Matter phases

Mn is the mass of the nucleon, jis Planck s constant divided by 2ti, m. is the mass of the electron. This expression omits some temis such as those involving relativistic interactions, but captures the essential features for most condensed matter phases. 

Another realistic approach is to constnict pseiidopotentials using density fiinctional tlieory. The implementation of the Kolm-Sham equations to condensed matter phases without the pseiidopotential approximation is not easy owing to the dramatic span in length scales of the wavefimction and the energy range of the eigenvalues. The pseiidopotential eliminates this problem by removing tlie core electrons from the problem and results in a much sunpler problem [27]. 

Since and depend only on die valence charge densities, they can be detennined once the valence pseudo- wavefiinctions are known. Because the pseudo-wavefiinctions are nodeless, the resulting pseudopotential is well defined despite the last temi in equation Al.3.78. Once the pseudopotential has been constructed from the atom, it can be transferred to the condensed matter system of interest. For example, the ionic pseudopotential defined by equation Al.3.78 from an atomistic calculation can be transferred to condensed matter phases without any significant loss of accuracy. 

Other methods for detennining the energy band structure include cellular methods. Green fiinction approaches and augmented plane waves [2, 3]. The choice of which method to use is often dictated by die particular system of interest. Details in applying these methods to condensed matter phases can be found elsewhere (see section B3.2). 

Abstract We discuss the high-density nuclear equation of state within the Brueckner-Hartree-Fock approach. Particular attention is paid to the effects of nucleonic three-body forces, the presence of hyperons, and the joining with an eventual quark matter phase. The resulting properties of neutron stars, in particular the mass-radius relation, are determined. It turns out that stars heavier than 1.3 solar masses contain necessarily quark matter. 

Figure f. Pressure as a function of //, for homogeneous neutral quark matter in the CFL phase (solid), 2SC (dashed), and the normal quark matter phase (dotted). Also shown is the pressure of the mixed phase solution (dash-dotted). 

From the above estimations we conclude that is it at least a good approximation to consider only homogeneous phases to describe the quark matter phase. In Fig. 4 we display the pressure as a function of fi for neutral homogeneous quark matter phases. We see that at small // the 2SC phase (dashed line) is favored whereas at large // we find a CFL phase (solid line). Normal quark matter (dotted line) turns out to be never favored. This will be our input for the description of the quark matter phase. Of course, in order to construct a compact star, we also have to take into account the possibility of a hadronic component in the equation of state (EOS). To this end, we take a given hadronic EOS and construct a phase transition to quark matter from the requirement of maximal pressure. This is shown in the left panel of Fig. 5 for an example hadronic EOS [53], At the transition point to the quark-matter phase we directly enter the CFL phase and normal or 2SC quark matter is completely irrelevant in this... 

Figure 6. Mass-radius relation of different compact star configurations. The left panels correspond to calculations with parameter set RKH for the quark matter phase and the right panels to parameter set HK, respectively. From the upper panel downwards the hadronic phase is described by a BHF calculation without hyperons [55], a relativistic mean field calculation [57] and a chiral SU(3) model [53].

We can find the magnetic field in the hadronic matter phase from the solution (51) by taking into account that proton vortices in this phase generate a homogeneous mean magnetic field with amplitude B and direction parallel to the axis of rotation of the star [22], For the components of the magnetic field Bp in the hadronic phase (for a [Pg.273]

As a first step in this direction we will discuss here the two flavor color superconducting (2SC) quark matter phase which occurs at lower baryon densities than the color-flavor-locking (CFL) one, see [18, 32], Studies of three-flavor quark models have revealed a very rich phase structure (see [32] and references therein). However, for applications to compact stars the omission of the strange quark flavor within the class of nonlocal chiral quark models considered here may be justified by the fact that central chemical potentials in stable star configurations do barely reach the threshold value at which the mass gap for strange quarks breaks down and they appear in the system [20], Therefore we will not discuss here first applications to calculate compact star configurations with color superconducting quark matter phases that have employed non-dynamical quark models... 

We compare results in the chiral limit (mo = 0) with those for finite current quark mass mo = 2.41 MeV and observe that the diquark gap is not sensitive to the presence of the current quark mass, which holds for all form-factors However, the choice of the form-factor influences the critical values of the phase transition as displayed in the quark matter phase diagram (/j,q — T plane) of Fig. 2, see also Fig. 1. A softer form-factor in momentum space gives lower critical values for Tc and at the borders of chiral symmetry restoration and diquark condensation. 

