RG Method Research Articles

The standard block RG and DMRG for open systems

For physical models that can be described by a lattice, a coarse-graining transformation is defined according to the numerical Wilson renormgroup. We formulated a numerical RG method for open quantum systems. To create it, on the one hand, we used the information about how the Hamiltonian is transformed in the standard method defined for Hamiltonian systems and, on the other hand, the knowledge how the Hamiltonian enters the right part of the GKLS equation. After that we have shown exactly how the environment given by Lindblad operators can be inscribed into a well known alternative to the standard method – the DMRG. In the prospects using the methods of numerical renormgroup for open systems allow us to investigate the time behaviour of quantum entanglement. Using the DMRG example for the Ising model in the transverse field, we have demonstrated the behaviour of entanglement for a small iteration number.

Influences of different freezing and thawing methods on the physico-chemical, flavor, and sensory properties of durian puree (cv. Monthong)

Influences of air blast freezing (AF method), cryogenic freezing (CF method), and freezing by direct immersion in liquid nitrogen (LN method) and thawing by refrigerator (RG method) and microwave (MW method) on qualities of durian puree (cv. Monthong) were investigated. After the freezing process and frozen storage, all frozen samples greatly tended to change physico-chemical parameters; drip loss (7.94–97.98%) and a* (17.45–69.75%), flavor properties; aldehydes (1.35–136.99%) and alcohols (4.86–107.22%), and sensory scores; overall flavor (4.76–26.89%) and overall liking (4.48–22.19%) from zero months of storage. However, the lowest change in almost all parameters resulted from using the CF method. Furthermore, at zero months of frozen storage, the MW method changed some physico-chemical properties less than the RG method, but there were no differences in any parameters between both methods after 6 months. Moreover, during frozen storage the MW method developed a new volatile compound, namely 3-methylbutanal, which presented an off-flavor. Practical applications Determining the shelf life of fresh fruit and processed fruit has been much more important in research and development for providing the best quality for consumers as well as international fruit trade. However, some reports have studied preserving durian, no studies are available on the influence of freezing and thawing methods on physico-chemical, flavor, and sensory changes in durian puree (cv. Monthong). Therefore, in the current study, freezing methods (air blast freezing, cryogenic freezing, and freezing by direct immersion in liquid nitrogen) and thawing methods (refrigerator and microwave) were used to study their effects on the quality changes of durian puree after the freezing process and frozen storage. The results could provide best practice and guidance for the fruit industry.

Salient object detection method using random graph

In this paper, a bottom-up salient object detection method is proposed by modeling image as a random graph. The proposed method starts with portioning input image into superpixels and extracting color and spatial features for each superpixel. Then, a complete graph is constructed by employing superpixels as nodes. A high edge weight is assigned into a pair of superpixels if they have high similarity. Next, a random walk prior on nodes is assumed to generate the probability distribution on edges. On the other hand, a complete directed graph is created that each edge weight represents the probability for transmitting random walker from current node to next node. By considering a threshold and eliminating edges with higher probability than the threshold, a random graph is created to model input image. The inbound degree vector of a random graph is computed to determine the most salient nodes (regions). Finally, a propagation technique is used to form saliency map. Experimental results on two challenging datasets: MSRA10K and SED2 demonstrate the efficiency of the proposed unsupervised RG method in comparison with the state-of-the-art unsupervised methods.

The true methodology for rhamnolipid: Various solvents affect rhamnolipid characteristics

