phase of tire chain requires introducing tliree- and and four-body interaction tenns. Thus, tire total Hamiltonian is... 

The random-bond heteropolymer is described by a Hamiltonian similar to (C2.5.A3) except that the short-range two-body tenn v.j is taken to be random with a Gaussian distribution. In this case a tliree-body tenn with a positive value of cu is needed to describe the collapsed phase. The Hamiltonian is... 

In the collapse phase the monomer density p = N/R is constant (for large N). Thus, the only confonnation dependent tenn in (C2.5.A1) comes from the random two-body tenn. Because this tenn is a linear combination of Gaussian variables we expect that its distribution is also Gaussian and, hence, can be specified by the two moments. Let us calculate the correlation i,) / between the energies and E2 of two confonnations rj ]and ry jof the chain in the collapsed state. The mean square of E is... 

Intensity of collapse, rate of the reaction, threshold/ nucleation, almost all physical properties Gas content, nucleation, collapse phase... 

In this simulation, the initial collapse phase was accompanied by partial formation of the native helices and reduction of hydrophobic surface in an apparent simple... 

Murayama, H. and Yoshikawa, K. (1999) Thermodynamics of the collapsing phase transition in a single duplex DNA molecule. J. Phys. Chem. B., 103, 10517-10523. 

During this initial collapse phase the rotational degrees of freedom of H2 are not excited (A /Xc = 512 K for the J = 2—0 transition). If the temperature approaches 100K the ratio y = cp/cv of specific heats changes from y = 5/3 (rotation of H2 not excited), to y =7/5 (rotation excited). The critical y for a self-gravitating adiabatic gaseous sphere to be stable is y =4/3. The pressure in the central core then supports the matter against further collapse and the inflow steepens to a shock at the border of the opaque core. The first core has formed. 

The continued addition of matter increases the density and temperature of the core until H2 begins to dissociate. The dissociation consumes heat, which holds temperature approximately constant, i.e. the heat capacity becomes very high and y - 1. The stability condition y >4/3 becomes violated and a new collapse of the core ensues. The core collapses until all H2 is dissociated and the H finally becomes ionized. The temperature then increases again with further contraction and the second core is formed that approaches stellar density. The second collapse phase is short and lasts for a solar-type star of the order of 103 years. By this event a protostellar embryo is born, which continues to grow in mass by collecting the remaining material from its environment. 

Figure 2.10 Cylindrically symmetric hydrodynamical model of accretion flow with rotation during the early collapse phase, showing the inflow of matter in the meridional plane and the build-up of a flat rotating disk structure after about 1.05 free-fall times. Arrows indicate matter flow direction and velocity, gray lines indicate cuts of isodensity surfaces with meridional plane. Dark crosses outline locations of supersonic to subsonic transition of inflow velocity this corresponds to the position of the accretion shock. Matter falling along the polar axis and within the equatorial plane arrive within 1600 yr almost simultaneously, which results in an almost instantaneous formation of an extended initial accretion disk [new model calculation following the methods in Tscharnuter (1987), figure kindly contributed by W. M. Tscharnuter],...

Fig. 3.13. Time duration of the edge plasma collapse phase determined from the edge soft X-ray emission for a large range of JET Type I ELMy H-mode plasmas [27]...

Onset of collapse phase. 04.2.1.3 Outcome of collapse phase... 

Dissolved gas solubility Gas content, nucleation, collapse phase Low solubility... 

At TT > TTg the relaxation phenomena for insoluble monolayers are caused by the transformation of a homogeneous monolayer phase into a heterogeneous monolayer-collapse phase system. However, some differences exist between saturated-LMWE and unsaturated-LMWE monolayers (Eigure 14.6b). Relaxation phenomena in saturated-LMWE monolayer are controlled predominantly by the collapse mechanism because the surface pressure relaxes to TTg. Eor these systems the monolayer collapses by nucleation and growth of critical nuclei. Unsaturated-LMWE monolayers behave differently to saturated-LMWE monolayers. As the surface pressure relaxes from the collapse value, which is close to TTg, towards values lower than TTg at longer times, the collapse competes with a desorption mechanism (Patino and Nino, 1999). 

This article is organized essentially in the same sequence that a massive star burns successively higher atomic number elements in its core, until it collapses and explodes in a supernova. The introductory part discusses how the rates of thermonuclear reactions in (massive) stars are calculated, what the different classes of reactions are and how the stars (usually) manage to burn their fuels so slowly6. The middle part describes the nuclear physics during the collapse phase of the massive star. The last part describes a few typical examples of what can be learned by optical, IR and X-ray studies about nucleosynthesis and dynamics of explosion in supernovae and supernova remnants such as Cassiopeia A, SN 1987A etc. Only core-collapse supernovae are discussed in these lectures, those that arise from massive stars (e.g. stars more massive than 8Mq with typical solar metallicity at the time they start... 

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