WorldWideScience

Sample records for renormalized drop diameter

  1. Evaluation of the nugget diameter in spot welded joints between two steel sheets by means of a potential drop technique

    International Nuclear Information System (INIS)

    Tohmyoh, Hironori; Ikarashi, Hidetomo; Matsui, Yoichi; Hasegawa, Yuta; Obara, Satoshi

    2015-01-01

    A potential drop technique which utilizes the electrical circuit used in resistance spot welding is reported. Spot welded samples comprising two steel sheets were inserted between the two Cu electrodes and a constant direct current was supplied between the electrodes. The potential drop between two points, one on each electrode, was determined by analysis for various values of nugget diameter and various values of the contact resistance between the Cu electrodes and the steel sheet sample. The nugget diameter of the spot welded joint could be quantitatively evaluated from the measured potential drop and the equation obtained from the analysis. (paper)

  2. Evaluation of the nugget diameter in spot welded joints between two steel sheets by means of a potential drop technique

    Science.gov (United States)

    Tohmyoh, Hironori; Ikarashi, Hidetomo; Matsui, Yoichi; Hasegawa, Yuta; Obara, Satoshi

    2015-08-01

    A potential drop technique which utilizes the electrical circuit used in resistance spot welding is reported. Spot welded samples comprising two steel sheets were inserted between the two Cu electrodes and a constant direct current was supplied between the electrodes. The potential drop between two points, one on each electrode, was determined by analysis for various values of nugget diameter and various values of the contact resistance between the Cu electrodes and the steel sheet sample. The nugget diameter of the spot welded joint could be quantitatively evaluated from the measured potential drop and the equation obtained from the analysis.

  3. An experimental study on two-phase pressure drop in small diameter horizontal, downward inclined and vertical tubes

    Directory of Open Access Journals (Sweden)

    Autee Arun

    2015-01-01

    Full Text Available An experimental study of two-phase pressure drop in small diameter tubes orientated horizontally, vertically and at two other downward inclinations of θ= 300 and θ = 600 is described in this paper. Acrylic transparent tubes of internal diameters 4.0, 6.0, and 8.0 mm with lengths of 400 mm were used as the test section. Air-water mixture was used as the working fluid. Two-phase pressure drop was measured and compared with the existing correlations. These correlations are commonly used for calculation of pressure drop in macro and mini-microchannels. It is observed that the existing correlations are inadequate in predicting the two-phase pressure drop in small diameter tubes. Based on the experimental data, a new correlation has been proposed for predicting the two-phase pressure drop. This correlation is developed by modification of Chisholm parameter C by incorporating different parameters. It was found that the proposed correlation predicted two-phase pressure drop at satisfactory level.

  4. Effect of airstream velocity on mean drop diameters of water sprays produced by pressure and air atomizing nozzles

    Science.gov (United States)

    Ingebo, R. D.

    1977-01-01

    A scanning radiometer was used to determine the effect of airstream velocity on the mean drop diameter of water sprays produced by pressure atomizing and air atomizing fuel nozzles used in previous combustion studies. Increasing airstream velocity from 23 to 53.4 meters per second reduced the Sauter mean diameter by approximately 50 percent with both types of fuel nozzles. The use of a sonic cup attached to the tip of an air assist nozzle reduced the Sauter mean diameter by approximately 40 percent. Test conditions included airstream velocities of 23 to 53.4 meters per second at 293 K and atmospheric pressure.

  5. Flow condensation pressure drop characteristics of R410A-oil mixture inside small diameter horizontal microfin tubes

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Xiangchao; Ding, Guoliang; Hu, Haitao; Zhu, Yu [Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai 200240 (China); Gao, Yifeng [International Copper Association Shanghai Office, Shanghai 200020 (China); Deng, Bin [Institute of Heat Transfer Technology, Golden Dragon Precise Copper Tube Group Inc., Shanghai 200135 (China)

    2010-11-15

    Flow condensation pressure drop characteristics of R410A-oil mixture inside small diameter (5.0 mm and 4.0 mm O.D.) horizontal microfin tubes were investigated experimentally covering nominal oil concentrations from 0% to 5%. The research results indicate that, comparing with the frictional pressure drop of pure R410A, the frictional pressure drop of R410A-oil mixture may decrease by maximum of 18% when the vapor quality is lower than 0.6, and increase by maximum of 13% when the vapor quality is higher than 0.6. A new frictional pressure drop correlation for R410A-oil mixture flow condensation inside microfin tubes is developed based on the refrigerant-oil mixture properties, and can agree with 94% of the experimental data within a deviation of -30% to +30%. (author)

  6. Sensitivity of C-Band Polarimetric Radar-Based Drop Size Distribution Measurements to Maximum Diameter Assumptions

    Science.gov (United States)

    Carey, Lawrence D.; Petersen, Walter A.

    2011-01-01

    The estimation of rain drop size distribution (DSD) parameters from polarimetric radar observations is accomplished by first establishing a relationship between differential reflectivity (Z(sub dr)) and the central tendency of the rain DSD such as the median volume diameter (D0). Since Z(sub dr) does not provide a direct measurement of DSD central tendency, the relationship is typically derived empirically from rain drop and radar scattering models (e.g., D0 = F[Z (sub dr)] ). Past studies have explored the general sensitivity of these models to temperature, radar wavelength, the drop shape vs. size relation, and DSD variability. Much progress has been made in recent years in measuring the drop shape and DSD variability using surface-based disdrometers, such as the 2D Video disdrometer (2DVD), and documenting their impact on polarimetric radar techniques. In addition to measuring drop shape, another advantage of the 2DVD over earlier impact type disdrometers is its ability to resolve drop diameters in excess of 5 mm. Despite this improvement, the sampling limitations of a disdrometer, including the 2DVD, make it very difficult to adequately measure the maximum drop diameter (D(sub max)) present in a typical radar resolution volume. As a result, D(sub max) must still be assumed in the drop and radar models from which D0 = F[Z(sub dr)] is derived. Since scattering resonance at C-band wavelengths begins to occur in drop diameters larger than about 5 mm, modeled C-band radar parameters, particularly Z(sub dr), can be sensitive to D(sub max) assumptions. In past C-band radar studies, a variety of D(sub max) assumptions have been made, including the actual disdrometer estimate of D(sub max) during a typical sampling period (e.g., 1-3 minutes), D(sub max) = C (where C is constant at values from 5 to 8 mm), and D(sub max) = M*D0 (where the constant multiple, M, is fixed at values ranging from 2.5 to 3.5). The overall objective of this NASA Global Precipitation Measurement

  7. Frictional pressure drop of steam-water two-phase flow in helical coils with small helix diameter of HTR-10

    International Nuclear Information System (INIS)

    Bi Qincheng; Chen Tingkuan; Luo Yushan; Zheng Jianxue

    1996-01-01

    Experiments of steam-water two-phase flow frictional pressure drop through five vertically and horizontally positioned helical coils were carried out in the high pressure steam water test loop of Xi'an Jiaotong University. Two kinds of tube with inner diameters of 10 mm and 12 mm were used to form the coils. The helix diameter was 115 mm with coil pitch 22.5 mm. The experimental conditions were: pressure p = 4-14 MPa, mass velocity G = 400-2000 kg/(m 2 ·s), and inner wall heat flux q = 0-750 kW/m 2 . Theoretical analysis with a semi-empirical correlation was made to predict the two-phase flow fictional pressure drop through these kinds of helical coils

  8. An experimental study on single phase convection heat transfer and pressure drop in two brazed plate heat exchangers with different chevron shapes and hydraulic diameters

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Man Bae; Park, Chang Yong [Seoul National University of Science and Technology, Seoul (Korea, Republic of)

    2017-05-15

    An experimental study on heat transfer and pressure drop characteristics was performed at single phase flow in two Brazed plate heat exchangers (BPHEs) with different geometries. The corrugation density of one of the BPHE (Type II) was two times as high as that of the other BPHE (Type I). The hydraulic diameter of the type II BPHE was 2.13 mm, which was 38 % smaller than that of the type I BPHE. Also, the cross section shape of the flow channels for the type II BPHE was different from that for conventional BPHEs due to the unusual corrugation patterns and brazing points. The experimental conditions for temperatures were varied from 4.6 °C to 49.1 °C, and for mass flow rates were changed from 0.07 kg/s to 1.24 kg/s. The measured results showed that pressure drop in the type II BPHE was about 110 % higher than that in the type I BPHE. Nu of the type II was higher than that of the type I BPHE and the enhancement became larger with the increase of Re at the ranges above 800. New correlations for fF and Nu were proposed by this study and their prediction accuracy could be improved by considering the surface enlargement factor in the correlations. The performance evaluation of the two BPHEs was performed by (j/f{sub F}1{sup /3}) which represented the ratio of heat transfer and pressure drop performance. Also, a new parameter, the capacity compactness of PHE, was proposed and it presented the PHE capacity per unit volume and unit log mean temperature difference. The comparison showed that the two BPHEs had similar values of the (j/f{sub F}1{sup /3}), whereas they had significantly different values of the capacity compactness. The capacity compactness of the type II BPHE was 1.5 times higher than that for the type I BPHE.

  9. An experimental study on single phase convection heat transfer and pressure drop in two brazed plate heat exchangers with different chevron shapes and hydraulic diameters

    International Nuclear Information System (INIS)

    Kim, Man Bae; Park, Chang Yong

    2017-01-01

    An experimental study on heat transfer and pressure drop characteristics was performed at single phase flow in two Brazed plate heat exchangers (BPHEs) with different geometries. The corrugation density of one of the BPHE (Type II) was two times as high as that of the other BPHE (Type I). The hydraulic diameter of the type II BPHE was 2.13 mm, which was 38 % smaller than that of the type I BPHE. Also, the cross section shape of the flow channels for the type II BPHE was different from that for conventional BPHEs due to the unusual corrugation patterns and brazing points. The experimental conditions for temperatures were varied from 4.6 °C to 49.1 °C, and for mass flow rates were changed from 0.07 kg/s to 1.24 kg/s. The measured results showed that pressure drop in the type II BPHE was about 110 % higher than that in the type I BPHE. Nu of the type II was higher than that of the type I BPHE and the enhancement became larger with the increase of Re at the ranges above 800. New correlations for fF and Nu were proposed by this study and their prediction accuracy could be improved by considering the surface enlargement factor in the correlations. The performance evaluation of the two BPHEs was performed by (j/f F 1 /3 ) which represented the ratio of heat transfer and pressure drop performance. Also, a new parameter, the capacity compactness of PHE, was proposed and it presented the PHE capacity per unit volume and unit log mean temperature difference. The comparison showed that the two BPHEs had similar values of the (j/f F 1 /3 ), whereas they had significantly different values of the capacity compactness. The capacity compactness of the type II BPHE was 1.5 times higher than that for the type I BPHE.

  10. Renormalized action improvements

    International Nuclear Information System (INIS)

    Zachos, C.

    1984-01-01

    Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references

  11. Convective heat transfer and pressure drop of aqua based TiO2 nanofluids at different diameters of nanoparticles: Data analysis and modeling with artificial neural network

    Science.gov (United States)

    Hemmat Esfe, Mohammad; Nadooshan, Afshin Ahmadi; Arshi, Ali; Alirezaie, Ali

    2018-03-01

    In this study, experimental data related to the Nusselt number and pressure drop of aqueous nanofluids of Titania is modeled and estimated by using ANN with 2 hidden layers and 8 neurons in each layer. Also in this study the effect of various effective variables in the Nusselt number and pressure drop is surveyed. This study indicated that the neural network modeling has been able to model experimental data with great accuracy. The modeling regression coefficient for the data of Nusselt number and relative pressure drop is 99.94% and 99.97% respectively. Besides, it represented that the increment of the Reynolds number and concentration made the increment of Nusselt number and pressure drop of aqueous nanofluid.

  12. Algebraic renormalization. Perturbative renormalization, symmetries and anomalies

    International Nuclear Information System (INIS)

    Piguet, O.

    1995-01-01

    This book is an introduction to the algebraic method in the perturbative renormalization of relativistic quantum field theory. After a general introduction to renormalized perturbation theory the quantum action principle and Ward identities are described. Then Yang-Mills gauge theories are considered. Thereafter the BRS cohomology and descent equations are described. Then nonrenormalization theorems and topological field theories are considered. Finally an application to the bosonic string is described. (HSI)

  13. Hadamard and minimal renormalizations

    International Nuclear Information System (INIS)

    Castagnino, M.A.; Gunzig, E.; Nardone, P.; Paz, J.P.

    1986-01-01

    A common language is introduced to study two, well-known, different methods for the renormalization of the energy-momentum tensor of a scalar neutral quantum field in curved space-time. Different features of the two renormalizations are established and compared

  14. Renormalization and effective lagrangians

    International Nuclear Information System (INIS)

    Polchinski, J.

    1984-01-01

    There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional lambda PHI 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed. (orig.)

  15. Non-Perturbative Renormalization

    CERN Document Server

    Mastropietro, Vieri

    2008-01-01

    The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi

  16. Renormalization of supersymmetric theories

    International Nuclear Information System (INIS)

    Pierce, D.M.

    1998-06-01

    The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M W and sin 2 θ eff . He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses

  17. Renormalization Group Theory

    International Nuclear Information System (INIS)

    Stephens, C. R.

    2006-01-01

    In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory -- the ''high temperature'' regime and the Regge regime

  18. Renormalization of fermion mixing

    International Nuclear Information System (INIS)

    Schiopu, R.

    2007-01-01

    Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

  19. Renormalization of fermion mixing

    Energy Technology Data Exchange (ETDEWEB)

    Schiopu, R.

    2007-05-11

    Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

  20. Dimensional renormalization and comparison of renormalization schemes in quantum electrodynamics

    International Nuclear Information System (INIS)

    Coquereaux, R.

    1979-02-01

    The method of dimensional renormalization as applied to quantum electrodynamics is discussed. A general method is given which allows one to compare the various quantities like coupling constants and masses that appear in different renormalization schemes

  1. Perturbative and constructive renormalization

    International Nuclear Information System (INIS)

    Veiga, P.A. Faria da

    2000-01-01

    These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)

  2. Renormalization and plasma physics

    International Nuclear Information System (INIS)

    Krommes, J.A.

    1980-02-01

    A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields

  3. Renormalization and plasma physics

    Energy Technology Data Exchange (ETDEWEB)

    Krommes, J.A.

    1980-02-01

    A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.

  4. On renormalization of axial anomaly

    International Nuclear Information System (INIS)

    Efremov, A.V.; Teryaev, O.V.

    1989-01-01

    It is shown that multiplicative renormalization of the axial singlet current results in renormalization of the axial anomaly in all orders of perturbation theory. It is a necessary condition for the Adler - Bardeen theorem being valid. 10 refs.; 2 figs

  5. Renormalization group and asymptotic freedom

    International Nuclear Information System (INIS)

    Morris, J.R.

    1978-01-01

    Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions

  6. Renormalization of Hamiltonian QCD

    International Nuclear Information System (INIS)

    Andrasi, A.; Taylor, John C.

    2009-01-01

    We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

  7. Constructive renormalization theory

    International Nuclear Information System (INIS)

    Rivasseau, Vincent

    2000-01-01

    These notes are the second part of a common course on Renormalization Theory given with Professor P. da Veiga. I emphasize here the rigorous non-perturbative or constructive aspects of the theory. The usual formalism for the renormalization group in field theory or statistical mechanics is reviewed, together with its limits. The constructive formalism is introduced step by step. Taylor forest formulas allow to perform easily the cluster and Mayer expansions which are needed for a single step of the renormalization group in the case of Bosonic theories. The iteration of this single step leads to further difficulties whose solution is briefly sketched. The second part of the course is devoted to Fermionic models. These models are easier to treat on the constructive level so they are very well suited to beginners in constructive theory. It is shown how the Taylor forest formulas allow to reorganize perturbation theory nicely in order to construct the Gross-Neveu 2 model without any need for cluster or Mayer expansions. Finally applications of this technique to condensed matter and renormalization group around Fermi surface are briefly reviewed. (author)

  8. Renormalizing Entanglement Distillation

    Science.gov (United States)

    Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens

    2016-01-01

    Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.

  9. Holographic renormalization and supersymmetry

    Energy Technology Data Exchange (ETDEWEB)

    Genolini, Pietro Benetti [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom); Cassani, Davide [LPTHE, Sorbonne Universités UPMC Paris 6 and CNRS, UMR 7589,F-75005, Paris (France); Martelli, Dario [Department of Mathematics, King’s College London,The Strand, London, WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom)

    2017-02-27

    Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N=2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.

  10. Renormalization Group Functional Equations

    CERN Document Server

    Curtright, Thomas L

    2011-01-01

    Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.

  11. Renormalization of gauge theories

    International Nuclear Information System (INIS)

    Becchi, C.; Rouet, A.; Stora, R.

    1975-04-01

    Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts. These identities are proved to all orders of renormalized perturbation theory, within the BPHZ framework, when the underlying Lie algebra is semi-simple and the gauge function is chosen to be linear in the fields in such a way that all fields are massive. An example, the SU2 Higgs Kibble model is analyzed in detail: the asymptotic theory is formulated in the perturbative sense, and shown to be reasonable, namely, the physical S operator is unitary and independant from the parameters which define the gauge function [fr

  12. Renormalized Lie perturbation theory

    International Nuclear Information System (INIS)

    Rosengaus, E.; Dewar, R.L.

    1981-07-01

    A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another

  13. Impact of granular drops

    KAUST Repository

    Marston, J. O.

