The Experts below are selected from a list of 285 Experts worldwide ranked by ideXlab platform
Giulio Biroli - One of the best experts on this subject based on the ideXlab platform.
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real space Renormalization Group Theory of disordered models of glasses
Proceedings of the National Academy of Sciences of the United States of America, 2017Co-Authors: Maria Chiara Angelini, Giulio BiroliAbstract:We develop a real space Renormalization Group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition Theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their Renormalization Group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition.
Ye Zhou - One of the best experts on this subject based on the ideXlab platform.
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Renormalization Group Theory for fluid and plasma turbulence
Physics Reports, 2010Co-Authors: Ye ZhouAbstract:Abstract For the last several decades, Renormalization Group (RG, or RNG) methods have been applied to a wide variety of problems of turbulence in hydrodynamics and plasma physics. A comprehensive review of this work will be presented, covering RG methods in hydrodynamic turbulence and in turbulent systems with coupled fluctuating fields like magnetohydrodynamic (MHD) turbulence. This review will attempt to specifically consider several questions about RG: (1) Does RG provide an improvement over previous analytical theories like the direct interaction approximation, or is RG a useful simplification of those theories? (2) How are nonlocal, or ‘sweeping’ effects treated in RG formalisms, or are they ignored entirely? (3) Can RG theories treat both local and nonlocal interactions in turbulence?
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Classical closure Theory and Lam's interpretation of epsilon -Renormalization Group Theory.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 1995Co-Authors: Ye ZhouAbstract:It is shown that Lam's formulation of Renormalization Group Theory [Phys. Fluids A 4, 1007 (1992)] is essentially the physical space version of the spectral classical closure Theory [Leslie and Quarini, J. Fluid Mech. 91, 65 (1979)].
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Development of a turbulence model based on recursion Renormalization Group Theory.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 1994Co-Authors: Ye Zhou, George Vahala, S. ThangamAbstract:An anisotropic turbulence model for the local interaction part of the Reynolds stresses is developed using the recursion Renormalization Group Theory (r-RNG)---an interaction contribution that has been omitted in all previous Reynolds stress RNG calculations. The local interactions arise from the nonzero wave number range, 0k${\mathit{k}}_{\mathit{c}}$, where ${\mathit{k}}_{\mathit{c}}$ is the wave number separating the subgrid from resolvable scales while the nonlocal interactions arise in the k\ensuremath{\rightarrow}0 limit. From \ensuremath{\epsilon}-RNG, which can only treat nonlocal interactions, it has been shown that the nonlocal contributions to the Reynolds stress give rise to terms that are quadratic in the mean strain rate. Based on comparisons of nonlocal contributions to the eddy viscosity and Prandtl number from r-RNG and \ensuremath{\epsilon}-RNG theories (\ensuremath{\epsilon} is a small parameter), it is assumed that the nonlocal contribution to the Reynolds stress will also be very similar. It is shown here, by r-RNG, that the local interaction effects give rise to significant higher-order dispersive effects. The importance of these new terms for separated flows is investigated by considering turbulent flow past a backward facing step. On incorporating this r-RNG model for the Reynolds stress into the conventional transport models for turbulent kinetic energy and dissipation, it is found that very good predictions for the turbulent separated flow past a backward facing step are obtained. The r-RNG model performance is also compared with that of the standard K-\ensuremath{\varepsilon} model (K is the kinetic energy of the turbulence and \ensuremath{\varepsilon} is the turbulence dissipation), the \ensuremath{\epsilon}-RNG model, and other two-equation models for this back step problem to demonstrate the importance of the local interactions.
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Recursive Renormalization Group Theory based subgrid modeling
1991Co-Authors: Ye ZhouAbstract:Advancing the knowledge and understanding of turbulence Theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.
Takashi Yanagisawa - One of the best experts on this subject based on the ideXlab platform.
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Renormalization Group Theory of generalized multi-vertex sine-Gordon model
Progress of Theoretical and Experimental Physics, 2021Co-Authors: Takashi YanagisawaAbstract:Abstract We investigate the Renormalization Group Theory of the generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson Renormalization Group method. The vertex interaction is given by $\cos(k_j\cdot \phi)$, where $k_j$ ($j=1,2,\ldots,M$) are momentum vectors and $\phi$ is an $N$-component scalar field. The beta functions are calculated for the sine-Gordon model with multiple cosine interactions. The second-order correction in the Renormalization procedure is given by the two-point scattering amplitude for tachyon scattering. We show that new vertex interaction with the momentum vector $k_{\ell}$ is generated from two vertex interactions with vectors $k_i$ and $k_j$ when $k_i$ and $k_j$ meet the condition $k_{\ell}=k_i\pm k_j$, called the triangle condition. A further condition $k_i\cdot k_j=\pm 1/2$ is required within the dimensional regularization method. The Renormalization Group equations form a set of closed equations when $\{k_j\}$ form an equilateral triangle for $N=2$ or a regular tetrahedron for $N=3$. The Wilsonian Renormalization Group method gives qualitatively the same result for beta functions.