At nonzero temperatures the mass gap decreases as a function of the chemical potential already in the phase with broken chiral symmetry. Hence the model here gives unphysical low-density excitations of quasi-free quarks. A systematic improvement of this situation should be obtained by including the phase transition construction to hadronic matter. However, in the present work we circumvent the confinement problem by considering the quark matter phase only for densities above the nuclear saturation density no, i.e. ub > 0.5 no. 

In order to answer the question whether strange quark matter phases should be expected in the neutron star interiors, we consider here a three-flavor generalization of a NCQM with the action... 

The EoS HHJ - INCQM with 2SC quark matter phase has a type of hard -soft - hard EoS [40], Therefore critical line is mainly orthogonal to the mass axis and the expected population clustering seems to be not frequency but mass clustering. As already reported by M.C. Miller at this conference, there is observational evidence that the population of LMXB s is mainly homogeneous. 

Nicotine aa> values in tobacco smoke particulate matter can be estimated based on nicotine volatility from the smoke particulate matter phase, as controlled by the gas/partitioning constant Kp (Pankow et al. 1997) ... 

Here Cp (ng 4g ) is the total (protonated -I- free - base) nicotine concentration in the particulate matter phase and Cg (ngm ) is the equilibrium concentration of nicotine s free-base form in the gas phase. Only the free-base form has appreciable volatility and would be present in the gas phase, so only the free-base form of nicotine can transfer between the particle and gas phases. The concentration of free-base nicotine is afbCp. An underlying partitioning constant for free-base nicotine is given by (Pankow et al. 1997 Pankow 2001) ... 

Property parameters. The physical property parameters include state of matter, phase equilibrium, thermal, mechanical, optical, and electromagnetic properties. The chemical property parameters include preparation, reactivity, reactants and products, kinetics, flash point, and explosion limit. The biological property parameters include toxicity, physiological and pharmaceutical effects, nutrition value, odor, and taste. 

MWom Molecular weight of the organic matter phase... 

Great Lake suspended matter, phase partitioning-reversed phase chromatography by Sep Pak, Eadie... 

The stepwise dissolution of the mineral matter phase was accomplished in a series of acid and ether extractions which are summarized in flow-chart form in Figure 1. All traces of physi-sorbed water were removed by vacuum drying (P=400 torr) at 85°C with continuous purging of nitrogen gas for approximately 24 h. Bitumen was then separated using the Soxhlet extraction procedure based on a 7 3 mixture of benzene methanol. 

The reduction of mineral matter by physical separation procedures of the free mineral matter phase from the coal phase is directly related to the log of the mode of the particle size distribution of the raw coal. That relationship also appears to be insensitive to some of the common chemical additives that are introduced to enhance the rate of milling. 

Stillinger, F. H., and Weber, T. A., Computer simulation of local order in condensed matter phases of silicon. Phys. Rev. B 31,5262-5271 (1985). 

COMPETENCY 15.0 APPLY KNOWLEDGE OF THE KINETIC MOLECULAR THEORY TO THE STATES OF MATTER, PHASE CHANGES, AND THE GAS LAWS. 

Condensed matter phases and structures are commonly reached via symmetry breaking transitions. In such systems, when the continuous symmetry is broken, temporary domain-t5q)e patterns are formed. The domain structures eventually coarsen, and disappear in the long-time limit, leaving a uniform broken-symmetry state. This state possesses so-called long-range order (LRO), in which the spatially dependent order parameter correlation function does not decay to zero in the limit of large distances. 

As a method, TRXRD is still in its infancy. While it has already proven to be a powerful, information-dense structural and kinetic probe there is much room for improvement. In what follows I draw upon my own experience as to the limitations of the method and will address these at four levels facility, sample, instrumentation, and experimental design. The view held here is that deficits in the technique will be corrected more expeditiously if attention is drawn to them at an early stage. Alas, in some cases, a solution must await the development of new technologies. This exercise also serves to emphasize that TRXRD is not the panacea but rather another tool in an arsenal of physicochemical techniques with which to tackle critical issues in condensed matter phase science. 

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