    2013-07-15

    We investigate the spreading and splashing of granular drops during impact with a solid target. The granular drops are formed from roughly spherical balls of sand mixed with water, which is used as a binder to hold the ball together during free-fall. We measure the instantaneous spread diameter for different impact speeds and find that the normalized spread diameter d/D grows as (tV/D)1/2. The speeds of the grains ejected during the “splash” are measured and they rarely exceed twice that of the impact speed.

  14. Impact of granular drops

    KAUST Repository

    Marston, J. O.; Mansoor, Mohammad M.; Thoroddsen, Sigurdur T

    2013-01-01

    We investigate the spreading and splashing of granular drops during impact with a solid target. The granular drops are formed from roughly spherical balls of sand mixed with water, which is used as a binder to hold the ball together during free-fall. We measure the instantaneous spread diameter for different impact speeds and find that the normalized spread diameter d/D grows as (tV/D)1/2. The speeds of the grains ejected during the “splash” are measured and they rarely exceed twice that of the impact speed.

  15. Compositeness condition in the renormalization group equation

    International Nuclear Information System (INIS)

    Bando, Masako; Kugo, Taichiro; Maekawa, Nobuhiro; Sasakura, Naoki; Watabiki, Yoshiyuki; Suehiro, Kazuhiko

    1990-01-01

    The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted. (orig.)

  16. Unambiguity of renormalization group calculations in QCD

    International Nuclear Information System (INIS)

    Vladimirov, A.A.

    1979-01-01

    A detailed analysis of the reduction of ambiguities determined by an arbitrary renormalization scheme is presented for the renormalization group calculations of physical quantities in quantum chromodynamics (QCD). Some basic formulas concerning the renormalization-scheme dependence of Green's and renormalization group functions are given. A massless asymptotically free theory with one coupling constant g is considered. In conclusion, several rules for renormalization group calculations in QCD are formulated

  17. Differential renormalization of gauge theories

    International Nuclear Information System (INIS)

    Aguila, F. del; Perez-Victoria, M.

    1998-01-01

    The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author)

  18. Differential renormalization of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)

    1998-10-01

    The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab

  19. The analytic renormalization group

    Directory of Open Access Journals (Sweden)

    Frank Ferrari

    2016-08-01

    Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

  20. Practical algebraic renormalization

    International Nuclear Information System (INIS)

    Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias

    2001-01-01

    A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ

  1. Renormalization of Hamiltonians

    International Nuclear Information System (INIS)

    Glazek, S.D.; Wilson, K.G.

    1993-01-01

    This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

  2. Holographic Renormalization in Dense Medium

    International Nuclear Information System (INIS)

    Park, Chanyong

    2014-01-01

    The holographic renormalization of a charged black brane with or without a dilaton field, whose dual field theory describes a dense medium at finite temperature, is investigated in this paper. In a dense medium, two different thermodynamic descriptions are possible due to an additional conserved charge. These two different thermodynamic ensembles are classified by the asymptotic boundary condition of the bulk gauge field. It is also shown that in the holographic renormalization regularity of all bulk fields can reproduce consistent thermodynamic quantities and that the Bekenstein-Hawking entropy is nothing but the renormalized thermal entropy of the dual field theory. Furthermore, we find that the Reissner-Nordström AdS black brane is dual to a theory with conformal matter as expected, whereas a charged black brane with a nontrivial dilaton profile is mapped to a theory with nonconformal matter although its leading asymptotic geometry still remains as AdS space

  3. Renormalization group in modern physics

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    1988-01-01

    Renormalization groups used in diverse fields of theoretical physics are considered. The discussion is based upon functional formulation of group transformations. This attitude enables development of a general method by using the notion of functional self-similarity which generalizes the usual self-similarity connected with power similarity laws. From this point of view the authors present a simple derivation of the renorm-group (RG) in QFT liberated from ultra-violet divergences philosophy, discuss the RG approach in other fields of physics and compare different RG's

  4. Renormalized modes in cuprate superconductors

    Science.gov (United States)

    Gupta, Anushri; Kumari, Anita; Verma, Sanjeev K.; Indu, B. D.

    2018-04-01

    The renormalized mode frequencies are obtained with the help of quantum dynamical approach of many body phonon Green's function technique via a general Hamiltonian (excluding BCS Hamiltonian) including the effects of phonons and electrons, anharmonicities and electron-phonon interactions. The numerical estimates have been carried out to study the renormalized mode frequency of high temperature cuprate superconductor (HTS) YBa2Cu3O7-δ using modified Born-Mayer-Huggins interaction potential (MBMHP) best applicable to study the dynamical properties of all HTS.

  5. Point transformations and renormalization in the unitary gauge. III. Renormalization effects

    International Nuclear Information System (INIS)

    Sherry, T.N.

    1976-06-01

    An analysis of two simple gauge theory models is continued using point transformations rather than gauge transformations. The renormalization constants are examined directly in two gauges, the renormalization (Landau) and unitary gauges. The result is that the individual coupling constant renormalizations are identical when calculated in each of the above two gauges, although the wave-function and proper vertex renormalizations differ

  6. Renormalization group and Mayer expansions

    International Nuclear Information System (INIS)

    Mack, G.

    1984-02-01

    Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U(1) lattice gauge theory by Goepfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear sigma-model, and elsewhere. (orig.)

  7. Renormalization group and mayer expansions

    International Nuclear Information System (INIS)

    Mack, G.

    1984-01-01

    Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U (1) lattice gauge theory by Gopfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear σ-model, and elsewhere

  8. Renormalization group in quantum mechanics

    International Nuclear Information System (INIS)

    Polony, J.

    1996-01-01

    The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright copyright 1996 Academic Press, Inc

  9. Superfield perturbation theory and renormalization

    International Nuclear Information System (INIS)

    Delbourgo, R.

    1975-01-01

    The perturbation theory graphs and divergences in super-symmetric Lagrangian models are studied by using superfield techniques. In super PHI 3 -theory very little effort is needed to arrive at the single infinite (wave function) renormalization counterterm, while in PHI 4 -theory the method indicates the counter-Lagrangians needed at the one-loop level and possibly beyond

  10. On renormalization-invariant masses

    International Nuclear Information System (INIS)

    Fleming, H.; Furuya, K.

    1978-02-01

    It is shown that spontaneous generation of renormalization invariant mass is possible in infra-red stable theories with more than one coupling constant. If relations among the coupling constants are permitted the effect can be made compatible with pertubation theory

  11. Fixed point of the parabolic renormalization operator

    CERN Document Server

    Lanford III, Oscar E

    2014-01-01

    This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...

  12. Controlling charge on levitating drops.

    Science.gov (United States)

    Hilger, Ryan T; Westphall, Michael S; Smith, Lloyd M

    2007-08-01

    Levitation technologies are used in containerless processing of materials, as microscale manipulators and reactors, and in the study of single drops and particles. Presented here is a method for controlling the amount and polarity of charge on a levitating drop. The method uses single-axis acoustic levitation to trap and levitate a single, initially neutral drop with a diameter between 400 microm and 2 mm. This drop is then charged in a controllable manner using discrete packets of charge in the form of charged drops produced by a piezoelectric drop-on-demand dispenser equipped with a charging electrode. The magnitude of the charge on the dispensed drops can be adjusted by varying the voltage applied to the charging electrode. The polarity of the charge on the added drops can be changed allowing removal of charge from the trapped drop (by neutralization) and polarity reversal. The maximum amount of added charge is limited by repulsion of like charges between the drops in the trap. This charging scheme can aid in micromanipulation and the study of charged drops and particles using levitation.

  13. Renormalization group theory of earthquakes

    Directory of Open Access Journals (Sweden)

    H. Saleur

    1996-01-01

    Full Text Available We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995. The discrete scaling symmetries which may be present at smaller scales are shown to be robust on a global scale with respect to disorder. Furthermore, a single complex exponent is sufficient in practice to capture the essential properties of the leading correction to scaling, whose real part may be renormalized by disorder, and thus be specific to the system. We then propose a new mechanism for discrete scale invariance, based on the interplay between dynamics and disorder. The existence of non-linear corrections to the renormalization group flow implies that an earthquake is not an isolated 'critical point', but is accompanied by an embedded set of 'critical points', its foreshocks and any subsequent shocks for which it may be a foreshock.

  14. Renormalization group and critical phenomena

    International Nuclear Information System (INIS)

    Ji Qing

    2004-01-01

    The basic clue and the main steps of renormalization group method used for the description of critical phenomena is introduced. It is pointed out that this method really reflects the most important physical features of critical phenomena, i.e. self-similarity, and set up a practical solving method from it. This way of setting up a theory according to the features of the physical system is really a good lesson for today's physicists. (author)

  15. QCD: Renormalization for the practitioner

    International Nuclear Information System (INIS)

    Pascual, P.; Tarrach, R.

    1984-01-01

    These notes correspond to a GIFT (Grupo Interuniversitario de Fisica Teorica) course which was given by us in autumn 1983 at the University of Barcelona. Their main subject is renormalization in perturbative QCD and only the last chapter goes beyond perturbation theory. They are essentially self contained and their aim is to teach the student the techniques of perturbative QCD and the QCD sum rules. (orig./HSI)

  16. Experimental studies on the evaporative heat transfer and pressure drop of CO{sub 2} and CO{sub 2}/propane mixtures flowing upward in smooth and micro-fin tubes with outer diameter of 5 mm for an inclination angle of 45

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Jin Min; Kim, Min Soo [School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744 (Korea); Kim, Yong Jin [School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 (United States)

    2010-08-15

    Heat transfer characteristics show different tendency according to the tube orientations such as horizontal, vertical, and inclined positions. In this study, evaporative heat transfer characteristics and pressure drop of CO{sub 2} and CO{sub 2}/propane mixtures flowing upward are investigated in inclined smooth and micro-fin tubes. Smooth and micro-fin tubes with outer diameter of 5 mm and length of 1.44 m with inclination angle of 45 were chosen as test tubes. Average inner diameters of test tubes are 4.0 mm (smooth tube) and 4.13 mm (micro-fin tube). The tests were conducted at mass fluxes from 212 to 656 kg/m{sup 2} s, saturation temperatures from -10 to 30 C and heat fluxes from 15 to 60 kW/m{sup 2} for CO{sub 2}. In addition, for CO{sub 2}/propane mixtures, the test was carried out at inlet temperatures from -10 to 30 C for several compositions (75/25, 50/50, 25/75 wt%) with the same mass fluxes, heat fluxes applied for CO{sub 2}. Heat transfer coefficients in inclined tube are approximately 1.8-3 times higher than those in horizontal tube and the average pressure drop of inclined tube exists between that of horizontal and vertical tubes. (author)

  17. Drop trampoline

    Science.gov (United States)

    Chantelot, Pierre; Coux, Martin; Clanet, Christophe; Quere, David

    2017-11-01

    Superhydrophobic substrates inspired from the lotus leaf have the ability to reflect impacting water drops. They do so very efficiently and contact lasts typically 10 ms for millimetric droplets. Yet unlike a lotus leaf most synthetic substrates are rigid. Focusing on the interplay between substrate flexibility and liquid repellency might allow us to understand the dynamic properties of natural surfaces. We perform liquid marbles impacts at velocity V onto thin ( 0.01 mm) stretched circular PDMS membranes. We obtain contact time reductions of up to 70%. The bouncing mechanism is drastically modified compared to that on a rigid substrate: the marble leaves the substrate while it is still spread in a disk shape as it is kicked upwards by the membrane. We show that the bouncing is controlled by an interplay between the dynamics of the drop and the membrane.

  18. Real space renormalization tecniques for disordered systems

    International Nuclear Information System (INIS)

    Anda, E.V.

    1984-01-01

    Real space renormalization techniques are applied to study different disordered systems, with an emphasis on the understanding of the electronic properties of amorphous matter, mainly semiconductors. (Authors) [pt

  19. The renormalization of the electroweak standard model

    International Nuclear Information System (INIS)

    Boehm, M.; Spiesberger, H.; Hollik, W.

    1984-03-01

    A renormalization scheme for the electroweak standard model is presented in which the electric charge and the masses of the gauge bosons, Higgs particle and fermions are used as physical parameters. The photon is treated such that quantum electrodynamics is contained in the usual form. Field renormalization respecting the gauge symmetry gives finite Green functions. The Ward identities between the Green functions of the unphysical sector allow a renormalization that maintains the simple pole structure of the propagators. Explicit results for the renormalization self energies and vertex functions are given. They can be directly used as building blocks for the evaluation of l-loop radiative corrections. (orig.)

  20. Introduction to the functional renormalization group

    International Nuclear Information System (INIS)

    Kopietz, Peter; Bartosch, Lorenz; Schuetz, Florian

    2010-01-01

    This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. (orig.)

  1. Renormalization of Extended QCD2

    International Nuclear Information System (INIS)

    Fukaya, Hidenori; Yamamura, Ryo

    2015-01-01

    Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N c , to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region

  2. Renormalization of gauge fields models

    International Nuclear Information System (INIS)

    Becchi, C.; Rouet, A.; Stora, R.

    1974-01-01

    A new approach to gauge field models is described. It is based on the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme making extensive use of the quantum action principle, and the Slavnov invariance. The quantum action principle being first summarized in the framework of the BPHZ is then applied to a global symmetry problem. The symmetry property of the gauge field Lagrangians in the tree approximation is exhibited, and the preservation of this property at the quantum level is discussed. The main results relative to the Abelian and SU(2) Higgs-Kibble models are briefly reviewed [fr

  3. Renormalization in few body nuclear physics

    Energy Technology Data Exchange (ETDEWEB)

    Tomio, L.; Biswas, R. [Instituto de Fisica Teorica, UNESP, 01405-900 Sao Paulo (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminenese, Niteroi (Brazil); Frederico, T. [Instituto Tecnologico de Aeronautica, CTA 12228-900 Sao Jose dos Campos (Brazil)

    2001-09-01

    Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the {sup 3}S{sub l} -{sup 3} D{sub 1} states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three

  4. Renormalization in few body nuclear physics

    International Nuclear Information System (INIS)

    Tomio, L.; Biswas, R.; Delfino, A.; Frederico, T.

    2001-01-01

    Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the 3 S l - 3 D 1 states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three-body halo nuclei is also

  5. Dropped Ceiling

    OpenAIRE

    Tabet, Rayyane

    2012-01-01

    On December 2nd 1950 the first drop of Saudi oil arrived to Lebanon via the newly constructed Trans-Arabian Pipeline, the world's longest pipeline and the largest American private investment in a foreign land. The 30inch wide structure which spanned 1213 kilometers passing through Saudi Arabia, Jordan, and Syria to end in Lebanon had required 3 years of planning and surveying, 2 years of installation, the fabrication of 256,000 tons of steel tubes, the employment of 30,000 workers, the ratifi...

  6. Renormalization methods in solid state physics

    Energy Technology Data Exchange (ETDEWEB)

    Nozieres, P [Institut Max von Laue - Paul Langevin, 38 - Grenoble (France)

    1976-01-01

    Renormalization methods in various solid state problems (e.g., the Kondo effect) are analyzed from a qualitative vantage point. Our goal is to show how the renormalization procedure works, and to uncover a few simple general ideas (universality, phenomenological descriptions, etc...).

  7. Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)

    2013-08-01

    In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).

  8. Renormalization in charged colloids: non-monotonic behaviour with the surface charge

    International Nuclear Information System (INIS)

    Haro-Perez, C; Quesada-Perez, M; Callejas-Fernandez, J; Schurtenberger, P; Hidalgo-Alvarez, R

    2006-01-01

    The static structure factor S(q) is measured for a set of deionized latex dispersions with different numbers of ionizable surface groups per particle and similar diameters. For a given volume fraction, the height of the main peak of S(q), which is a direct measure of the spatial ordering of latex particles, does not increase monotonically with the number of ionizable groups. This behaviour cannot be described using the classical renormalization scheme based on the cell model. We analyse our experimental data using a renormalization model based on the jellium approximation, which predicts the weakening of the spatial order for moderate and large particle charges. (letter to the editor)

  9. Pressure drop in ET-RR-1

    International Nuclear Information System (INIS)

    Khattab, M.; Mina, A.R.

    1990-01-01

    Measurements of pressure drop through a bundle comprising 16 rods and their lower arrangement grid as well as orifices similar to those of ET-RR-1 core have been done. Experiments are carried out under adiabatic turbulent flow conditions at about 35 degree C. Bundle Reynolds number range is 4 x 10 -2 x 10. Orifices of diameters 4.5, 3.25 or 2.5 cm. are mounted underneath the bundle. The bundle and lower grid pressure drop coefficients are 3.75 and 1.8 respectively. Orifices pressure drop coefficients are 2.65, 19.67 and 53.55 respectively. The ratio of bundle pressure drop to that of 4.5 cm. Orifice diameter is 1.415. The pressure drop coefficients are utilizer to calculate flow through bundles. The flow rate per bundle is 39.1, 20.4 or 13.1 m 3 /hr. Depending on orifice diameter

  10. Gauge invariance and holographic renormalization

    Directory of Open Access Journals (Sweden)

    Keun-Young Kim

    2015-10-01

    Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.

  11. Class renormalization: islands around islands

    International Nuclear Information System (INIS)

    Meiss, J.D.