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Renormalization Group Theory of generalized multi-vertex sine-Gordon model
arXiv: High Energy Physics - Theory, 2021Co-Authors: Takashi YanagisawaAbstract:We investigate the Renormalization Group Theory of generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson Renormalization Group method. The vertex interaction is given by $\cos(k_j\cdot \phi)$ where $k_j$ ($j=1,2,\cdots,M$) are momentum vectors and $\phi$ is an $N$-component scalar field. The beta functions are calculated for the sine-Gordon model with multi cosine interactions. The second-order correction in the Renormalization procedure is given by the two-point scattering amplitude for tachyon scattering. We show that new vertex interaction with momentum vector $k_{\ell}$ is generated from two vertex interactions with vectors $k_i$ and $k_j$ when $k_i$ and $k_j$ meet the condition $k_{\ell}=k_i\pm k_j$ called the triangle condition. Further condition $k_i\cdot k_j=\pm 1/2$ is required within the dimensional regularization method. The Renormalization Group equations form a set of closed equations when $\{k_j\}$ form an equilateral triangle for $N=2$ or a regular tetrahedron for $N=3$. The Wilsonian Renormalization Group method gives qualitatively the same result for beta functions.
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Dimensional Regularization Approach to the Renormalization Group Theory of the Generalized Sine-Gordon Model
Advances in Mathematical Physics, 2018Co-Authors: Takashi YanagisawaAbstract:We present the dimensional regularization approach to the Renormalization Group Theory of the generalized sine-Gordon model. The generalized sine-Gordon model means the sine-Gordon model with high frequency cosine modes. We derive Renormalization Group equations for the generalized sine-Gordon model by regularizing the divergence based on the dimensional method. We discuss the scaling property of Renormalization Group equations. The generalized model would present a new class of scaling property.
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Renormalization Group Theory of Effective Field Theory Models in Low Dimensions
Recent Studies in Perturbation Theory, 2017Co-Authors: Takashi YanagisawaAbstract:This is a lecture note on the Renormalization Group Theory for field Theory models based on the dimensional regularization method. We discuss the Renormalization Group approach to fundamental field theoretic models in low dimensions. We consider the models that are universal and frequently appear in physics, both in high-energy physics and condensed-matter physics. They are the non-linear sigma model, the $\phi^4$ model and the sine-Gordon model. We use the dimensional regularization method to regularize the divergence and derive the Renormalization Group equations called the beta functions. The dimensional method is described in detail.
Maria Chiara Angelini - One of the best experts on this subject based on the ideXlab platform.
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real space Renormalization Group Theory of disordered models of glasses
Proceedings of the National Academy of Sciences of the United States of America, 2017Co-Authors: Maria Chiara Angelini, Giulio BiroliAbstract:We develop a real space Renormalization Group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition Theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their Renormalization Group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition.
Quan Liu - One of the best experts on this subject based on the ideXlab platform.
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probing the symmetries of the dirac hamiltonian with axially deformed scalar and vector potentials by similarity Renormalization Group
Physical Review Letters, 2014Co-Authors: Jianyou Guo, Shouwan Chen, Zhongming Niu, Quan LiuAbstract:Symmetry is an important and basic topic in physics. The similarity Renormalization Group Theory provides a novel view to study the symmetries hidden in the Dirac Hamiltonian, especially for the deformed system. Based on the similarity Renormalization Group Theory, the contributions from the nonrelativistic term, the spin-orbit term, the dynamical term, the relativistic modification of kinetic energy, and the Darwin term are self-consistently extracted from a general Dirac Hamiltonian and, hence, we get an accurate description for their dependence on the deformation. Taking an axially deformed nucleus as an example, we find that the self-consistent description of the nonrelativistic term, spin-orbit term, and dynamical term is crucial for understanding the relativistic symmetries and their breaking in a deformed nuclear system.
