Thorn and Seesselberg Reply

Thorn, Matthias; Seeßelberg, M.

doi:10.1103/physrevlett.75.3778

Cited by 10 publications

(17 citation statements)

References 7 publications

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“…In conclusion, in this work we have shown that numerical simulations of DLCA model in a box can account for the growth process of several experimental systems. On the other hand, our numerical calculation of S(q, t) during the DLCA process is an original investigation that extends previous numerical analysis of this growth process [1,16,17,20], leading to the theoretical explanation of additional interesting properties during the aggregation process and confirming some predictions made in some experimental studies. In particular the power law given in equation (7b) and the shape of our S(q, t) curves are experimentally observed.…”

Section: Discussionsupporting

confidence: 84%

“…Using small-angle scattering techniques it has been suggested that some of these systems [5,[7][8][9]11,12] grow like diffusion-limited clustercluster aggregation (DLCA) [13][14][15]. Numerically, the gelation process in DLCA has been investigated by analyzing the cluster size distribution and the mean cluster size, as a function of the time t using both the Smoluchowski equation [16] and the DLCA model in 2 dimensions [17]. On the other hand, recently [18,19] it has been shown that, when the volumic fraction c, or concentration, is greater than a characteristic gel concentration c g , DLCA model leads to a homogeneous gelling network of connected fractal clusters of mean size ξ.…”

Section: Introductionmentioning

confidence: 99%

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Sol-gel process simulation by cluster-cluster aggregation

Hasmy¹,

Jullien²

1995

Journal of Non-Crystalline Solids

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The pair-correlation function g(r, t) and its Fourier transform, the structure factor S(q, t), are computed during the gelation process of identical spherical particles using the diffusion-limited cluster-cluster aggregation model in abox. This numerical analysis shows that the time evolution of the characteristic cluster size ξ exhibits a crossover close to the gel time t g which depends on the volumic fraction c. In this model t g tends to infinity when the box size L tends to infinity. For systems of finite size, it is shown numerically that, when t < t g , the wave vector q m , at which S(q, t) has a maximum, decreases as S(q m , t) −1/D , where D is an apparent fractal dimension of clusters, as measured from the slope of S(q, t) . The time evolution of the mean number of particles per clustern is also investigated. Our numerical results are in qualitative agreement with small angle scattering experiments in several systems.

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Section: Discussionsupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Sol-gel process simulation by cluster-cluster aggregation

Hasmy¹,

Jullien²

1995

Journal of Non-Crystalline Solids

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“…Here we follow a similar strategy and replace the continuum equations (19) by a sequence of discretized approximations, such that the eigenvalues of the discretized problems eventually converge to the eigenvalues of (19). In the light-cone quantization, a simple discretized approximation is obtained by replacing the continuous momentum fractions x by a discrete set n/K, where n are odd positive integers, and the positive integer K is sent to infinity as the cut-off is removed [10,3]. Thus, the functions…”

Section: The Discretized Approximationmentioning

confidence: 99%

“…Therefore, this model seems to be the simplest setting where one can study some genuine QCD effects, such as the pair creation of partons. We will argue that the light-cone quantization supplemented with a regulator in the form of discretized longitudinal momenta [3,10] allows one to extract significant amount of physical information about the large-N theory.…”

Section: Introductionmentioning

confidence: 99%

(1+1)-dimensional large-NQCD coupled to adjoint fermions

1993

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We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group SU(N). Pair creation of partons (fermion quanta) is not suppressed in the large-N limit, where the glueball-like bound states become free. In this limit the spectrum is given by a linear light-cone Schrödinger equation, which we study numerically using the discretized light-cone quantization. We find a discrete spectrum of bound states, with the logarithm of the level density growing approximately linearly with the mass. The wave function of a typical excited state is a complicated mixture of components with different parton numbers. A few low-lying states, however, are surprisingly close to being eigenstates of the parton number, and their masses can be accurately calculated by truncated diagonalizations. 7/93⋆ On leave of absence from the Ruder Bošković Institute, Zagreb, Croatia

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“…To establish that the entropy does jump by an amount proportional to N 2 , [22,4], we need to look at the expression for F . Actually it is trivially proportional to N 2 always because of the presence of Newton's constant.…”

Section: Calculation Of the Deconfinement Temperaturementioning

confidence: 99%

THE HAGEDORN TRANSITION, DECONFINEMENT AND THE AdS/CFT CORRESPONDENCE

Rama

Sathiapalan

1998

Mod. Phys. Lett. A

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A connection between the Hagedorn transition in string theory and the deconfinement transition in (non-supersymmetric) Yang-Mills theory is made using the AdS/CFT correspondence. We modify the model of zero temperature QCD proposed by Witten by compactifying an additional space-time coordinate with supersymmetry breaking boundary conditions thus introducing a finite temperature in the boundary theory. There is a Hagedorn-like transition associated with winding modes around this coordinate, which signals a topology changing phase transition to a new AdS/Schwarzschild blackhole where this coordinate is the time coordinate. In the boundary gauge theory time like Wilson loops acquire an expectation value above this temperature. 2

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Thorn and Seesselberg Reply

Abstract: Thorn and Seesselberg Reply: In a recent Letter [1], we used a stochastic simulation method to investigate the

Cited by 10 publications

References 7 publications

Sol-gel process simulation by cluster-cluster aggregation

Sol-gel process simulation by cluster-cluster aggregation

(1+1)-dimensional large-NQCD coupled to adjoint fermions

THE HAGEDORN TRANSITION, DECONFINEMENT AND THE AdS/CFT CORRESPONDENCE

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