    1986-01-01

    An orbit of 'class' is one that rotates about a periodic orbit of one lower class with definite frequency. This contrasts to the 'level' of a periodic orbit which is the number of elements in its continued fraction expansion. Level renormalization is conventionally used to study the structure of quasi-periodic orbits. The scaling structure of periodic orbits encircling other periodic orbits in area preserving maps is discussed here. Fixed points corresponding to the accumulation of p/q bifurcations are found and scaling exponents determined. Fixed points for q > 2 correspond to self-similar islands around islands. Frequencies of the island boundary circles at the fixed points are obtained. Importance of this scaling for the motion of particles in stochastic regions is emphasized. (author)

  12. Golden mean Siegel disk universality and renormalization

    OpenAIRE

    Gaidashev, Denis; Yampolsky, Michael

    2016-01-01

    We provide a computer-assisted proof of one of the central open questions in one-dimensional renormalization theory -- universality of the golden-mean Siegel disks. We further show that for every function in the stable manifold of the golden-mean renormalization fixed point the boundary of the Siegel disk is a quasicircle which coincides with the closure of the critical orbit, and that the dynamics on the boundary of the Siegel disk is rigid. Furthermore, we extend the renormalization from on...

  13. Critical phenomena and renormalization group transformations

    International Nuclear Information System (INIS)

    Castellani, C.; Castro, C. di

    1980-01-01

    Our main goal is to guide the reader to find out the common rational behind the various renormalization procedures which have been proposed in the last ten years. In the first part of these lectures old arguments on universality and scaling will be briefly recalled. To our opinion these introductory remarks allow one to stress the physical origin of the two majore renormalization procedures, which have been used in the theory of critical phenomena: the Wilson and the field theoretic approach. All the general properties of a ''good'' renormalization transformation will also come out quite naturally. (author)

  14. Sigma models and renormalization of string loops

    International Nuclear Information System (INIS)

    Tseytlin, A.A.

    1989-05-01

    An extension of the ''σ-model β-functions - string equations of motion'' correspondence to the string loop level is discussed. Special emphasis is made on how the renormalization group acts in string loops and, in particular, on the renormalizability property of the generating functional Z-circumflex for string amplitudes (related to the σ model partition function integrated over moduli). Renormalization of Z-circumflex at one and two loop order is analyzed in some detail. We also discuss an approach to renormalization based on operators of insertion of topological fixtures. (author). 70 refs

  15. The renormalization group and lattice QCD

    International Nuclear Information System (INIS)

    Gupta, R.

    1989-01-01

    This report discusses the following topics: scaling of thermodynamic quantities and critical exponents; scaling relations; block spin idea of Kadanoff; exact RG solution of the 1-d Ising model; Wilson's formulation of the renormalization group; linearized transformation matrix and classification of exponents; derivation of exponents from the eigenvalues of Τ αβ ; simple field theory: the gaussian model; linear renormalization group transformations; numerical methods: MCRG; block transformations for 4-d SU(N) LGT; asymptotic freedom makes QCD simple; non-perturbative β-function and scaling; and the holy grail: the renormalized trajectory

  16. Higher derivatives and renormalization in quantum cosmology

    International Nuclear Information System (INIS)

    Mazzitelli, F.D.

    1991-10-01

    In the framework of the canonical quantization of general relativity, quantum field theory on a fixed background formally arises in an expansion in powers of the Planck length. In order to renormalize the theory, quadratic terms in the curvature must be included in the gravitational action from the beginning. These terms contain higher derivatives which change the Hamiltonian structure of the theory completely, making the relation between the renormalized-theory and the original one not clear. We show that it is possible to avoid this problem. We replace the higher derivative theory by a second order one. The classical solutions of the latter are also solutions of the former. We quantize the theory, renormalize the infinities and show that there is a smooth limit between the classical and the renormalized theories. We work in a Robertson Walker minisuperspace with a quantum scalar field. (author). 32 refs

  17. Renormalization scheme-invariant perturbation theory

    International Nuclear Information System (INIS)

    Dhar, A.

    1983-01-01

    A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)

  18. New renormalization group approach to multiscale problems

    Energy Technology Data Exchange (ETDEWEB)

    Einhorn, M B; Jones, D R.T.

    1984-02-27

    A new renormalization group is presented which exploits invariance with respect to more than one scale. The method is illustrated by a simple model, and future applications to fields such as critical phenomena and supersymmetry are speculated upon.

  19. Real space renormalization techniques for disordered systems

    International Nuclear Information System (INIS)

    Anda, E.V.

    1985-01-01

    Real Space renormalization techniques are applied to study different disordered systems, with an emphasis on the under-standing of the electronic properties of amorphous matter, mainly semiconductors. (author) [pt

  20. Renormalization of the inflationary perturbations revisited

    Science.gov (United States)

    Markkanen, Tommi

    2018-05-01

    In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

  1. Non-perturbative quark mass renormalization

    CERN Document Server

    Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.

    1998-01-01

    We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.

  2. Effective AdS/renormalized CFT

    OpenAIRE

    Fan, JiJi

    2011-01-01

    For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory. In particular, we define anomalous dimension holographically as the dependence of the wave-function renormalization factor on the radial cutoff in the Poincare patch of AdS. With this definition, the anomalous dimensions of both single- and double- trace operators are calculated. Three different dualities are considered with the field theory being CFT, CFT with a dou...

  3. Finite cluster renormalization and new two step renormalization group for Ising model

    International Nuclear Information System (INIS)

    Benyoussef, A.; El Kenz, A.

    1989-09-01

    New types of renormalization group theory using the generalized Callen identities are exploited in the study of the Ising model. Another type of two-step renormalization is proposed. Critical couplings and critical exponents y T and y H are calculated by these methods for square and simple cubic lattices, using different size clusters. (author). 17 refs, 2 tabs

  4. Problems with the definition of renormalized Hamiltonians for momentum-space renormalization transformations

    NARCIS (Netherlands)

    Enter, Aernout C.D. van; Fernández, Roberto

    For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the

  5. Failure Diameter Resolution Study

    Energy Technology Data Exchange (ETDEWEB)

    Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-12-19

    Previously the SURFplus reactive burn model was calibrated for the TATB based explosive PBX 9502. The calibration was based on fitting Pop plot data, the failure diameter and the limiting detonation speed, and curvature effect data for small curvature. The model failure diameter is determined utilizing 2-D simulations of an unconfined rate stick to find the minimum diameter for which a detonation wave propagates. Here we examine the effect of mesh resolution on an unconfined rate stick with a diameter (10mm) slightly greater than the measured failure diameter (8 to 9 mm).

  6. Renormalization of QED with planar binary trees

    International Nuclear Information System (INIS)

    Brouder, C.

    2001-01-01

    The Dyson relations between renormalized and bare photon and electron propagators Z 3 anti D(q)=D(q) and Z 2 anti S(q)=S(q) are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure. (orig.)

  7. Perturbatively improving RI-MOM renormalization constants

    Energy Technology Data Exchange (ETDEWEB)

    Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-03-15

    The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.

  8. Renormalization group theory of critical phenomena

    International Nuclear Information System (INIS)

    Menon, S.V.G.

    1995-01-01

    Renormalization group theory is a framework for describing those phenomena that involve a multitude of scales of variations of microscopic quantities. Systems in the vicinity of continuous phase transitions have spatial correlations at all length scales. The renormalization group theory and the pertinent background material are introduced and applied to some important problems in this monograph. The monograph begins with a historical survey of thermal phase transitions. The background material leading to the renormalization group theory is covered in the first three chapters. Then, the basic techniques of the theory are introduced and applied to magnetic critical phenomena in the next four chapters. The momentum space approach as well as the real space techniques are, thus, discussed in detail. Finally, brief outlines of applications of the theory to some of the related areas are presented in the last chapter. (author)

  9. Renormalization group approach in the turbulence theory

    International Nuclear Information System (INIS)

    Adzhemyan, L.Ts.; Vasil'ev, A.N.; Pis'mak, Yu.M.

    1983-01-01

    In the framework of the renormalization groUp approach in the turbulence theory sUggested in another paper, the problem of renormalization and evaluation of critical dimensions of composite operators is discussed. Renormalization of a system of operators of canonical dimension equal to 4, including the operator F=phiΔphi (where phi is the velocity field), is considered. It is shown that the critical dimension Δsub(F)=0. The appendice includes the brief proofs of two theorems: 1) the theorem on the equivalence between the arbitrary stochastic problem and quantum field theory; 2) the theorem which determines the reduction of Green functions of the stochastic problem to the hypersurface of coinciding times

  10. Renormalization: infinity in today microscopic physics

    International Nuclear Information System (INIS)

    Zinn-Justin, J.

    2000-01-01

    The expectations put in quantum electrodynamics were deceived when first calculations showed that divergencies, due to the pinpoint aspect of the electron, continued to exist. Later, as a consequence of new experimental data and theoretical progress, an empirical method called renormalization was proposed to allow the evaluation of expressions involving infinite terms. The development of this method opened the way to the theory of re-normalizing fields and gave so successful results that it was applied to all fundamental interactions except gravity. This theory allowed the standard model in weak, electromagnetic and strong interactions to be confronted successfully with experimental data during more than 25 years. This article presents the progressive evolution of ideas in the concept of renormalization. (A.C.)

  11. Renormalization transformation of periodic and aperiodic lattices

    International Nuclear Information System (INIS)

    Macia, Enrique; Rodriguez-Oliveros, Rogelio

    2006-01-01

    In this work we introduce a similarity transformation acting on transfer matrices describing the propagation of elementary excitations through either periodic or Fibonacci lattices. The proposed transformation can act at two different scale lengths. At the atomic scale the transformation allows one to express the systems' global transfer matrix in terms of an equivalent on-site model one. Correlation effects among different hopping terms are described by a series of local phase factors in that case. When acting on larger scale lengths, corresponding to short segments of the original lattice, the similarity transformation can be properly regarded as describing an effective renormalization of the chain. The nature of the resulting renormalized lattice significantly depends on the kind of order (i.e., periodic or quasiperiodic) of the original lattice, expressing a delicate balance between chemical complexity and topological order as a consequence of the renormalization process

  12. Exact renormalization group equations: an introductory review

    Science.gov (United States)

    Bagnuls, C.; Bervillier, C.

    2001-07-01

    We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.

  13. Renormalization using the background-field method

    International Nuclear Information System (INIS)

    Ichinose, S.; Omote, M.

    1982-01-01

    Renormalization using the background-field method is examined in detail. The subtraction mechanism of subdivergences is described with reference to multi-loop diagrams and one- and two-loop counter-term formulae are explicitly given. The original one-loop counter-term formula of 't Hooft is thereby improved. The present method of renormalization is far easier to manage than the usual one owing to the fact only gauge-invariant quantities are to be considered when worked in an appropriate gauge. Gravity and Yang-Mills theories are studied as examples. (orig.)

  14. Hypercuboidal renormalization in spin foam quantum gravity

    Science.gov (United States)

    Bahr, Benjamin; Steinhaus, Sebastian

    2017-06-01

    In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

  15. Renormalization of a distorted gauge: invariant theory

    International Nuclear Information System (INIS)

    Hsu, J.P.; Underwood, J.A.

    1976-02-01

    A new type of renormalizable theory involving massive Yang-Mills fields whose mass is generated by an intrinsic breakdown of the usual local gauge symmetry is considered. However, the Lagrangian has a distorted gauge symmetry which leads to the Ward-Takahashi (W-T) identities. Also, the theory is independent of the gauge parameter xi. An explicit renormalization at the oneloop level is completely carried out by exhibiting counter terms, defining the physical parameters and computing all renormalization constants to check the W-T identities

  16. Field renormalization in photonic crystal waveguides

    DEFF Research Database (Denmark)

    Colman, Pierre

    2015-01-01

    A novel strategy is introduced in order to include variations of the nonlinearity in the nonlinear Schro¨dinger equation. This technique, which relies on renormalization, is in particular well adapted to nanostructured optical systems where the nonlinearity exhibits large variations up to two...... orders of magnitude larger than in bulk material. We show that it takes into account in a simple and efficient way the specificity of the nonlinearity in nanostructures that is determined by geometrical parameters like the effective mode area and the group index. The renormalization of the nonlinear...

  17. Physical renormalization condition for de Sitter QED

    Science.gov (United States)

    Hayashinaka, Takahiro; Xue, She-Sheng

    2018-05-01

    We considered a new renormalization condition for the vacuum expectation values of the scalar and spinor currents induced by a homogeneous and constant electric field background in de Sitter spacetime. Following a semiclassical argument, the condition named maximal subtraction imposes the exponential suppression on the massive charged particle limit of the renormalized currents. The maximal subtraction changes the behaviors of the induced currents previously obtained by the conventional minimal subtraction scheme. The maximal subtraction is favored for a couple of physically decent predictions including the identical asymptotic behavior of the scalar and spinor currents, the removal of the IR hyperconductivity from the scalar current, and the finite current for the massless fermion.

  18. Similarity renormalization group evolution of N N interactions within a subtractive renormalization scheme

    Directory of Open Access Journals (Sweden)

    Durães F.O.

    2010-04-01

    Full Text Available We apply the similarity renormalization group (SRG approach to evolve a nucleon-nucleon (N N interaction in leading-order (LO chiral effective field theory (ChEFT, renormalized within the framework of the subtracted kernel method (SKM. We derive a fixed-point interaction and show the renormalization group (RG invariance in the SKM approach. We also compare the evolution of N N potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS equation and the evolution with the similarity cutoff through the SRG transformation.

  19. Optimization of renormalization group transformations in lattice gauge theory

    International Nuclear Information System (INIS)

    Lang, C.B.; Salmhofer, M.

    1988-01-01

    We discuss the dependence of the renormalization group flow on the choice of the renormalization group transformation (RGT). An optimal choice of the transformation's parameters should lead to a renormalized trajectory close to a few-parameter action. We apply a recently developed method to determine an optimal RGT to SU(2) lattice gauge theory and discuss the achieved improvement. (orig.)

  20. Renormalization group in statistical physics - momentum and real spaces

    International Nuclear Information System (INIS)

    Yukalov, V.I.

    1988-01-01

    Two variants of the renormalization group approach in statistical physics are considered, the renormalization group in the momentum and the renormalization group in the real spaces. Common properties of these methods and their differences are cleared up. A simple model for investigating the crossover between different universality classes is suggested. 27 refs

  1. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    International Nuclear Information System (INIS)

    Actis, S.; Passarino, G.

    2006-12-01

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  2. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

    2006-12-15

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  3. Perturbative renormalization of QED via flow equations

    International Nuclear Information System (INIS)

    Keller, G.; Kopper, C.

    1991-01-01

    We prove the perturbative renormalizability of euclidean QED 4 with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.)

  4. Perturbative renormalization of QED via flow equations

    Energy Technology Data Exchange (ETDEWEB)

    Keller, G. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany)); Kopper, C. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany) Inst. fuer Theoretische Physik, Univ. Goettingen (Germany))

    1991-12-19

    We prove the perturbative renormalizability of euclidean QED{sub 4} with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.).

  5. Renormalization and asymptotic freedom in quantum gravity

    International Nuclear Information System (INIS)

    Tomboulis, E.T.

    1984-01-01

    The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)

  6. Renormalization of Magnetic Excitations in Praseodymium

    DEFF Research Database (Denmark)

    Lindgård, Per-Anker

    1975-01-01

    The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev...

  7. Mass renormalization in sine-Gordon model

    International Nuclear Information System (INIS)

    Xu Bowei; Zhang Yumei

    1991-09-01

    With a general gaussian wave functional, we investigate the mass renormalization in the sine-Gordon model. At the phase transition point, the sine-Gordon system tends to a system of massless free bosons which possesses conformal symmetry. (author). 8 refs, 1 fig

  8. Renormalization of Supersymmetric QCD on the Lattice

    Science.gov (United States)

    Costa, Marios; Panagopoulos, Haralambos

    2018-03-01

    We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

  9. Finite size scaling and phenomenological renormalization

    International Nuclear Information System (INIS)

    Derrida, B.; Seze, L. de; Vannimenus, J.

    1981-05-01

    The basic equations of the phenomenological renormalization method are recalled. A simple derivation using finite-size scaling is presented. The convergence of the method is studied analytically for the Ising model. Using this method we give predictions for the 2d bond percolation. Finally we discuss how the method can be applied to random systems

  10. Two-loop renormalization in the standard model, part II. Renormalization procedures and computational techniques

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

    2006-12-15

    In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, are discussed in part III where numerical results, e.g. for the complex poles of the unstable gauge bosons, are shown. An attempt is made to define the running of the electromagnetic coupling constant at the two-loop level. (orig.)

  11. Renormalization and effective actions for general relativity

    International Nuclear Information System (INIS)

    Neugebohrn, F.

    2007-05-01

    Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

  12. Renormalization and effective actions for general relativity

    Energy Technology Data Exchange (ETDEWEB)

    Neugebohrn, F.

    2007-05-15

    Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

  13. Estimation of the diameter-charge distribution in polydisperse electrically charged sprays of electrically insulating liquids

    Science.gov (United States)

    Rigit, A. R. H.; Shrimpton, John S.

    2009-06-01

    The majority of scientific and industrial electrical spray applications make use of sprays that contain a range of drop diameters. Indirect evidence suggests the mean drop diameter and the mean drop charge level are usually correlated. In addition, within each drop diameter class there is every reason to suspect a distribution of charge levels exist for a particular drop diameter class. This paper presents an experimental method that uses the joint PDF of drop velocity and diameter, obtained from phase Doppler anemometry measurements, and directly obtained spatially resolved distributions of the mass and charge flux to obtain a drop diameter and charge frequency distribution. The method is demonstrated using several data-sets obtained from experimental measurements of steady poly-disperse sprays of an electrically insulating liquid produced with the charge injection technique. The space charge repulsion in the spray plume produces a hollow cone spray structure. In addition an approximate self-similarity is observed, with the maximum radial mass and charge flow occurring at r/ d ~ 200. The charge flux profile is slightly offset from the mass flux profile, and this gives direct evidence that the spray specific charge increases from approximately 20% of the bulk mean spray specific charge on the spray axis to approximately 200% of the bulk mean specific charge in the periphery of the spray. The results from the drop charge estimation model suggest a complex picture of the correlation between drop charge and drop diameter, with spray specific charge, injection velocity and orifice diameter all contributing to the shape of the drop diameter-charge distribution. Mean drop charge as a function of the Rayleigh limit is approximately 0.2, and is invariant with drop diameter and also across the spray cases tested.