Rhamnolipid, among the most effective biosurfactants, is a glycolipid‐type biosurfactant primarily produced by Pseudomonas aeruginosa. In this study, rhamnolipid production was carried out using a strain of P. aeruginosa and it is aimed to compare rhamnolipid biopolymers obtained from various extraction methods using glycine (RG), hydrochloric acid (RH), diethyl ether (RD), ethyl acetate (RE). Comparison analyses were performed through NMR, FTIR techniques and viscosity, density measurements apart from determination of rhamnolipid yields. It can be concluded that rhamnolipid from diethyl ether for extraction is far from molecular structure to reference rhamnolipid molecule according to instrumental analyses performed. Besides, the yield of this rhamnolipid is much more than other rhamnolipids extracted through other methods but this is misleading because the value in there may be total sugar content apart from rhamnolipid. Therefore, RD extraction method can be said to be non‐selective process for rhamnolipid obtained. In RH method, some functional group peaks belonging to rhamnolipid were not observed. NMR analysis showed that some CH groups were not observed in the RG method. However, especially NMR and FTIR analyses showed that rhamnolipid obtained from RE method represented more accurate rhamnolipid based on reference molecule.Practical applications: This study showed that rhamnolipid production and its comparative analyses using various solvent extraction methods. Comparison analyses were carried out through NMR, FTIR techniques and viscosity, density measurements as well as determination of rhamnolipid yields. Different solvents affect seriously characteristics of rhamnolipid, which were defined in the previous literature reports. Especially, some methods are not selective ways for mentioning true biomolecule. To avoid misleading characterization information in the literature, these extraction methods were discussed through comparison methods such as NMR, FTIR analyses, and quantification measurements.Rhamnolipid biopolymers obtained from various extraction methods using glycine (RG), hydrochloric acid (RH), diethyl ether (RD), ethyl acetate (RE) are compared through NMR, FTIR techniques, and viscosity, density measurements. These analyses show that rhamnolipid obtained from RE method represents more accurate rhamnolipid based on reference molecule.

화학 플랜트에서의 비상발전기 용량선정 방안(PG3)에 관한 연구

PG and RG methods are widely known method for calculating the capacity of the emergency generator in construction electrical installation. PG and RG methods are mainly used as a saving a life, fire protection, fire fighting in construction. Because no long distance between the emergency generator and electric motor feeder, the relatively small motor power in construction electrical installation, the capacity of generator in PG and RG methods are little problem of voltage and reactive power of generator. However in many cases the application of the PG and RG method is difficult in the Chemical Plant because it is long distance between the generator and the motor Feeder and motor capacity is very large. Motor starting power factor is about 0.2 lagging power factor and motor starting current is about 6times during motor staring. Also Most of the staring current component is a reactive power component. therefore, it is many cases that lack of reactive power and excess of allowable voltage drop limit and After selection of emergency diesel generator, problems happen during motor starting. Therefore, to be selection of effective emergency generator, active generator power, reactive power and the required reactive power during large motor starting should be considered in chemical plant. It is also required of the verification process through simulation because hand calculation is very difficult considering study cases.

IR fixed points in [formula omitted] gauge theories

We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the SU(3) gauge theories with Nf fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cutoff, which we cannot remove in the conformal field theories in sharp contrast to the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for Nf=16,12,8 and Nf=7 and indeed identify the location of the IR fixed points in all cases.

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An analysis of the renormalization group method for asymptotic expansions with logarithmic switchback terms

The renormalization group method of Chen, Goldenfeld, and Oono offers a comprehensive approach to formally computing asymptotic expansions of the solutions to singular perturbation problems and multi-scale problems. In particular, the RG method applies to a broad array of problems customarily treated with disparate methods, such as the method of multiple scales, boundary layer theory, matched asymptotic expansions, Poincare-Lindstedt theory, the WKBJ method with and without turning points, the method of averaging, and others. For problems in which the expansions are in powers of the small parameter, it has been shown that the RG method leads to uniformly valid asymptotic expansions of the solutions. In addition, it has been shown that the RG condition constitutes an invariance condition, that the RG method is effectively a resummation technique, and that it is equivalent to normal form theory for certain broad classes of perturbed ordinary differential equations. However, there has not yet been an analysis of the validity of the RG method, i.e.,i> a demonstration that it leads to uniformly valid asymptotic expansions, for problems in which the expansions also involve logarithms of the small parameter as gauge functions. The aim of this article is to provide this justification of the RG method. In particular, we extend the approach developed in DeVille, et ali>. Physica D 237 no. 8, 1029 {-}1052] from the classes of autonomous and non-autonomous perturbations considered there to include the non-autonomous systems subject to singular perturbations for which the solutions involve logarithmic gauge functions. This framework is built upon the relationship between the RG method and normal form theory. We apply the RG method to three successively-more complex examples and also elucidate the common general features.

