Thermal stability of normal incidence multilayer mirrors for x-ray wavelength near carbon K-edge

Bugaev, E. A.; Fedorenko, A. I.; Кондратенко, В. В.; Zubarev, E. N.

doi:10.1117/12.200278

Cited by 3 publications

(2 citation statements)

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“…[36] following (2.13) cannot be applied for the SMM. Thus, the exponent inequalities (29) and (30) have to be modified for the SMM. Using results of Table 4., one finds the following scaling relations…”

Section: The Critical Indices and Scaling Relations Of The Smmmentioning

confidence: 99%

Exactly solvable models: The road towards a rigorous treatment of phase transitions in finite systems

Bugaev

2007

Phys. Part. Nuclei

108

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Abstract. We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the LaplaceFourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed. There is always a sufficient amount of facts. Imagination is what we lack.D. I. Blokhintsev I. THEORETICAL DESCRIPTION OF PHASE TRANSITIONS IN FINITE SYSTEMSA rigorous theory of critical phenomena in finite systems was not built up to now. However, the experimental studies of phase transitions (PTs) in some systems demand the formulation of such a theory. In particular, the investigations of the nuclear liquid-gas PT [1, 2, 3] require the development of theoretical approaches which would allow us to study the critical phenomena without going into the thermodynamic limit V → ∞ (V is the volume of the system) because such a limit does not exist due the long range Coulomb interaction. Therefore, there is a great need in the theoretical approaches which may shed light on the "internal mechanism" of how the PTs happen in finite systems. The general situation in the theory of critical phenomena for finite (small) systems is not very optimistic at the moment because theoretical progress in this field has been slow. It is well known that the mathematical theory of phase transitions was worked out by T. D. Lee and C. N. Yang [4]. Unfortunately, there is no direct generic relation between the physical observables and zeros of the grand canonical partition in a complex fugacity plane. Therefore, we know very well what are the gaseous phase and liquid at infinite volumes: mixture of fragments of all sizes and ocean, respectively. This is known both for pure phases and for their mixture, but, despite some limited success [5], this general approach is not useful for the specific problems of critical phenomena in finite systems (see Sect. VIII below).The tremendous complexity of critical phenomena in finite systems prevented their systematic and rigorous theoretical study. For instance, even the best formulation of the statistical mechanics and thermodynamics of finite systems by Hill [6] is not rigorous while discussing PTs...

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Section: The Critical Indices and Scaling Relations Of The Smmmentioning

confidence: 99%

Exactly solvable models: The road towards a rigorous treatment of phase transitions in finite systems

Bugaev

2007

Phys. Part. Nuclei

108

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show abstract

“…More recently, light nuclei production in relativistic heavy-ion collisions have further been used to search for the possible critical point [10][11][12][13] in the phase diagram of strongly interacting quark matter [14][15][16][17]. However, how and when these light nuclei are produced during relativistic heavy-ion collisions are still under debate because of their small binding energies and finite sizes [18][19][20][21][22][23][24][25][26]. On the one hand, they are assumed to be produced at hadronization of the QGP created in these collisions as in the statistical model for particle production [27,28].…”

Section: Introductionmentioning

confidence: 99%

Suppression of light nuclei production in collisions of small systems at the Large Hadron Collider

Sun

Dönigus

2019

Physics Letters B

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Computer simulation of damage to CrB/sub 2/-C multilayer mirror in double-pass experiment with Ta laser

Balakireva

Кожевников

1995

IEEE J. Select. Topics Quantum Electron.

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Thermal stability of normal incidence multilayer mirrors for x-ray wavelength near carbon K-edge

Cited by 3 publications

References 0 publications

Exactly solvable models: The road towards a rigorous treatment of phase transitions in finite systems

Exactly solvable models: The road towards a rigorous treatment of phase transitions in finite systems

Suppression of light nuclei production in collisions of small systems at the Large Hadron Collider

Computer simulation of damage to CrB/sub 2/-C multilayer mirror in double-pass experiment with Ta laser

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