  14. Estimation of the diameter-charge distribution in polydisperse electrically charged sprays of electrically insulating liquids

    Energy Technology Data Exchange (ETDEWEB)

    Rigit, A.R.H. [University of Sarawak, Faculty of Engineering, Kota Samarahan, Sarawak (Malaysia); Shrimpton, John S. [University of Southampton, Energy Technology Research Group, School of Engineering Sciences, Southampton (United Kingdom)

    2009-06-15

    The majority of scientific and industrial electrical spray applications make use of sprays that contain a range of drop diameters. Indirect evidence suggests the mean drop diameter and the mean drop charge level are usually correlated. In addition, within each drop diameter class there is every reason to suspect a distribution of charge levels exist for a particular drop diameter class. This paper presents an experimental method that uses the joint PDF of drop velocity and diameter, obtained from phase Doppler anemometry measurements, and directly obtained spatially resolved distributions of the mass and charge flux to obtain a drop diameter and charge frequency distribution. The method is demonstrated using several data-sets obtained from experimental measurements of steady poly-disperse sprays of an electrically insulating liquid produced with the charge injection technique. The space charge repulsion in the spray plume produces a hollow cone spray structure. In addition an approximate self-similarity is observed, with the maximum radial mass and charge flow occurring at r/d{proportional_to}200. The charge flux profile is slightly offset from the mass flux profile, and this gives direct evidence that the spray specific charge increases from approximately 20% of the bulk mean spray specific charge on the spray axis to approximately 200% of the bulk mean specific charge in the periphery of the spray. The results from the drop charge estimation model suggest a complex picture of the correlation between drop charge and drop diameter, with spray specific charge, injection velocity and orifice diameter all contributing to the shape of the drop diameter-charge distribution. Mean drop charge as a function of the Rayleigh limit is approximately 0.2, and is invariant with drop diameter and also across the spray cases tested. (orig.)

  15. Dynamics of deforming drops

    OpenAIRE

    Bouwhuis, W.

    2015-01-01

    Liquid drops play a dominant role in numerous industrial applications, such as spray coating, spray painting, inkjet printing, lithography processes, and spraying/sprinkling in agriculture or gardening. In all of these examples, the generation, flight, impact, and spreading of drops are separate stages of the corresponding industrial processes, which are all thoroughly studied for many years. This thesis focuses on drop dynamics, impact phenomena, Leidenfrost drops, and pouring flows. Based o...

  16. Displacer Diameter Effect in Displacer Pulse Tube Refrigerator

    Science.gov (United States)

    Zhu, Shaowei

    2017-12-01

    Gas driving displacer pulse tube refrigerators are one of the work recovery type of pulse tube refrigerators whose theoretical efficiency is the same as Stirling refrigerators'. Its cooling power is from the displacement of the displacer. Displace diameter, rod diameter and pressure drop of the regenerator influence the displacement, which are investigated by numerical simulation. It is shown that the displacement ratio of the displacer over the piston is almost not affected by the displacer diameter at the same rod diameter ratio, or displacer with different diameters almost has the same performance.

  17. Probing renormalization group flows using entanglement entropy

    International Nuclear Information System (INIS)

    Liu, Hong; Mezei, Márk

    2014-01-01

    In this paper we continue the study of renormalized entanglement entropy introduced in http://dx.doi.org/10.1007/JHEP04(2013)162. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen

  18. Poissonian renormalizations, exponentials, and power laws

    Science.gov (United States)

    Eliazar, Iddo

    2013-05-01

    This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

  19. Poissonian renormalizations, exponentials, and power laws.

    Science.gov (United States)

    Eliazar, Iddo

    2013-05-01

    This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

  20. Renormalization group flow of the Higgs potential.

    Science.gov (United States)

    Gies, Holger; Sondenheimer, René

    2018-03-06

    We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).

  1. Renormalization group treatment of nonrenormalizable interactions

    International Nuclear Information System (INIS)

    Kazakov, D I; Vartanov, G S

    2006-01-01

    The structure of the UV divergences in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergences (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. An explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the naive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms

  2. On the renormalization of string functionals

    International Nuclear Information System (INIS)

    Dietz, K.; Filk, T.

    1982-09-01

    We investigate analytic renormalization procedures for functional integrals, corresponding to field theories defined on compact manifolds, which arise e.g. from string functionals of the Nambu-Schild-Eguchi type. Although these models belong to the nonrenormalizable class of quantum field theories, we prove finiteness for a rectangular string shape up to three loop level, for circular boundary up to two loop order, and for a variety of graphs in higher order, thus indicating that the result might hold in general. From the explicit calculation of the two loop approximation we extract the first model dependent corrections to the qanti q - potential or the Casimir effect. The importance of dilation transformations for the properties of the renormalization procedure are investigated. We prove that under certain conditions, forced by symmetry properties, the association of finite values to divergent series is unique, independent of the regularization procedure. (orig.)

  3. Renormalization group evolution of Dirac neutrino masses

    International Nuclear Information System (INIS)

    Lindner, Manfred; Ratz, Michael; Schmidt, Michael Andreas

    2005-01-01

    There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large tan β comparable to the precision of future experiments

  4. Temperature dependent quasiparticle renormalization in nickel metal

    Energy Technology Data Exchange (ETDEWEB)

    Ovsyannikov, Ruslan; Sanchez-Barriga, Jaime; Fink, Joerg; Duerr, Hermann A. [Helmholtz Zentrum Berlin (Germany). BESSY II

    2009-07-01

    One of the fundamental consequences of electron correlation effects is that the bare particles in solids become 'dressed', i.e. they acquire an increased effective mass and a lifetime. We studied the spin dependent quasiparticle band structure of Ni(111) with high resolution angle resolved photoemission spectroscopy. At low temperatures (50 K) a renormalization of quasiparticle energy and lifetime indicative of electron-phonon coupling is observed in agreement with literature. With increasing temperature we observe a decreasing quasiparticle lifetime at the Fermi level for all probed minority spin bands as expected from electron phonon coupling. Surprisingly the majority spin states behave differently. We actually observe a slightly increased lifetime at room temperature. The corresponding increase in Fermi velocity points to a temperature dependent reduction of the majority spin quasiparticle renormalization.

  5. Renormalization Methods - A Guide For Beginners

    International Nuclear Information System (INIS)

    Cardy, J

    2004-01-01

    The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard φ 4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent

  6. Renormalization of gauge theories without cohomology

    International Nuclear Information System (INIS)

    Anselmi, Damiano

    2013-01-01

    We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

  7. Loop optimization for tensor network renormalization

    Science.gov (United States)

    Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

    We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

  8. Covariant Derivatives and the Renormalization Group Equation

    Science.gov (United States)

    Dolan, Brian P.

    The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

  9. Renormalized powers of quantum white noise

    International Nuclear Information System (INIS)

    Accardi, L.; Boukas, A.

    2009-01-01

    Giving meaning to the powers of the creation and annihilation densities (quantum white noise) is an old and important problem in quantum field theory. In this paper we present an account of some new ideas that have recently emerged in the attempt to solve this problem. We emphasize the connection between the Lie algebra of the renormalized higher powers of quantum white noise (RHPWN), which can be interpreted as a suitably deformed (due to renormalization) current algebra over the 1-mode full oscillator algebra, and the current algebra over the centerless Virasoro (or Witt)-Zamolodchikov-ω ∞ Lie algebras of conformal field theory. Through a suitable definition of the action on the vacuum vector we describe how to obtain a Fock representation of all these algebras. We prove that the restriction of the vacuum to the abelian subalgebra generated by the field operators gives an infinitely divisible process whose marginal distribution is the beta (or continuous binomial). (authors)

  10. A renormalization group theory of cultural evolution

    OpenAIRE

    Fath, Gabor; Sarvary, Miklos

    2003-01-01

    We present a theory of cultural evolution based upon a renormalization group scheme. We consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment. These representations are built around the most important degrees of freedom of their world. Cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequa...

  11. The Bogolyubov renormalization group. Second English printing

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    1996-01-01

    We begin with personal notes describing the atmosphere of 'Bogolyubov renormalization group' birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to proliferation of RG ideas into diverse parts of theoretical physics. We conclude with discussing the perspective of RG method further development and its application in mathematical physics. 58 refs

  12. Zero Point Energy of Renormalized Wilson Loops

    OpenAIRE

    Hidaka, Yoshimasa; Pisarski, Robert D.

    2009-01-01

    The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero wh...

  13. Generalized Hubbard Hamiltonian: renormalization group approach

    International Nuclear Information System (INIS)

    Cannas, S.A.; Tamarit, F.A.; Tsallis, C.

    1991-01-01

    We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs

  14. Quarkonia from charmonium and renormalization group equations

    International Nuclear Information System (INIS)

    Ditsas, P.; McDougall, N.A.; Moorhouse, R.G.

    1978-01-01

    A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters αsub(s) are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit Hamiltonian for obtaining the charmonium hyperfine splitting is criticized. (Auth.)

  15. Renormalization group equations with multiple coupling constants

    International Nuclear Information System (INIS)

    Ghika, G.; Visinescu, M.

    1975-01-01

    The main purpose of this paper is to study the renormalization group equations of a renormalizable field theory with multiple coupling constants. A method for the investigation of the asymptotic stability is presented. This method is applied to a gauge theory with Yukawa and self-quartic couplings of scalar mesons in order to find the domains of asymptotic freedom. An asymptotic expansion for the solutions which tend to the origin of the coupling constants is given

  16. Chaotic renormalization group approach to disordered systems

    International Nuclear Information System (INIS)

    Oliveira, P.M.C. de; Continentino, M.A.; Makler, S.S.; Anda, E.V.

    1984-01-01

    We study the eletronic properties of the disordered linear chain using a technique previously developed by some of the authors for an ordered chain. The equations of motion for the one electron Green function are obtained and the configuration average is done according to the GK scheme. The dynamical problem is transformed, using a renormalization group procedure, into a bidimensional map. The properties of this map are investigated and related to the localization properties of the eletronic system. (Author) [pt

  17. A shape dynamical approach to holographic renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Gomes, Henrique [University of California at Davis, Davis, CA (United States); Gryb, Sean [Utrecht University, Institute for Theoretical Physics, Utrecht (Netherlands); Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Koslowski, Tim [University of New Brunswick, Fredericton, NB (Canada); Mercati, Flavio; Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

    2015-01-01

    We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)

  18. Introduction to the nonequilibrium functional renormalization group

    International Nuclear Information System (INIS)

    Berges, J.; Mesterházy, D.

    2012-01-01

    In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.

  19. NLO renormalization in the Hamiltonian truncation

    Science.gov (United States)

    Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

    2017-09-01

    Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

  20. Exact renormalization group for gauge theories

    International Nuclear Information System (INIS)

    Balaban, T.; Imbrie, J.; Jaffe, A.

    1984-01-01

    Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study

  1. Renormalization and Interaction in Quantum Field Theory

    International Nuclear Information System (INIS)

    RATSIMBARISON, H.M.

    2008-01-01

    This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory. [fr

  2. The Physical Renormalization of Quantum Field Theories

    International Nuclear Information System (INIS)

    Binger, Michael William.; Stanford U., Phys. Dept.; SLAC

    2007-01-01

    The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, α(k 1 2 , k 2 2 , k 3 2 ), depends on three momentum scales and gives rise to an effective scale Q eff 2 (k 1 2 , k 2 2 , k 3 2 ) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green

  3. Renormalization of g-boson effects under weak coupling condition

    International Nuclear Information System (INIS)

    Zhang Zhanjun; Yang Jie; Liu Yong; Sang Jianping

    1998-01-01

    An approach based on perturbation theory is proposed to renormalized g-boson effects for sdgIBM system, which modifies that presented earlier by Druce et al. The weak coupling condition as the usage premise of the two approaches is proved to be satisfied. Two renormalization spectra are calculated for comparison and analyses. Results show that the g-boson effects are renormalized more completely by the approach proposed

  4. Renormalization group and fixed points in quantum field theory

    International Nuclear Information System (INIS)

    Hollowood, Timothy J.

    2013-01-01

    This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.

  5. Renormalization in general theories with inter-generation mixing

    International Nuclear Information System (INIS)

    Kniehl, Bernd A.; Sirlin, Alberto

    2011-11-01

    We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties. (orig.)

  6. Zeta Functions, Renormalization Group Equations, and the Effective Action

    International Nuclear Information System (INIS)

    Hochberg, D.; Perez-Mercader, J.; Molina-Paris, C.; Visser, M.

    1998-01-01

    We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley-DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action and use this to derive the leading logarithms in the one-loop effective action for arbitrary quantum field theories. copyright 1998 The American Physical Society

  7. On the renormalization group equations of quantum electrodynamics

    International Nuclear Information System (INIS)

    Hirayama, Minoru

    1980-01-01

    The renormalization group equations of quantum electrodynamics are discussed. The solution of the Gell-Mann-Low equation is presented in a convenient form. The interrelation between the Nishijima-Tomozawa equation and the Gell-Mann-Low equation is clarified. The reciprocal effective charge, so to speak, turns out to play an important role to discuss renormalization group equations. Arguments are given that the reciprocal effective charge vanishes as the renormalization momentum tends to infinity. (author)

  8. The Background-Field Method and Noninvariant Renormalization

    International Nuclear Information System (INIS)

    Avdeev, L.V.; Kazakov, D.I.; Kalmykov, M.Yu.

    1994-01-01

    We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional σ model it is demonstrated that the background-field method gives incorrect results when the regularization (and/or renormalization) is noninvariant. In particular, it is found that the cut-off regularization and the differential renormalization belong to this class and are incompatible with the background-field method in theories with nonlinear symmetries. 17 refs

  9. Renormalization in the complete Mellin representation of Feynman amplitudes

    International Nuclear Information System (INIS)

    Calan, C. de; David, F.; Rivasseau, V.

    1981-01-01

    The Feynmann amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM intergrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched. (orig.)

  10. Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics

    International Nuclear Information System (INIS)

    Heckathorn, D.

    1979-01-01

    Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)

  11. The two-loop renormalization of general quantum field theories

    International Nuclear Information System (INIS)

    Damme, R.M.J. van.

    1984-01-01

    This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)

  12. Scanning drop sensor

    Energy Technology Data Exchange (ETDEWEB)

    Jin, Jian; Xiang, Chengxiang; Gregoire, John

    2017-05-09

    Electrochemical experiments are performed on a collection of samples by suspending a drop of electrolyte solution between an electrochemical experiment probe and one of the samples that serves as a test sample. During the electrochemical experiment, the electrolyte solution is added to the drop and an output solution is removed from the drop. The probe and collection of samples can be moved relative to one another so the probe can be scanned across the samples.

  13. Scanning drop sensor

    Energy Technology Data Exchange (ETDEWEB)

    Jin, Jian; Xiang, Chengxiang; Gregoire, John M.; Shinde, Aniketa A.; Guevarra, Dan W.; Jones, Ryan J.; Marcin, Martin R.; Mitrovic, Slobodan

    2017-05-09

    Electrochemical or electrochemical and photochemical experiments are performed on a collection of samples by suspending a drop of electrolyte solution between an electrochemical experiment probe and one of the samples that serves as a test sample. During the electrochemical experiment, the electrolyte solution is added to the drop and an output solution is removed from the drop. The probe and collection of samples can be moved relative to one another so the probe can be scanned across the samples.

  14. Drop size measurements in Venturi scrubbers

    Energy Technology Data Exchange (ETDEWEB)

    Fernandez Alonso, D.; Azzopardi, B.J. [Nottingham Univ. (United Kingdom). Dept. of Chemical Engineering; Goncalves, J.A.S.; Coury, J.R. [Universidade Federal de Sao Carlos (Brazil). Departamento de Engenharia Quimica

    2001-07-01

    Venturi scrubbers are high efficiency gas cleaners in which suspended particles are removed from gas streams by drops formed by liquid atomisation, usually in the Venturi throat. The size of the drops formed are of fundamental importance to the performance of the equipment, both in terms of pressure drop and dust removal efficiency. In this study, drop sizes in a cylindrical laboratory-scale Venturi scrubber were measured using a laser diffraction technique. Gas velocity and liquid to gas ratios varied from 50 to 90 m/s and 0.5 to 2.0 1/m{sup 3}, respectively. Water was injected using two different arrangements: either as jets in the throat or as a film just upstream of the convergence. Drop size measurements were performed at three positions in the case of jet injection: two located along the throat, and the last one at the end of the diffuser. The present data shows that the Sauter mean diameter of the spray can be well correlated by the equation of Boll et al. (J. Air Pollut. Control Assoc. 24 (1974) 932). Drop size distributions are satisfactorily represented by a Rosin-Rammler function. This paper also provides a simple method for calculating the parameters of the Rosin-Rammler function. As a result of this work, drop sizes in Venturi scrubbers can be estimated with much higher accuracy. (Author)

  15. Renormalization group flows and continual Lie algebras

    International Nuclear Information System (INIS)

    Bakas, Ioannis

    2003-01-01

    We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by (d/dt;1), with anti-symmetric Cartan kernel K(t,t') = δ'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N vertical bar N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Baecklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra (d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown. (author)

  16. The evolution of Bogolyubov's renormalization group

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    2000-01-01

    We review the evolution of the concept of Renormalization Group (RG). This notion, as was first introduced in quantum field theory (QFT) in the mid-fifties in N.N.Bogolyubov's formulation, is based upon a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of a boundary condition) specifying some particular solution. To illustrate this approach's effectiveness, we end with its application to the analysis of the laser beam self-focusing in a non-linear medium

  17. Indefinite metric fields and the renormalization group

    International Nuclear Information System (INIS)

    Sherry, T.N.