Renormalization group for quantum walks

We present a detailed introduction to the discrete-time quantum walk problem, in close analogy with the classical ordinary and persistent random walk. This approach facilitates a uniform application of the renormalization group that highlights similarities and differences between the classical and the quantum walk problem. Specifically, we discuss the renormalization group treatment for the mean-square displacement of a walker starting from a single site on the 1d-line for ordinary and persistent random walks and the quantum walk. We outline the significance of universality for quantum walks and the control this might provide for quantum algorithms. We use our RG method to verify that all 2-state quantum walks on the 1d-line are in the same universality class.

Holographic RG flow of the shear viscosity to entropy density ratio in strongly coupled anisotropic plasma

We study holographic RG flow of the shear viscosity tensor of anisotropic, strongly coupled N=4 super-Yang-Mills plasma by using its type IIB supergravity dual in anisotropic bulk spacetime. We find that the shear viscosity tensor has three independent components in the anisotropic bulk spacetime away from the boundary, and one of the components has a non-trivial RG flow while the other two have a trivial one. For the component of the shear viscosity tensor with non-trivial RG flow, we derive its RG flow equation, and solve the equation analytically to second order in the anisotropy parameter 'a'. We derive the RG equation using the equation of motion, holographic Wilsonian RG method, and Kubo's formula. All methods give the same result. Solving the equation, we find that the ratio of the component of the shear viscosity tensor to entropy density 'eta/s' flows from above '1/4pi' at the horizon (IR) to below '1/4pi' at the boundary (UV) where it violates the holographic shear viscosity (Kovtun-Son-Starinets) bound and where it agrees with the other longitudinal component.

Dochody realne pracowników sektora przedsiębiorstw i emerytów w 2010 r.

The author analyses a real income of enterprise employees and pensioners of the nonagricultural social security system as well as individual farmers. The monthly income dynamic as well as components (nominal income and prices) were studied by the rg method (simple geometric mean) as well as the r method (taking into account a sum of time series terms).

On the Renormalization Group Approach to Perturbation Theory for PDEs

We investigate the rigorous application of the renormalization group method to (singular) perturbation theory for nonlinear partial differential equations. As a paradigm, we consider the concrete example of the nonlinear Schrödinger equation with quadratic nonlinearity in three spatial dimensions. We obtain an approximate solution using the RG method together with an estimate of the difference between the true and approximate solutions. Our analysis applies to cases where (space–time) resonances are present.

Reply to “Comment on ‘Renormalization-group theory for the phase-field crystal equation’ ”

In a recent Comment [Y. Shiwa, Phys. Rev. E 79, 013601 (2009)], Shiwa points out that our multiple-scales analysis of the Van der Pol equation [Appendix of Phys. Rev. E 74, 011601 (2006)] contained an error, and thus there may be no ordering ambiguity for renormalization and differentiation operations, as we had proposed for the phase-field crystal equation and other conservation laws. The Van der Pol analysis was indeed incorrect, and while his Comment casts doubt over our treatment of the multiple-scales analysis of the phase-field crystal (PFC) equation, there is no substantial change to our renormalization (RG) group results or simulations of the PFC model. This example highlights the merits of the RG approach to singular perturbation problems: the RG method is more mechanical and requires less user-insight than traditional methods.

Statistics of the two self-avoiding random walks on the three-dimensional fractal lattices

Abstract We present results of the effects of interpenetration of two interacting self-avoiding walks that take place in a member of a three-dimensional Sierpinski Gasket (SG) fractal family. We focus our attention on finding number of point contacts between the two SAW paths, which turns out to be a set of power laws whose characteristics depend predominantly on the given interactions between SAW steps. To establish statistics of the defining model, we apply an exact Renormalization Group Method for the few members ( b = 2 , 3 and 4 ) of the SG fractal family, as well as a Monte Carlo RG method for 2 ⩽ b ⩽ 25 . The phase diagrams have been established and relevant values of the contact critical exponents, associated with the two-path mutual contacts, are determined.