    1976-11-01

    The renormalization group equations are derived for the Green functions of an indefinite metric field theory. In these equations one retains the mass dependence of the coefficient functions, since in the indefinite metric theories the masses cannot be neglected. The behavior of the effective coupling constant in the asymptotic and infrared limits is analyzed. The analysis is illustrated by means of a simple model incorporating indefinite metric fields. The model scales at first order, and at this order also the effective coupling constant has both ultra-violet and infra-red fixed points, the former being the bare coupling constant

  18. Zero point energy of renormalized Wilson loops

    International Nuclear Information System (INIS)

    Hidaka, Yoshimasa; Pisarski, Robert D.

    2009-01-01

    The quark-antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero when terms for extrinsic curvature are included. At one loop order, the nonperturbative contribution to the zero point energy is negative, regardless of the sign of the extrinsic curvature term.

  19. Perturbative and nonperturbative renormalization in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)

    2010-03-15

    We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)

  20. Axisymmetric Liquid Hanging Drops

    Science.gov (United States)

    Meister, Erich C.; Latychevskaia, Tatiana Yu

    2006-01-01

    The geometry of drops hanging on a circular capillary can be determined by numerically solving a dimensionless differential equation that is independent on any material properties, which enables one to follow the change of the height, surface area, and contact angle of drops hanging on a particular capillary. The results show that the application…

  1. Turbulence, bubbles and drops

    NARCIS (Netherlands)

    van der Veen, Roeland

    2016-01-01

    In this thesis, several questions related to drop impact and Taylor-Couette turbulence are answered. The deformation of a drop just before impact can cause a bubble to be entrapped. For many applications, such as inkjet printing, it is crucial to control the size of this entrapped bubble. To study

  2. Drop Tower Physics

    Science.gov (United States)

    Dittrich, William A.

    2014-01-01

    The drop towers of yesteryear were used to make lead shot for muskets, as described in "The Physics Teacher" in April 2012. However, modern drop towers are essentially elevators designed so that the cable can "break" on demand, creating an environment with microgravity for a short period of time, currently up to nine seconds at…

  3. Dynamics of deforming drops

    NARCIS (Netherlands)

    Bouwhuis, W.

    2015-01-01

    Liquid drops play a dominant role in numerous industrial applications, such as spray coating, spray painting, inkjet printing, lithography processes, and spraying/sprinkling in agriculture or gardening. In all of these examples, the generation, flight, impact, and spreading of drops are separate

  4. Critical asymmetry in renormalization group theory for fluids.

    Science.gov (United States)

    Zhao, Wei; Wu, Liang; Wang, Long; Li, Liyan; Cai, Jun

    2013-06-21

    The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.

  5. Renormalized plasma turbulence theory: A quasiparticle picture

    International Nuclear Information System (INIS)

    DuBois, D.F.

    1981-01-01

    A general renormalized statistical theory of Vlasov turbulence is given which proceeds directly from the Vlasov equation and does not assume prior knowledge of sophisticated field-theoretic techniques. Quasiparticles are the linear excitations of the turbulent system away from its instantaneous mean (ensemble-averaged) state or background; the properties of this background state ''dress'' or renormalize the quasiparticle responses. It is shown that all two-point responses (including the dielectric) and all two-point correlation functions can be completely described by the mean distribution function and three fundamental quantities. Two of these are the quasiparticle responses: the propagator and the potential source: which measure, respectively, the separate responses of the mean distribution function and the mean electrostatic potential to functional changes in an external phase-space source added to Vlasov's equation. The third quantity is the two-point correlation function of the incoherent part of the phase-space density which acts as a self-consistent source of quasiparticle and potential fluctuations. This theory explicitly takes into account the self-consistent nature of the electrostatic-field fluctuations which introduces new effects not found in the usual ''test-particle'' theories. Explicit equations for the fundamental quantities are derived in the direct interaction approximation. Special attention is paid to the two-point correlations and the relation to theories of phase-space granulation

  6. Optimal renormalization scales and commensurate scale relations

    International Nuclear Information System (INIS)

    Brodsky, S.J.; Lu, H.J.

    1996-01-01

    Commensurate scale relations relate observables to observables and thus are independent of theoretical conventions, such as the choice of intermediate renormalization scheme. The physical quantities are related at commensurate scales which satisfy a transitivity rule which ensures that predictions are independent of the choice of an intermediate renormalization scheme. QCD can thus be tested in a new and precise way by checking that the observables track both in their relative normalization and in their commensurate scale dependence. For example, the radiative corrections to the Bjorken sum rule at a given momentum transfer Q can be predicted from measurements of the e+e - annihilation cross section at a corresponding commensurate energy scale √s ∝ Q, thus generalizing Crewther's relation to non-conformal QCD. The coefficients that appear in this perturbative expansion take the form of a simple geometric series and thus have no renormalon divergent behavior. The authors also discuss scale-fixed relations between the threshold corrections to the heavy quark production cross section in e+e - annihilation and the heavy quark coupling α V which is measurable in lattice gauge theory

  7. The large-Nc renormalization group

    International Nuclear Information System (INIS)

    Dorey, N.

    1995-01-01

    In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N c , limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N c , selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N c . We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Λ -1 (Λ being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r ≤ Λ -1 . The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-Δ hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N c , renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as Λ → ∞

  8. Ultracold atoms and the Functional Renormalization Group

    International Nuclear Information System (INIS)

    Boettcher, Igor; Pawlowski, Jan M.; Diehl, Sebastian

    2012-01-01

    We give a self-contained introduction to the physics of ultracold atoms using functional integral techniques. Based on a consideration of the relevant length scales, we derive the universal effective low energy Hamiltonian describing ultracold alkali atoms. We then introduce the concept of the effective action, which generalizes the classical action principle to full quantum status and provides an intuitive and versatile tool for practical calculations. This framework is applied to weakly interacting degenerate bosons and fermions in the spatial continuum. In particular, we discuss the related BEC and BCS quantum condensation mechanisms. We then turn to the BCS-BEC crossover, which interpolates between both phenomena, and which is realized experimentally in the vicinity of a Feshbach resonance. For its description, we introduce the Functional Renormalization Group approach. After a general discussion of the method in the cold atoms context, we present a detailed and pedagogical application to the crossover problem. This not only provides the physical mechanism underlying this phenomenon. More generally, it also reveals how the renormalization group can be used as a tool to capture physics at all scales, from few-body scattering on microscopic scales, through the finite temperature phase diagram governed by many-body length scales, up to critical phenomena dictating long distance physics at the phase transition. The presentation aims to equip students at the beginning PhD level with knowledge on key physical phenomena and flexible tools for their description, and should enable to embark upon practical calculations in this field.

  9. Some applications of renormalized RPA in bosonic field theories

    International Nuclear Information System (INIS)

    Hansen, H.; Chanfray, G.

    2003-01-01

    We present some applications of the renormalized RPA in bosonic field theories. We first present some developments for the explicit calculation of the total energy in Φ 4 theory and discuss its phase structure in 1 + 1 dimensions. We also demonstrate that the Goldstone theorem is satisfied in the O(N) model within the renormalized RPA. (authors)

  10. Renormalization of loop functions for all loops

    International Nuclear Information System (INIS)

    Brandt, R.A.; Neri, F.; Sato, M.

    1981-01-01

    It is shown that the vacuum expectation values W(C 1 ,xxx, C/sub n/) of products of the traces of the path-ordered phase factors P exp[igcontour-integral/sub C/iA/sub μ/(x)dx/sup μ/] are multiplicatively renormalizable in all orders of perturbation theory. Here A/sub μ/(x) are the vector gauge field matrices in the non-Abelian gauge theory with gauge group U(N) or SU(N), and C/sub i/ are loops (closed paths). When the loops are smooth (i.e., differentiable) and simple (i.e., non-self-intersecting), it has been shown that the generally divergent loop functions W become finite functions W when expressed in terms of the renormalized coupling constant and multiplied by the factors e/sup -K/L(C/sub i/), where K is linearly divergent and L(C/sub i/) is the length of C/sub i/. It is proved here that the loop functions remain multiplicatively renormalizable even if the curves have any finite number of cusps (points of nondifferentiability) or cross points (points of self-intersection). If C/sub γ/ is a loop which is smooth and simple except for a single cusp of angle γ, then W/sub R/(C/sub γ/) = Z(γ)W(C/sub γ/) is finite for a suitable renormalization factor Z(γ) which depends on γ but on no other characteristic of C/sub γ/. This statement is made precise by introducing a regularization, or via a loop-integrand subtraction scheme specified by a normalization condition W/sub R/(C-bar/sub γ/) = 1 for an arbitrary but fixed loop C-bar/sub γ/. Next, if C/sub β/ is a loop which is smooth and simple except for a cross point of angles β, then W(C/sub β/) must be renormalized together with the loop functions of associated sets S/sup i//sub β/ = ]C/sup i/ 1 ,xxx, C/sup i//sub p/i] (i = 2,xxx,I) of loops C/sup i//sub q/ which coincide with certain parts of C/sub β/equivalentC 1 1 . Then W/sub R/(S/sup i//sub β/) = Z/sup i/j(β)W(S/sup j//sub β/) is finite for a suitable matrix Z/sup i/j

  11. On renormalization group flow in matrix model

    International Nuclear Information System (INIS)

    Gao, H.B.

    1992-10-01

    The renormalization group flow recently found by Brezin and Zinn-Justin by integrating out redundant entries of the (N+1)x(N+1) Hermitian random matrix is studied. By introducing explicitly the RG flow parameter, and adding suitable counter terms to the matrix potential of the one matrix model, we deduce some interesting properties of the RG trajectories. In particular, the string equation for the general massive model interpolating between the UV and IR fixed points turns out to be a consequence of RG flow. An ambiguity in the UV region of the RG trajectory is remarked to be related to the large order behaviour of the one matrix model. (author). 7 refs

  12. A renormalization group theory of cultural evolution

    Science.gov (United States)

    Fáth, Gábor; Sarvary, Miklos

    2005-03-01

    We present a theory of cultural evolution based upon a renormalization group scheme. We consider rational but cognitively limited agents who optimize their decision-making process by iteratively updating and refining the mental representation of their natural and social environment. These representations are built around the most important degrees of freedom of their world. Cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequate order parameter. As the importance of social interactions increases or agents become more intelligent, we observe and quantify a series of dynamic phase transitions by which cultural coherence advances in the society. A similar phase transition may explain the so-called “cultural explosion’’ in human evolution some 50,000 years ago.

  13. Renormalization group approach to soft gluon resummation

    International Nuclear Information System (INIS)

    Forte, Stefano; Ridolfi, Giovanni

    2003-01-01

    We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single dimensionful variable, and then using the renormalization group to resum them. Beyond the next-to-leading log level, our result is somewhat less predictive than previous all-order resummation formulae, but it does not rely on non-standard factorization, and it is thus possibly more general. We use our result to settle issues of convergence of the resummed series, we discuss scheme dependence at the resummed level, and we provide explicit resummed expressions in various factorization schemes

  14. Nonlinear relativistic plasma resonance: Renormalization group approach

    Energy Technology Data Exchange (ETDEWEB)

    Metelskii, I. I., E-mail: metelski@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: vfkvvfkv@gmail.com [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)

    2017-02-15

    An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

  15. The Renormalization Group in Nuclear Physics

    International Nuclear Information System (INIS)

    Furnstahl, R.J.

    2012-01-01

    Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.

  16. Functional renormalization and ultracold quantum gases

    International Nuclear Information System (INIS)

    Floerchinger, Stefan

    2010-01-01

    Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic properties and few-body phenomena as bound state formation or the Efimov effect. The non-perturbative treatment with renormalization group flow equations can account for all known limiting cases by solving one single equation. It improves previous results quantitatively and brings qualitatively new insights. As an example, new quantum phase transitions are found for fermions with three spin states. Ultracold atomic gases can be seen as an interesting model for features of high energy physics and for condensed matter theory. The research reported in this thesis helps to solve the difficult complexity problem in modern theoretical physics. (orig.)

  17. On truncations of the exact renormalization group

    CERN Document Server

    Morris, T R

    1994-01-01

    We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.

  18. Fermionic functional integrals and the renormalization group

    CERN Document Server

    Feldman, Joel; Trubowitz, Eugene

    2002-01-01

    This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...

  19. Semihard processes with BLM renormalization scale setting

    Energy Technology Data Exchange (ETDEWEB)

    Caporale, Francesco [Instituto de Física Teórica UAM/CSIC, Nicolás Cabrera 15 and U. Autónoma de Madrid, E-28049 Madrid (Spain); Ivanov, Dmitry Yu. [Sobolev Institute of Mathematics and Novosibirsk State University, 630090 Novosibirsk (Russian Federation); Murdaca, Beatrice; Papa, Alessandro [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, Arcavacata di Rende, I-87036 Cosenza (Italy)

    2015-04-10

    We apply the BLM scale setting procedure directly to amplitudes (cross sections) of several semihard processes. It is shown that, due to the presence of β{sub 0}-terms in the NLA results for the impact factors, the obtained optimal renormalization scale is not universal, but depends both on the energy and on the process in question. We illustrate this general conclusion considering the following semihard processes: (i) inclusive production of two forward high-p{sub T} jets separated by large interval in rapidity (Mueller-Navelet jets); (ii) high-energy behavior of the total cross section for highly virtual photons; (iii) forward amplitude of the production of two light vector mesons in the collision of two virtual photons.

  20. Large neutrino mixing from renormalization group evolution

    International Nuclear Information System (INIS)

    Balaji, K.R.S.; Mohapatra, R.N.; Parida, M.K.; Paschos, E.A.

    2000-10-01

    The renormalization group evolution equation for two neutrino mixing is known to exhibit nontrivial fixed point structure corresponding to maximal mixing at the weak scale. The presence of the fixed point provides a natural explanation of the observed maximal mixing of ν μ - ν τ , if the ν μ and ν τ are assumed to be quasi-degenerate at the seesaw scale without constraining the mixing angles at that scale. In particular, it allows them to be similar to the quark mixings as in generic grand unified theories. We discuss implementation of this program in the case of MSSM and find that the predicted mixing remains stable and close to its maximal value, for all energies below the O(TeV) SUSY scale. We also discuss how a particular realization of this idea can be tested in neutrinoless double beta decay experiments. (author)

  1. Renormalization and the breakup of magnetic surfaces

    International Nuclear Information System (INIS)

    Greene, J.M.

    1983-02-01

    There has been very considerable progress in the last few years on problems that are equivalent to finding the global structure of magnetic field lines in toroidal systems. A general problem of this class has a solution that is so complicated that it is impossible to find equations for the location of a field line which are valid everywhere along an infinitely long line. However, recent results are making it possible to find the asymptotic behavior of such systems in the limit of long lengths. This is just the information that is desired in many situations, since it includes the determination of the existence, or nonexistence, of magnetic surfaces. The key to our present understanding is renormalization. The present state-of-the-art has been described in Robert MacKay's thesis, for which this is an advertisement

  2. Renormalization group theory impact on experimental magnetism

    CERN Document Server

    Köbler, Ulrich

    2010-01-01

    Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are calle...

  3. Renormalization of NN scattering: Contact potential

    International Nuclear Information System (INIS)

    Yang Jifeng; Huang Jianhua

    2005-01-01

    The renormalization of the T matrix for NN scattering with a contact potential is re-examined in a nonperturbative regime through rigorous nonperturbative solutions. Based on the underlying theory, it is shown that the ultraviolet divergences in the nonperturbative solutions of the T matrix should be subtracted through 'endogenous' counterterms, which in turn leads to a nontrivial prescription dependence. Moreover, employing the effective range expansion, the importance of imposing physical boundary conditions to remove the nontrivial prescription dependence, especially before making any physical claims, is discussed and highlighted. As by-products, some relations between the effective range expansion parameters are derived. We also discuss the power counting of the couplings for the nucleon-nucleon interactions and other subtle points related to the EFT framework beyond perturbative treatment

  4. Gauge field theories. Part three. Renormalization

    International Nuclear Information System (INIS)

    Frampon, P.H.

    1978-01-01

    The renormalization of nonabelian gauge theories both with exact symmetry and with spontaneous symmetry breaking is discussed. The method of dimensional regularization is described and used in the ensuing discussion. Triangle anomalies and their implications and the method for cancellation of anomalies in an SU(2) x U(1) theory, introduction of the BRS form of local gauge transformation and its use for the iterative proof of renormalizability to all orders for pure Yang--Mills and with fermion and scalar matter fields are considered. Lastly for massive vectors arising from spontaneous breaking, the demonstration of renormalizability is given, using the 't Hooft gauges introduced first in 1971. While the treatment is not totally rigorous, all the principle steps are given. 108 references

  5. Renormalized semiclassical quantization for rescalable Hamiltonians

    International Nuclear Information System (INIS)

    Takahashi, Satoshi; Takatsuka, Kazuo

    2004-01-01

    A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum

  6. Non-perturbative renormalization on the lattice

    International Nuclear Information System (INIS)

    Koerner, Daniel

    2014-01-01

    Strongly-interacting theories lie at the heart of elementary particle physics. Their distinct behaviour shapes our world sui generis. We are interested in lattice simulations of supersymmetric models, but every discretization of space-time inevitably breaks supersymmetry and allows renormalization of relevant susy-breaking operators. To understand the role of such operators, we study renormalization group trajectories of the nonlinear O(N) Sigma model (NLSM). Similar to quantum gravity, it is believed to adhere to the asymptotic safety scenario. By combining the demon method with blockspin transformations, we compute the global flow diagram. In two dimensions, we reproduce asymptotic freedom and in three dimensions, asymptotic safety is demonstrated. Essential for these results is the application of a novel optimization scheme to treat truncation errors. We proceed with a lattice simulation of the supersymmetric nonlinear O(3) Sigma model. Using an original discretization that requires to fine tune only a single operator, we argue that the continuum limit successfully leads to the correct continuum physics. Unfortunately, for large lattices, a sign problem challenges the applicability of Monte Carlo methods. Consequently, the last chapter of this thesis is spent on an assessment of the fermion-bag method. We find that sign fluctuations are thereby significantly reduced for the susy NLSM. The proposed discretization finally promises a direct confirmation of supersymmetry restoration in the continuum limit. For a complementary analysis, we study the one-flavor Gross-Neveu model which has a complex phase problem. However, phase fluctuations for Wilson fermions are very small and no conclusion can be drawn regarding the potency of the fermion-bag approach for this model.

  7. Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

    Science.gov (United States)

    Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

    2015-12-01

    A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme—this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the ‘principle of maximum conformality’ (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the ‘principle of minimum sensitivity’ (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R e+e- and Γ(H\\to b\\bar{b}) up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on

  8. Renormalization method and singularities in the theory of Langmuir turbulence

    International Nuclear Information System (INIS)

    Pelletier, G.

    1977-01-01

    The method of renormalization, using propagators and diagrams, is recalled with enough mathematical details to be read and used by a non-specialist. The Markovian models are discussed and applied to plasma turbulence. The physical meaning of the diagrams is exhibited. In addition to the usual resonance broadening, an improved renormalization is set out, including broadening of the nonlinear resonance with a beat wave by induced scattering. This improved renormalization is emphasized. In the case of Langmuir turbulence, it removes difficulties arising at the group velocity, and enhances large-scale induced-scattering diffusion. (author)

  9. Renormalization group theory of phase transitions in square Ising systems

    International Nuclear Information System (INIS)

    Nienhuis, B.

    1978-01-01

    Some renormalization group calculations are presented on a number of phase transitions in a square Ising model, both second and first order. Of these transitions critical exponents are calculated, the amplitudes of the power law divergences and the locus of the transition. In some cases attention is paid to the thermodynamic functions also far from the critical point. Universality and scaling are discussed and the renormalization group theory is reviewed. It is shown how a renormalization transformation, which relates two similar systems with different macroscopic dimensions, can be constructed, and how some critical properties of the system follow from this transformation. Several numerical and analytical applications are presented. (Auth.)

  10. Phases of renormalized lattice gauge theories with fermions

    International Nuclear Information System (INIS)

    Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)

    1979-01-01

    Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory

  11. Cohomology and renormalization of BFYM theory in three dimensions

    International Nuclear Information System (INIS)

    Accardi, A.; Belli, A.; Zeni, M.

    1997-01-01

    The first-order formalism for the 3D Yang-Mills theory is considered and two different formulations are introduced, in which the gauge theory appears to be a deformation of the topological BF theory. We perform the quantization and the algebraic analysis of the renormalization of both the models, which are found to be anomaly free. We discuss also their stability against radiative corrections, giving the full structure of possible counterterms, requiring an involved matricial renormalization of fields and sources. Both models are then proved to be equivalent to the Yang-Mills theory at the renormalized level. (orig.)

  12. 75 FR 37311 - Airplane and Engine Certification Requirements in Supercooled Large Drop, Mixed Phase, and Ice...

    Science.gov (United States)

    2010-06-29

    ... level up to 30,000 feet. Appendix C defines icing cloud characteristics in terms of mean effective drop... that contain drops with mean effective diameters that are larger than the cloud mean effective drop... proposed. The benefits and costs are summarized below. The estimated benefits are $405.6 million ($99.5...

  13. Measurement of an Evaporating Drop on a Reflective Substrate

    Science.gov (United States)

    Chao, David F.; Zhang, Nengli

    2004-01-01

    A figure depicts an apparatus that simultaneously records magnified ordinary top-view video images and laser shadowgraph video images of a sessile drop on a flat, horizontal substrate that can be opaque or translucent and is at least partially specularly reflective. The diameter, contact angle, and rate of evaporation of the drop as functions of time can be calculated from the apparent diameters of the drop in sequences of the images acquired at known time intervals, and the shadowgrams that contain flow patterns indicative of thermocapillary convection (if any) within the drop. These time-dependent parameters and flow patterns are important for understanding the physical processes involved in the spreading and evaporation of drops. The apparatus includes a source of white light and a laser (both omitted from the figure), which are used to form the ordinary image and the shadowgram, respectively. Charge-coupled-device (CCD) camera 1 (with zoom) acquires the ordinary video images, while CCD camera 2 acquires the shadowgrams. With respect to the portion of laser light specularly reflected from the substrate, the drop acts as a plano-convex lens, focusing the laser beam to a shadowgram on the projection screen in front of CCD camera 2. The equations for calculating the diameter, contact angle, and rate of evaporation of the drop are readily derived on the basis of Snell s law of refraction and the geometry of the optics.

  14. Vacuum polarization and renormalized charge in ν-dimensions

    International Nuclear Information System (INIS)

    Marinho Junior, R.M.; Lucinda, J.

    1984-01-01

    The expression for the vacuum polarization is obtained for any momentum transfer in ν dimensions. Using the Wilson loop for QED, the renormalized electric charge in ν dimensions is calculated. (Author) [pt

  15. Exact renormalization group as a scheme for calculations

    International Nuclear Information System (INIS)

    Mack, G.

    1985-10-01

    In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)

  16. Propagators and renormalization transformations for lattice gauge theories. Pt. 2

    International Nuclear Information System (INIS)

    Balaban, T.

    1984-01-01

    We continue the studies of the Paper I and extend the results of this paper to operators defined by restrictions on different scales, or by renormalization transformations of different orders. (orig.)

  17. Renormalization and operator product expansion in theories with massless particles

    International Nuclear Information System (INIS)

    Anikin, S.A.; Smirnov, V.A.

    1985-01-01

    Renormalization procedure in theories including massless particles is presented. With the help of counterterm formalism the operator product expansion for arbitrary composite fields is derived. The coefficient functions are explicitly expressed in terms of certain Green's functions. (author)

  18. Generalized Callan-Symanzik equations and the Renormalization Group

    International Nuclear Information System (INIS)

    MacDowell, S.W.

    1975-01-01

    A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg

  19. Noncommutative quantum field theory: attempts on renormalization

    International Nuclear Information System (INIS)

    Popp, L.

    2002-05-01

    Quantum field theory is the art of dealing with problems at small distances or, equivalently, large momenta. Although there are different approaches (string theory, for example), it is generally accepted that these principles cannot be extrapolated to arbitrarily small distances as can be shown by applying simple, heuristic arguments. Therefore, the concept of space-time as a differential manifold has to be replaced by something else at such scales, the road we have chosen to follow is noncommutative geometry. We start from the basic relation [ x μ , x ν ] = i θ { μν}, where θ is a (usually) constant, antisymmetric matrix. This relation amounts to a noncommutativity of position measurements, or, put differently, the points are somehow 'smeared' out, which should have a positive effect on field theory since infinities arise from point-like interactions. However, it was shown that the effects of the commutation relation (leading to the so-called Moyal product) do not necessarily cure the divergences but introduce a new kind of problem: whereas UV-divergent integrals are rendered finite by phase factors (that arise as a consequence of the Moyal product), this same kind of 'regularization' introduces IR-divergences which led to the name 'UV/IR-mixing' for this problem. In order to overcome this peculiarity, one expands the action in θ which is immediate for the phase factors but requires the so-called Seiberg-Witten map for the fields. In this thesis, we emphasize the derivation of the Seiberg-Witten map by using noncommutative Lorentz symmetries, which is more general than the original derivation. After that, we concentrate on a treatment of θ-expanded theories and their renormalization, where it can be shown that the photon self-energy of noncommutative Maxwell theory can be renormalized to all orders in hbar and θ when the freedom in the Seiberg-Witten map (there are ambiguities in the map) is exploited. Although this is very promising, it cannot be

  20. Renormalization of the QEMD of a dyon field

    International Nuclear Information System (INIS)

    Panagiotakopoulos, C.

    1983-01-01

    A renormalized quantum electromagnetodynamics (QEMD) of a dyon field is defined. Finite and n-independent answers can be obtained in each order of the loop expansion for all processes. The electric and magnetic charges are not constrained with the Dirac condition and therefore perturbation theory can be made reliable. The renormalized theory is found to possess exact dual invariance. Comparisons with the general QEMD of electric and magnetic charges are made. (orig.)

  1. Renormalization of the QEMD of a dyon field

    International Nuclear Information System (INIS)

    Panagiotakopoulos, C.

    1982-05-01

    A renormalized quantum electromagnetodynamics (QEMD) of a dyon field is defined. Finite and n independent answers can be obtained in each order of the loop expansion for all processes. The electric and magnetic charges are not constrained with the Dirac condition and therefore perturbation theory can be made reliable. The renormalized theory is found to possess exact dual invariance. Comparisons with the general QEMD of electric and magnetic charges are made. (author)

  2. Non-perturbative versus perturbative renormalization of lattice operators

    International Nuclear Information System (INIS)

    Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.

    1995-09-01

    Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)

  3. Renormalization of the g-boson effects for Os isotopes

    International Nuclear Information System (INIS)

    Zhang Zhanjun; Liu Yong; Sang Jianping

    1996-01-01

    A modified renormalization approach based on that proposed by Druce et al. is presented. The overall agreement between the spectra calculated here and the accurate spectra is significantly improved. We also use Druce's approach to generate the renormalized spectra. It is shown that in our microscopic study, both of the approaches are very useful to the determination of several free parameters of fermion residual interactions

  4. The renormalization group: scale transformations and changes of scheme

    International Nuclear Information System (INIS)

    Roditi, I.

    1983-01-01

    Starting from a study of perturbation theory, the renormalization group is expressed, not only for changes of scale but also within the original view of Stueckelberg and Peterman, for changes of renormalization scheme. The consequences that follow from using that group are investigated. Following a more general point of view a method to obtain an improvement of the perturbative results for physical quantities is proposed. The results obtained with this method are compared with those of other existing methods. (L.C.) [pt

  5. Anisotropic square lattice Potts ferromagnet: renormalization group treatment

    International Nuclear Information System (INIS)

    Oliveira, P.M.C. de; Tsallis, C.

    1981-01-01

    The choice of a convenient self-dual cell within a real space renormalization group framework enables a satisfactory treatment of the anisotropic square lattice q-state Potts ferromagnet criticality. The exact critical frontier and dimensionality crossover exponent PHI as well as the expected universality behaviour (renormalization flow sense) are recovered for any linear scaling factor b and all values of q(q - [pt

  6. Renormalization in p-adic quantum field theory

    International Nuclear Information System (INIS)

    Smirnov, V.A.

    1990-01-01

    A version of p-adic perturbative Euclidean quantum field theory is presented. It is based on the new type of propagator which happens to be rather natural for p-adic space-time. Low-order Feynamn diagrams are explicity calculated and typical renormalization schemes are introduced: analytic, dimensional and BPHZ renormalizations. The calculations show that in p-adic Feynman integrals only logarithmic divergences appear. 14 refs.; 1 fig

  7. Products of composite operators in the exact renormalization group formalism

    Science.gov (United States)

    Pagani, C.; Sonoda, H.

    2018-02-01

    We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

  8. Non-perturbative renormalization of HQET and QCD

    International Nuclear Information System (INIS)

    Sommer, Rainer

    2003-01-01

    We discuss the necessity of non-perturbative renormalization in QCD and HQET and explain the general strategy for solving this problem. A few selected topics are discussed in some detail, namely the importance of off shell improvement in the MOM-scheme on the lattice, recent progress in the implementation of finite volume schemes and then particular emphasis is put on the recent idea to carry out a non-perturbative renormalization of the Heavy Quark Effective Theory (HQET)

  9. A note on nonperturbative renormalization of effective field theory

    Energy Technology Data Exchange (ETDEWEB)

    Yang Jifeng [Department of Physics, East China Normal University, Shanghai 200062 (China)

    2009-08-28

    Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.

  10. A note on nonperturbative renormalization of effective field theory

    International Nuclear Information System (INIS)

    Yang Jifeng

    2009-01-01

    Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.

  11. Renormalization of an abelian gauge theory in stochastic quantization

    International Nuclear Information System (INIS)

    Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.

    1987-01-01

    The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)

  12. Investigation of renormalization effects in high temperature cuprate superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Zabolotnyy, Volodymyr B.

    2008-04-16

    It has been found that the self-energy of high-T{sub C} cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} and YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T{sub C} suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

  13. Investigation of renormalization effects in high temperature cuprate superconductors

    International Nuclear Information System (INIS)

    Zabolotnyy, Volodymyr B.

    2008-01-01

    It has been found that the self-energy of high-T C cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi 2 Sr 2 CaCu 2 O 8+δ and YBa 2 Cu 3 O 7-δ were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T C suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

  14. Technical fine-tuning problem in renormalized perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E.

    1983-01-01

    The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

  15. Technical fine-tuning problem in renormalized perturbation theory

    International Nuclear Information System (INIS)

    Foda, O.E.

    1983-01-01

    The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes

  16. Renormalization group analysis of a simple hierarchical fermion model

    International Nuclear Information System (INIS)

    Dorlas, T.C.

    1991-01-01

    A simple hierarchical fermion model is constructed which gives rise to an exact renormalization transformation in a 2-dimensional parameter space. The behaviour of this transformation is studied. It has two hyperbolic fixed points for which the existence of a global critical line is proven. The asymptotic behaviour of the transformation is used to prove the existence of the thermodynamic limit in a certain domain in parameter space. Also the existence of a continuum limit for these theories is investigated using information about the asymptotic renormalization behaviour. It turns out that the 'trivial' fixed point gives rise to a two-parameter family of continuum limits corresponding to that part of parameter space where the renormalization trajectories originate at this fixed point. Although the model is not very realistic it serves as a simple example of the appliclation of the renormalization group to proving the existence of the thermodynamic limit and the continuum limit of lattice models. Moreover, it illustrates possible complications that can arise in global renormalization group behaviour, and that might also be present in other models where no global analysis of the renormalization transformation has yet been achieved. (orig.)

  17. Aspects of renormalization in finite-density field theory

    Energy Technology Data Exchange (ETDEWEB)

    Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia

    2015-05-26

    We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

  18. Quantum field theory and phase transitions: universality and renormalization group

    International Nuclear Information System (INIS)

    Zinn-Justin, J.

    2003-08-01

    In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)

  19. Nonperturbative Renormalization of Composite Operators with Overlap Fermions

    Energy Technology Data Exchange (ETDEWEB)

    J.B. Zhang; N. Mathur; S.J. Dong; T. Draper; I. Horvath; F. X. Lee; D.B. Leinweber; K.F. Liu; A.G. Williams

    2005-12-01

    We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

  20. Two secondary drops

    Indian Academy of Sciences (India)

    Figure shows formation of two secondary drops of unequal size and their merger. The process is same as the earlier process until t= 0.039 Tc with necking occurring at two places, one at the bottom of the column and the other at the middle. The necking at the middle of the liquid column is due to Raleigh instability.

  1. Lambda-dropping

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    1997-01-01

    Lambda-lifting a functional program transforms it into a set of recursive equations. We present the symmetric transformation: lambda-dropping. Lambda-dropping a set of recursive equations restores block structure and lexical scope.For lack of scope, recursive equations must carry around all...... the parameters that any of their callees might possibly need. Both lambda-lifting and lambda-dropping thus require one to compute a transitive closure over the call graph:• for lambda-lifting: to establish the Def/Use path of each free variable (these free variables are then added as parameters to each...... of the functions in the call path);• for lambda-dropping: to establish the Def/Use path of each parameter (parameters whose use occurs in the same scope as their definition do not need to be passed along in the call path).Without free variables, a program is scope-insensitive. Its blocks are then free...

  2. Marangoni Flow Induced Evaporation Enhancement on Binary Sessile Drops.

    Science.gov (United States)

    Chen, Pin; Harmand, Souad; Ouenzerfi, Safouene; Schiffler, Jesse

    2017-06-15

    The evaporation processes of pure water, pure 1-butanol, and 5% 1-butanol aqueous solution drops on heated hydrophobic substrates are investigated to determine the effect of temperature on the drop evaporation behavior. The evolution of the parameters (contact angle, diameter, and volume) during evaporation measured using a drop shape analyzer and the infrared thermal mapping of the drop surface recorded by an infrared camera were used in investigating the evaporation process. The pure 1-butanol drop does not show any thermal instability at different substrate temperatures, while the convection cells created by the thermal Marangoni effect appear on the surface of the pure water drop from 50 °C. Because 1-butanol and water have different surface tensions, the infrared video of the 5% 1-butanol aqueous solution drop shows that the convection cells are generated by the solutal Marangoni effect at any substrate temperature. Furthermore, when the substrate temperature exceeds 50 °C, coexistence of the thermal and solutal Marangoni flows is observed. By analyzing the relation between the ratio of the evaporation rate of pure water and 1-butanol aqueous solution drops and the Marangoni number, a series of empirical equations for predicting the evaporation rates of pure water and 1-butanol aqueous solution drops at the initial time as well as the equations for the evaporation rate of 1-butanol aqueous solution drop before the depletion of alcohol are derived. The results of these equations correspond fairly well to the experimental data.