Application of the renormalization-group method to the reduction of transport equations

We first give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and on the importance of the existence of invariant manifolds of the dynamics under consideration. We clarify that an essential point of the method is to convert the problem from solving differential equations to obtaining suitable initial (or boundary) conditions:The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. The RG method is applied to derive the Navier-Stokes equation from the Boltzmann equation, as an example of the reduction of dynamics. We work out to obtain the transport coefficients in terms of the one-body distribution function.

Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets

Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects (displacement field u, internal dimension d) pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energy T = 0) configurations, as well as thermal averages which, at any non-zero T as in the phenomenological droplet picture, are dominated by rare degeneracies between low lying minima. We show that this occurs through an essentially non-perturbative thermal boundary layer (TBL) in the (running) effective action Γ [ u] at T > 0 for which we find a consistent scaling ansatz to all orders. The TBL describes how temperature smoothes the singularities of the T = 0 theory and contains the physics of rare thermal excitations (droplets). The formal structure of this TBL, which involves all cumulants of the coarse grained disorder, is first explored around d = 4 using a one-loop Wilson RG. Next, a more systematic exact RG (ERG) method is employed, and first tested on d = 0 models where it can be pushed quite far. There we obtain precise relations between TBL quantities and droplet probabilities (those are constrained by exact identities which are then checked against recent exact results). Our analysis is then extended to higher d, where we illustrate how the TBL scaling remains consistent to all orders in the ERG and how droplet picture results can be retrieved. Since correlations are determined deep in the TBL (by derivatives of Γ [ u] at u = 0), it remains to be understood (in any d) how they can be retrieved (as u = 0 + limits in the non-analytic T = 0 effective action), i.e., how to recover a T = 0 critical theory. This formidable “matching problem” is solved in detail for d = 0, N = 1 by studying the (partial) TBL structure of higher cumulants when points are brought together. We thereby obtain the β-function at T = 0, all ambiguities removed, displayed here up to four loops. A discussion of the d > 4 case and an exact solution at large d are also provided.

Critical Hamiltonians with long range hopping

Critical states are studied by a real space RG in the problem with strong diagonal disorder and long range power law hopping. The RG flow of the distribution of coupling parameters is characterized by a family of non-trivial fix points. We consider the RG flow of the distribution of participation ratios of eigenstates. Scaling of participation ratios is sensitive to the nature of the RG fix point. For some fix points, scaling of participation ratios is characterized by a distribution of exponents, rather than by a single exponent. The RG method can be generalized to treat certain fermionic Hamiltonians with disorder and long range hopping. We derive the RG for a model of interacting two-level systems. Besides couplings, in this problem the RG includes the density of states. The density of states is renormalized so that it develops a singularity near zero energy.

Critical Hamiltonians with long range hopping

AbstractCritical states are studied by a real space RG in the problem with strong diagonal disorder and long range power law hopping. The RG ow of the distribution of coupling parameters is characterized by a family of non‐trivial fix points. We consider the RG flow of the distribution of participation ratios of eigenstates. Scaling of participation ratios is sensitive to the nature of the RG fix point. For some fix points, scaling of participation ratios is characterized by a distribution of exponents, rather than by a single exponent.The RG method can be generalized to treat certain fermionic Hamiltonians with disorder and long range hopping. We derive the RG for a model of interacting two‐level systems. Besides couplings, in this problem the RG includes the density of states. The density of states is renormalized so that it develops a singularity near zero energy.

Density Matrix Renormalization Group Approach to an Asymptotically Free Model with Bound States

We apply the DMRG method to the 2 dimensional delta function potential which is a simple quantum mechanical model with asymptotic freedom and formation of bound states. The system block and the environment block of the DMRG contain the low energy and high energy degrees of freedom, respectively. The ground state energy and the lowest excited states are obtained with very high accuracy. We compare the DMRG method with the Similarity RG method and propose its generalization to field theoretical models in high energy physics.

RATAN-600 and the early Universe

Abstract We discuss the status of the Russian-USA “the Big Trio” project, based on the steep spectra (SS) FRII RG method of the selection of old and distant galaxies. Some aspects of the integral efforts of high redshift radio galaxies (HZRG) groups and Cosmic Microwave Background (CMB) anisotropy project briefly discussed, and new generation “Sakcharov Oscillation” national project at RATAN-600 shortly mentioned.