  3. Renormalizations and operator expansion in sigma model

    International Nuclear Information System (INIS)

    Terentyev, M.V.

    1988-01-01

    The operator expansion (OPE) is studied for the Green function at x 2 → 0 (n(x) is the dynamical field ofσ-model) in the framework of the two-dimensional σ-model with the O(N) symmetry group at large N. As a preliminary step we formulate the renormalization scheme which permits introduction of an arbitrary intermediate scale μ 2 in the framework of 1/N expansion and discuss factorization (separation) of small (p μ) momentum region. It is shown that definition of composite local operators and coefficient functions figuring in OPE is unambiguous only in the leading order in 1/N expansion when dominant are the solutions with extremum of action. Corrections of order f(μ 2 )/N (here f(μ 2 ) is the effective interaction constant at the point μ 2 ) in composite operators and coefficient functions essentially depend on factorization method of high and low momentum regions. It is shown also that contributions to the power corrections of order m 2 x 2 f(μ 2 )/N in the Green function (here m is the dynamical mass-scale factor in σ-model) arise simultaneously from two sources: from the mean vacuum value of the composite operator n ∂ 2 n and from the hard particle contributions in the coefficient function of unite operator. Due to the analogy between σ-model and QCD the obtained result indicates theoretical limitations to the sum rule method in QCD. (author)

  4. Functional renormalization group methods in quantum chromodynamics

    International Nuclear Information System (INIS)

    Braun, J.

    2006-01-01

    We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

  5. Block generators for the similarity renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Huether, Thomas; Roth, Robert [TU Darmstadt (Germany)

    2016-07-01

    The Similarity Renormalization Group (SRG) is a powerful tool to improve convergence behavior of many-body calculations using NN and 3N interactions from chiral effective field theory. The SRG method decouples high and low-energy physics, through a continuous unitary transformation implemented via a flow equation approach. The flow is determined by a generator of choice. This generator governs the decoupling pattern and, thus, the improvement of convergence, but it also induces many-body interactions. Through the design of the generator we can optimize the balance between convergence and induced forces. We explore a new class of block generators that restrict the decoupling to the high-energy sector and leave the diagonalization in the low-energy sector to the many-body method. In this way one expects a suppression of induced forces. We analyze the induced many-body forces and the convergence behavior in light and medium-mass nuclei in No-Core Shell Model and In-Medium SRG calculations.

  6. Renormalization group approach to superfluid neutron matter

    Energy Technology Data Exchange (ETDEWEB)

    Hebeler, K.

    2007-06-06

    In the present thesis superfluid many-fermion systems are investigated in the framework of the Renormalization Group (RG). Starting from an experimentally determined two-body interaction this scheme provides a microscopic approach to strongly correlated many-body systems at low temperatures. The fundamental objects under investigation are the two-point and the four-point vertex functions. We show that explicit results for simple separable interactions on BCS-level can be reproduced in the RG framework to high accuracy. Furthermore the RG approach can immediately be applied to general realistic interaction models. In particular, we show how the complexity of the many-body problem can be reduced systematically by combining different RG schemes. Apart from technical convenience the RG framework has conceptual advantage that correlations beyond the BCS level can be incorporated in the flow equations in a systematic way. In this case however the flow equations are no more explicit equations like at BCS level but instead a coupled set of implicit equations. We show on the basis of explicit calculations for the single-channel case the efficacy of an iterative approach to this system. The generalization of this strategy provides a promising strategy for a non-perturbative treatment of the coupled channel problem. By the coupling of the flow equations of the two-point and four-point vertex self-consistency on the one-body level is guaranteed at every cutoff scale. (orig.)

  7. Renormalization-group theory of spinodal decomposition

    International Nuclear Information System (INIS)

    Mazenko, G.F.; Valls, O.T.; Zhang, F.C.

    1985-01-01

    Renormalization-group (RG) methods developed previously for the study of the growth of order in unstable systems are extended to treat the spinodal decomposition of the two-dimensional spin-exchange kinetic Ising model. The conservation of the order parameter and fixed-length sum rule are properly preserved in the theory. Various correlation functions in both coordinate and momentum space are calculated as functions of time. The scaling function for the structure factor is extracted. We compare our results with direct Monte Carlo (MC) simulations and find them in good agreement. The time rescaling parameter entering the RG analysis is temperature dependent, as was determined in previous work through a RG analysis of MC simulations. The results exhibit a long-time logarithmic growth law for the typical domain size, both analytically and numerically. In the time region where MC simulations have previously been performed, the logarithmic growth law can be fitted to a power law with an effective exponent. This exponent is found to be in excellent agreement with the result of MC simulations. The logarithmic growth law agrees with a physical model of interfacial motion which involves an interplay between the local curvature and an activated jump across the interface

  8. Functional renormalization group methods in quantum chromodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Braun, J.

    2006-12-18

    We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

  9. Nonperturbative Renormalization Group Approach to Polymerized Membranes

    Science.gov (United States)

    Essafi, Karim; Kownacki, Jean-Philippe; Mouhanna, Dominique

    2014-03-01

    Membranes or membrane-like materials play an important role in many fields ranging from biology to physics. These systems form a very rich domain in statistical physics. The interplay between geometry and thermal fluctuations lead to exciting phases such flat, tubular and disordered flat phases. Roughly speaking, membranes can be divided into two group: fluid membranes in which the molecules are free to diffuse and thus no shear modulus. On the other hand, in polymerized membranes the connectivity is fixed which leads to elastic forces. This difference between fluid and polymerized membranes leads to a difference in their critical behaviour. For instance, fluid membranes are always crumpled, whereas polymerized membranes exhibit a phase transition between a crumpled phase and a flat phase. In this talk, I will focus only on polymerized phantom, i.e. non-self-avoiding, membranes. The critical behaviour of both isotropic and anisotropic polymerized membranes are studied using a nonperturbative renormalization group approach (NPRG). This allows for the investigation of the phase transitions and the low temperature flat phase in any internal dimension D and embedding d. Interestingly, graphene behaves just as a polymerized membrane in its flat phase.

  10. Slowest kinetic modes revealed by metabasin renormalization

    Science.gov (United States)

    Okushima, Teruaki; Niiyama, Tomoaki; Ikeda, Kensuke S.; Shimizu, Yasushi

    2018-02-01

    Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the relaxation modes are determined by diagonalizing its transition rate matrix. However, for realistic systems of interest, numerical diagonalization, as well as extracting physical understanding from the diagonalization results, is difficult due to the high dimensionality. Here, we develop an alternative and generally applicable method of extracting the long-time scale relaxation dynamics by combining the metabasin analysis of Okushima et al. [Phys. Rev. E 80, 036112 (2009), 10.1103/PhysRevE.80.036112] and a Jacobi method. We test the method on an illustrative model of a four-funnel model, for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely. The method is successfully applied to the vacancy transport problem in ionic nanoparticles [Niiyama et al., Chem. Phys. Lett. 654, 52 (2016), 10.1016/j.cplett.2016.04.088], allowing a clear physical interpretation that the final relaxation consists of two successive, characteristic processes.

  11. Effects of Evaporation/Condensation on Spreading and Contact Angle of a Volatile Liquid Drop

    Science.gov (United States)

    Zhang, Nengli; Chao, David F.; Singh, Bhim S. (Technical Monitor)

    2000-01-01

    Effects of evaporation/condensation on spreading and contact angle were experimentally studied. A sessile drop of R-113 was tested at different vapor environments to determine the effects of evaporation/condensation on the evolution of contact diameter and contact angle of the drop. Condensation on the drop surface occurs at both the saturated and a nonsaturated vapor environments and promotes the spreading. When the drop is placed in the saturated vapor environment it tends to completely wetting and spreads rapidly. In a nonsaturated vapor environment, the evolution of the sessile drop is divided three stages: condensation-spreading stage, evaporation-retracting stage and rapid contracting stage. In the first stage the drop behaves as in the saturated environment. In the evaporation -retracting stage, the competition between spreading and evaporation of the drop determines the evolution characteristics of the contact diameter and the contact angle. A lower evaporation rate struggles against the spreading power to turn the drop from spreading to retracting with a continuous increase of the contact angle. The drop placed in open air has a much higher evaporation rate. The strong evaporation suppresses the spreading and accelerates the retraction of the drop with a linear decrease of the contact diameter. The contraction of the evaporating drops is gradually accelerated when the contact diameter decreases to 3 min and less till drying up, though the evaporation rate is gradually slowing down.

  12. Electrostatic charging and levitation of helium II drops

    International Nuclear Information System (INIS)

    Niemela, J.J.

    1997-01-01

    Liquid Helium II drops, of diameter 1 mm or less, are charged with positive helium ions and subsequently levitated by static electric fields. Stable levitation was achieved for drops of order 100-150 micrometers in diameter. The suspended drops could be translated to arbitrary positions within the levitator using additional superimposed DC electric fields, and also could be made to oscillate stably about their average positions by means of an applied time-varying electric field. A weak corona discharge was used to produce the necessary ions for levitation. A novel superfluid film flow device, developed for the controlled deployment of large charged drops, is described. Also discussed is an adjustable electric fountain that requires only a field emission tip operating at modest potentials, and works in both Helium I and Helium II

  13. Film behaviour of vertical gas-liquid flow in a large diameter pipe

    OpenAIRE

    Zangana, Mohammed Haseeb Sedeeq

    2011-01-01

    Gas-liquid flow commonly occurs in oil and gas production and processing system. Large diameter vertical pipes can reduce pressure drops and so minimize operating costs. However, there is a need for research on two-phase flow in large diameter pipes to provide confidence to designers of equipments such as deep water risers. In this study a number of experimental campaigns were carried out to measure pressure drop, liquid film thickness and wall shear in 127mm vertical pipe. Total pressur...

  14. Tensor hypercontraction. II. Least-squares renormalization

    Science.gov (United States)

    Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

    2012-12-01

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

  15. Analysis of coined quantum walks with renormalization

    Science.gov (United States)

    Boettcher, Stefan; Li, Shanshan

    2018-01-01

    We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.

  16. The applications of the renormalization group

    International Nuclear Information System (INIS)

    Hughes, J.L.

    1988-01-01

    Three applications of the exact renormalization group (RG) to field theory and string theory are developed. (1) First, β-functions are related to the flow of the relevant couplings in the exact RG. The specific case of a cutoff λφ 4 theory in four dimensions is discussed in detail. The underlying idea of convergence of the flow of effective lagrangians is developed to identify the β-functions. A perturbative calculations of the β-functions using the exact flow equations is then sketched. (2) Next, the operator product expansion (OPE) is motivated and developed within the context of effective lagrangians. The exact RG may be used to establish the asymptotic properties of the expansion. Again, the example field theory focused upon is a cutoff λφ 4 in four dimensions. A detailed proof of the asymptotics for the special case of the expansion of φ(χ)φ(0) is given. The ideas of the proof are sufficient to prove the general case of any two local operators. Although both of the above applications are developed for a cutoff λφ 4 , the analysis may be extended to any theory with a physical cutoff. (3) Finally, some consequences of the proposal by Banks and Martinec that the classical string field equation can be written as as exact RG equation are examined. Cutoff conformal field theories on the sphere are identified as possible string field configurations. The Wilson fixed-point equation is generalized to conformal invariance and then taken to be the equation of motion for the string field. The equation's solutions for a restricted set of configurations are examined - namely, closed bosonic strings in 26 dimensions. Tree-level Virasoro-Shapiro (VS) S-matrix elements emerge in what is interpreted as a weak component-field expansion of the solution

  17. Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD

    CERN Document Server

    Guagnelli, M; Peña, C; Sint, S; Vladikas, A

    2006-01-01

    We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\\Delta F = 1$ and $\\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.

  18. Building micro-soccer-balls with evaporating colloidal fakir drops

    Science.gov (United States)

    Gelderblom, Hanneke; Marín, Álvaro G.; Susarrey-Arce, Arturo; van Housselt, Arie; Lefferts, Leon; Gardeniers, Han; Lohse, Detlef; Snoeijer, Jacco H.

    2013-11-01

    Drop evaporation can be used to self-assemble particles into three-dimensional microstructures on a scale where direct manipulation is impossible. We present a unique method to create highly-ordered colloidal microstructures in which we can control the amount of particles and their packing fraction. To this end, we evaporate colloidal dispersion drops from a special type of superhydrophobic microstructured surface, on which the drop remains in Cassie-Baxter state during the entire evaporative process. The remainders of the drop consist of a massive spherical cluster of the microspheres, with diameters ranging from a few tens up to several hundreds of microns. We present scaling arguments to show how the final particle packing fraction of these balls depends on the drop evaporation dynamics, particle size, and number of particles in the system.

  19. Gauge-independent renormalization of the N2HDM

    Science.gov (United States)

    Krause, Marcel; López-Val, David; Mühlleitner, Margarete; Santos, Rui

    2017-12-01

    The Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) is an interesting benchmark model for a Higgs sector consisting of two complex doublet and one real singlet fields. Like the Next-to-Minimal Supersymmetric extension (NMSSM) it features light Higgs bosons that could have escaped discovery due to their singlet admixture. Thereby, the model allows for various different Higgs-to-Higgs decay modes. Contrary to the NMSSM, however, the model is not subject to supersymmetric relations restraining its allowed parameter space and its phenomenology. For the correct determination of the allowed parameter space, the correct interpretation of the LHC Higgs data and the possible distinction of beyond-the-Standard Model Higgs sectors higher order corrections to the Higgs boson observables are crucial. This requires not only their computation but also the development of a suitable renormalization scheme. In this paper we have worked out the renormalization of the complete N2HDM and provide a scheme for the gauge-independent renormalization of the mixing angles. We discuss the renormalization of the Z_2 soft breaking parameter m 12 2 and the singlet vacuum expectation value v S . Both enter the Higgs self-couplings relevant for Higgs-to-Higgs decays. We apply our renormalization scheme to different sample processes such as Higgs decays into Z bosons and decays into a lighter Higgs pair. Our results show that the corrections may be sizable and have to be taken into account for reliable predictions.

  20. G-Boson renormalizations and mixed symmetry states

    International Nuclear Information System (INIS)

    Scholten, O.

    1986-01-01

    In the IBA model the low-lying collective states are described in terms of a system of interacting s- and d-bosons. A boson can be interpreted as corresponding to collective J=0 or J=2 fermion pair states. As such the IBA model space can be seen as only a small subsector of the full shell model space. For medium heavy nuclei such a truncation of the model space is necessary to make calculations feasible. As is well known truncations of a model space make it necessary to renormalize the model parameters. In this work some renormalizations of the Hamiltonian and the E2 transition operator will be discussed. Special attention will be given to the implication of these renormalizations for the properties of mixed symmetry states. The effects of renormalization are obtained by considering the influence of fermion pair states that have been omitted from the model basis. Here the authors focus attention on the effect of the low-lying two particle J=4 state, referred to as g-boson or G-pair state. Renormalizations of the d-boson energy, the E2 effective charges, and symmetry force are discussed

  1. Impact of water drops on small targets

    Science.gov (United States)

    Rozhkov, A.; Prunet-Foch, B.; Vignes-Adler, M.

    2002-10-01

    The collision of water drops against small targets was studied experimentally by means of a high-speed photography technique. The drop impact velocity was about 3.5 m/s. Drop diameters were in the range of 2.8-4.0 mm. The target was a stainless steel disk of 3.9 mm diameter. The drop spread beyond the target like a central cap surrounded by a thin, slightly conical lamella bounded by a thicker rim. By mounting a small obstacle near the target, surface-tension driven Mach waves in the flowing lamella were generated, which are formally equivalent to the familiar compressibility driven Mach waves in gas dynamics. From the measurement of the Mach angle, the values of some flow parameters could be obtained as functions of time, which provided insight into the flow structure. The liquid flowed from the central cap to the liquid rim through the thin lamella at constant momentum flux. At a certain stage of the process, most of the liquid accumulated in the rim and the internal part of the lamella became metastable. In this situation, a rupture wave propagating through the metastable internal part of the lamella caused the rim to retract while forming outwardly directed secondary jets. The jets disintegrated into secondary droplets due to the Savart-Plateau-Rayleigh instability. Prior to the end of the retraction, an internal circular wave of rupture was formed. It originated at the target and then it propagated to meet the retracting rim. Their meeting resulted in a crown of tiny droplets. A theoretical analysis of the ejection process is proposed.

  2. Off-shell renormalization in Higgs effective field theories

    Science.gov (United States)

    Binosi, Daniele; Quadri, Andrea

    2018-04-01

    The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ˜ {({Φ}^{\\dagger}Φ -υ^2/2)}^N with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.

  3. Wetting transitions: A functional renormalization-group approach

    International Nuclear Information System (INIS)

    Fisher, D.S.; Huse, D.A.

    1985-01-01

    A linear functional renormalization group is introduced as a framework in which to treat various wetting transitions of films on substrates. A unified treatment of the wetting transition in three dimensions with short-range interactions is given. The results of Brezin, Halperin, and Leibler in their three different regimes are reproduced along with new results on the multicritical behavior connecting the various regimes. In addition, the critical behavior as the coexistence curve is approached at complete wetting is analyzed. Wetting in the presence of long-range substrate-film interactions that fall off as power laws is also studied. The possible effects of the nonlinear terms in the renormalization group are examined briefly and it appears that they do not alter the critical behavior found using the truncated linear renormalization group

  4. Non-perturbative renormalization of three-quark operators

    Energy Technology Data Exchange (ETDEWEB)

    Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Kaltenbrunner, Thomas [Regensburg Univ. (DE). Inst. fuer Theoretische Physik] (and others)

    2008-10-15

    High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS scheme at {mu}=2 GeV. (orig.)

  5. The ab-initio density matrix renormalization group in practice.

    Science.gov (United States)

    Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

    2015-01-21

    The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

  6. The ab-initio density matrix renormalization group in practice

    Energy Technology Data Exchange (ETDEWEB)

    Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Nakatani, Naoki [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Catalysis Research Center, Hokkaido University, Kita 21 Nishi 10, Sapporo, Hokkaido 001-0021 (Japan)

    2015-01-21

    The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

  7. Extended BPH renormalization of cutoff scalar field theories

    International Nuclear Information System (INIS)

    Chalmers, G.

    1996-01-01

    We show through the use of diagrammatic techniques and a newly adapted BPH renormalization method that general momentum cutoff scalar field theories in four dimensions are perturbatively renormalizable. Weinberg close-quote s convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. The naive use of the convergence theorem together with the BPH method is not appropriate for understanding the local divergences and renormalizability of these theories. We also show that the renormalized Green close-quote s functions are the same as in ordinary Φ 4 theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group. copyright 1996 The American Physical Society

  8. Renormalization group and the superconducting susceptibility of a Fermi liquid

    International Nuclear Information System (INIS)

    Parameswaran, S. A.; Sondhi, S. L.; Shankar, R.

    2010-01-01

    A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.

  9. Renormalization Group in different fields of theoretical physics

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    1992-02-01

    A very simple and general approach to the symmetry that is widely known as a Renormalization Group symmetry is presented. It essentially uses a functional formulation of group transformations that can be considered as a generalization of self-similarity transformations well known in mathematical physics since last century. This generalized Functional Self-Similarity symmetry and corresponding group transformations are discussed first for a number of simple physical problems taken from diverse fields of classical physics as well as for QED. Then we formulate the Renorm-Group Method as a regular procedure that essentially improves the approximate solutions near the singularity. After that we discuss relations between different formulations of Renormalization Group as they appear in various parts of a modern theoretical physics. Finally we present several topics of RGM application in modern QFT. (author)

  10. Fission tracks diameters in glasses

    International Nuclear Information System (INIS)

    Garzon Ruiperez, L.; Veiguela, J.

    1974-01-01

    Standard glass microscope slides have been irradiated with fission fragments from the uranium. The etching track conditions have been the same for the series, having changed the etching time only for each specimen. For each glass, a minimum of 250 measurements of the tracks diameters have been made, the distributions of which are the bimodal type. Diameters-etching dependence with time is roughly lineal. Energy determinations have been made with the help of the diameters-energy relations. The calculated values agree very well with the know ones. (author) [es

  11. On the performance of small diameter gas cyclones

    International Nuclear Information System (INIS)

    Halasz, Marcos Roberto Teixeira

    2002-02-01

    Small diameter cyclones represent a potential alternative for the removal of small diameter particles from gaseous mixtures as well as the environmental control of their emission. In order to establish feasible configurations of a small diameter cyclone applied in the separation of solid particles dispersed in a gas and considering a large quantify of experimental data in literature, neural networks were used to estimate the equipment grade efficiency and pressure drop. In order to evaluate a performance of many small diameters configurations and analysis was carried of parametrical sensibility which determines the most important variables on separation efficiency determination. A set of experimental runs was carried out in a lab-scale mini-cyclone in order to obtain the separation efficiency and pressure drop for different configurations, and evaluate the feasibility of coupling a post-cyclone device to improve the equipment overall performance. The cyclones used presented diameters of 0.03 and 0.05 m and the remaining dimensions varied proportionally about those found in Stairmand high-efficiency cyclones. Experimental separation efficiencies up to 99% were obtained in this work. These results confirm the feasibility of the experimental set-up configuration proposed. (author)

  12. Dropping out of school

    Directory of Open Access Journals (Sweden)

    M. Teneva

    2017-09-01

    Full Text Available The modern technological society needs educated people who, through their high professionalism, are called upon to create its progress. In this aspect, a serious problem stands out – the dropout from school of a large number of children, adolescents and young people. The object of the research is the premature interruption of training for a large number of Bulgarian students. The subject of the study is the causes that provoke the students’ dropping out of school. The aim is to differentiate the negative factors leading to dropping out of school, and to identify the motivating factors that encourage the individual to return to the educational environment. In order to realize the so set target, a specially designed test-questionnaire has been used. The survey was conducted among students attending evening courses who have left their education for various reasons and are currently back to the school institution. The contingent of the study includes 120 students from the evening schools. The results indicate that the reasons which prompted the students to leave school early differentiate into four groups: family, social, economic, educational, personal. The motivation to return to school has been dictated in the highest degree by the need for realization of the person on the labor market, followed by the possibility for full social functioning.

  13. Renormalization of three-quark operators for baryon distribution amplitudes

    International Nuclear Information System (INIS)

    Gruber, Michael

    2017-01-01

    In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI ' /SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

  14. Perturbative renormalization of composite operators via flow equations. Pt. 1

    Energy Technology Data Exchange (ETDEWEB)

    Keller, G. (Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany). Werner-Heisenberg-Inst. fuer Physik); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)

    1992-09-01

    We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive {Phi}{sub 4}{sup 4} theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.).

  15. Perturbative renormalization of composite operators via flow equations. Pt. 1

    International Nuclear Information System (INIS)

    Keller, G.; Kopper, C.

    1992-01-01

    We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive Φ 4 4 theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.)

  16. Renormalization in Large Momentum Effective Theory of Parton Physics.

    Science.gov (United States)

    Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong

    2018-03-16

    In the large-momentum effective field theory approach to parton physics, the matrix elements of nonlocal operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.

  17. Quantum renormalization group approach to geometric phases in spin chains

    International Nuclear Information System (INIS)

    Jafari, R.

    2013-01-01

    A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size

  18. Functional renormalization group approach to the two dimensional Bose gas

    Energy Technology Data Exchange (ETDEWEB)

    Sinner, A; Kopietz, P [Institut fuer Theoretische Physik, Universitaet Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt (Germany); Hasselmann, N [International Center for Condensed Matter Physics, Universidade de BrasIlia, Caixa Postal 04667, 70910-900 BrasIlia, DF (Brazil)], E-mail: hasselma@itp.uni-frankfurt.de, E-mail: sinner@itp.uni-frankfurt.de

    2009-02-01

    We investigate the small frequency and momentum structure of the weakly interacting Bose gas in two dimensions using a functional renormalization group approach. The flow equations are derived within a derivative approximation of the effective action up to second order in spatial and temporal variables and investigated numerically. The truncation we employ is based on the perturbative structure of the theory and is well described as a renormalization group enhanced perturbation theory. It allows to calculate corrections to the Bogoliubov spectrum and to investigate the damping of quasiparticles. Our approach allows to circumvent the divergences which plague the usual perturbative approach.

  19. Renormalization Group Reduction of Non Integrable Hamiltonian Systems

    International Nuclear Information System (INIS)

    Tzenov, Stephan I.

    2002-01-01

    Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail

  20. Renormalization Scale-Fixing for Complex Scattering Amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, Stanley J.; /SLAC; Llanes-Estrada, Felipe J.; /Madrid U.

    2005-12-21

    We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude which can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.

  1. Fine-grained entanglement loss along renormalization-group flows

    International Nuclear Information System (INIS)

    Latorre, J.I.; Rico, E.; Luetken, C.A.; Vidal, G.

    2005-01-01

    We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along renormalization group trajectories from the properties of the vacuum only, without need to study the whole Hamiltonian

  2. Renormalization of three-quark operators for baryon distribution amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Gruber, Michael

    2017-07-01

    In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI{sup '}/SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

  3. The renormalization scale-setting problem in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)

    2013-09-01

    A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending

  4. Effective-field renormalization-group method for Ising systems

    Science.gov (United States)

    Fittipaldi, I. P.; De Albuquerque, D. F.

    1992-02-01

    A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

  5. Renormalization in the stochastic quantization of field theories

    International Nuclear Information System (INIS)

    Brunelli, J.C.

    1991-01-01

    In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

  6. Diameter 2 properties and convexity

    Czech Academy of Sciences Publication Activity Database

    Abrahamsen, T. A.; Hájek, Petr Pavel; Nygaard, O.; Talponen, J.; Troyanski, S.

    2016-01-01

    Roč. 232, č. 3 (2016), s. 227-242 ISSN 0039-3223 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : diameter 2 property * midpoint locally uniformly rotund * Daugavet property Subject RIV: BA - General Mathematics Impact factor: 0.535, year: 2016 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia- mathematica /all/232/3/91534/diameter-2-properties-and-convexity

  7. Drop jumping. II. The influence of dropping height on the biomechanics of drop jumping

    NARCIS (Netherlands)

    Bobbert, M F; Huijing, P A; van Ingen Schenau, G J

    In the literature, athletes preparing for explosive activities are recommended to include drop jumping in their training programs. For the execution of drop jumps, different techniques and different dropping heights can be used. This study was designed to investigate for the performance of bounce

  8. Generic versus brand-name North American topical glaucoma drops.

    Science.gov (United States)

    Mammo, Zaid N; Flanagan, John G; James, David F; Trope, Graham E

    2012-02-01

    To determine whether brand-name glaucoma drops differ from generic equivalents in bottle design, viscosity, surface tension, and volume in North America. Experimental study. We studied 5 bottles each of 11 kinds of glaucoma drops. Density-based calculations of drop volume were assessed using 0.1 mg analytic balance. Viscosity was measured using rotational rheometery. Bottle tip diameter was measured using 0.05 mm Vernier calipers. Surface tension was measured using a Fisher Scientific (Ottawa, ON) tensiometer. For the American brand-name Timoptic XE, the average drop volume was 38 ± 3.1 μL versus 24 ± 1.5 μL of Timolol GFS (p brand-name Timoptic XE, the average drop volume was 42 ± 4.0 μL versus 25 ± 2 μL of timolol maleate EX (p brand-name Timoptic drop volume was 28 ± 1.4 μL versus 35 ± 1.9 μL Apo-Timop (p brand-name Timoptic delivered significantly smaller drop volumes than generic Apo-Timop. Careful consideration should be given to drop viscosity and bottle design when generic ophthalmic products are evaluated for interchangeability and market entry. Copyright © 2012 Canadian Ophthalmological Society. Published by Elsevier Inc. All rights reserved.

  9. Fragment size distribution in viscous bag breakup of a drop

    Science.gov (United States)

    Kulkarni, Varun; Bulusu, Kartik V.; Plesniak, Michael W.; Sojka, Paul E.

    2015-11-01

    In this study we examine the drop size distribution resulting from the fragmentation of a single drop in the presence of a continuous air jet. Specifically, we study the effect of Weber number, We, and Ohnesorge number, Oh on the disintegration process. The regime of breakup considered is observed between 12 phase Doppler anemometry. Both the number and volume fragment size probability distributions are plotted. The volume probability distribution revealed a bi-modal behavior with two distinct peaks: one corresponding to the rim fragments and the other to the bag fragments. This behavior was suppressed in the number probability distribution. Additionally, we employ an in-house particle detection code to isolate the rim fragment size distribution from the total probability distributions. Our experiments showed that the bag fragments are smaller in diameter and larger in number, while the rim fragments are larger in diameter and smaller in number. Furthermore, with increasing We for a given Ohwe observe a large number of small-diameter drops and small number of large-diameter drops. On the other hand, with increasing Oh for a fixed We the opposite is seen.

  10. Predictors of postoperative hemoglobin drop after laparoscopic myomectomy.

    Science.gov (United States)

    Watrowski, Rafał; Jäger, Christoph; Forster, Johannes

    2017-01-01

    Laparoscopic myomectomy (LM) can be associated with significant bleeding. To identify factors influencing the postoperative hemoglobin (Hb) drop after LM. This is a retrospective, single-center study. We evaluated data of 150 consecutive patients undergoing LM due to intramural myomas between 2010 and 2015. The median age of the patients was 37 (23-53) years. The mean diameter of the largest myoma was 5.7 ±2.3 (1.5-12) cm. The mean surgical time was 83 ±38 (35-299) min. The median number of sutures was 3 (1-11). The mean postoperative Hb drop was 1.6 ±1.2 (0-6) g/dl, and the mean estimated blood loss was 261 ±159 (50-1700) ml. In the univariate analysis, the postoperative Hb drop correlated with the duration of surgery (p < 0.001), diameter of the largest myoma (p < 0.001), cumulative myoma weight (p < 0.001), and number of sutures (p < 0.001), but not with patients' age or number of intramural myomas. In the multivariable analysis, the surgical time ( β = 0.395, p < 0.001), diameter of the largest myoma ( β = 0.292, p = 0.03) and preoperative Hb concentration ( β = 0.299, p < 0.001) predicted the postoperative Hb change. Surgical time and dominant myoma diameter are independent predictors of the postoperative Hb drop after LM.

  11. Steam explosion studies with single drops of molten refractory materials

    International Nuclear Information System (INIS)

    Nelson, L.S.

    1980-01-01

    Laser heating, levitation melting, and metal combustion were used to prepare individual drops of molten refractory materials which simulate LWR fuel melt products. Drop temperatures ranged from approx. = 1500 to > 3000K. These drops, several millimeters in diameter, were injected into water and subjected to pressure transients (approx. = 1MPa peak pressures) generated by a submerged exploding bridgewire. Molten oxides of Fe, Al and Zr could be induced to explode with bridgewire initiation. High speed films showed the explosions with exceptional clarity, and pressure transducer records could be correlated with individual frames in the films. Pressure spikes one or two MPa high were generated whenever an explosion occurred. Debris particles were mostly spheroidal, with diameters in the range 10 to 1000 μm

  12. Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange

    Energy Technology Data Exchange (ETDEWEB)

    Higa, R; Valderrama, M Pavon; Arriola, E Ruiz

    2007-06-14

    The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.

  13. Multiscale unfolding of real networks by geometric renormalization

    Science.gov (United States)

    García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

    2018-06-01

    Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

  14. On Newton-Cartan local renormalization group and anomalies

    Energy Technology Data Exchange (ETDEWEB)

    Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); INFN Sezione di Perugia,Via A. Pascoli, 06123 Perugia (Italy); Baiguera, Stefano; Filippini, Francesco [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento,38123 Povo (Italy)

    2016-11-28

    Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.

  15. Systematic renormalization of the effective theory of Large Scale Structure

    International Nuclear Information System (INIS)

    Abolhasani, Ali Akbar; Mirbabayi, Mehrdad; Pajer, Enrico

    2016-01-01

    A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k 2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

  16. RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

    International Nuclear Information System (INIS)

    Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

    2010-01-01

    We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

  17. Renormalization group coupling flow of SU(3) gauge theory

    OpenAIRE

    QCDTARO Collaboration

    1998-01-01

    We present our new results on the renormalization group coupling flow obtained i n 3 dimensional coupling space $(\\beta_{11},\\beta_{12},\\beta_{twist})$. The value of $\\beta_{twist}$ turns out to be small and the coupling flow projected on $(\\beta_{11},\\beta_{12})$ plane is very similar with the previous result obtained in the 2 dimensional coupling space.

  18. Simple perturbative renormalization scheme for supersymmetric gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)

    1983-06-30

    We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/..delta..)/sup -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.

  19. A simple perturbative renormalization scheme for supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Foda, O.E.

    1983-01-01

    We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of [(p+q)/δ] - delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, #betta# is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously. (orig.)

  20. Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation

    Energy Technology Data Exchange (ETDEWEB)

    Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)

    1975-01-04

    Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.

  1. Finite cluster renormalization group for disordered two-dimensional systems

    International Nuclear Information System (INIS)

    El Kenz, A.

    1987-09-01

    A new type of renormalization group theory using the generalized Callen identities is exploited in the study of the disordered systems. Bond diluted and frustrated Ising systems on a square lattice are analyzed with this new scheme. (author). 9 refs, 2 figs, 2 tabs

  2. RENORMALIZATION FACTOR AND ODD-OMEGA GAP SINGLET SUPERCONDUCTIVITY

    NARCIS (Netherlands)

    DOLGOV, OV; LOSYAKOV, VV

    1994-01-01

    Abrahams et al. [Phys. Rev. B 47 (1993) 513] have considered the possibility of a nonzero critical temperature of the superconductor transition to the state with odd-omega pp function and shown that the condition for it is the following inequality for the renormalization factor. Z (k, omega(n)) <1.

  3. Renormalization group decimation technique for disordered binary harmonic chains

    International Nuclear Information System (INIS)

    Wiecko, C.; Roman, E.

    1983-10-01

    The density of states of disordered binary harmonic chains is calculated using the Renormalization Group Decimation technique on the displacements of the masses from their equilibrium positions. The results are compared with numerical simulation data and with those obtained with the current method of Goncalves da Silva and Koiller. The advantage of our procedure over other methods is discussed. (author)

  4. Running with rugby balls: bulk renormalization of codimension-2 branes

    Science.gov (United States)

    Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.

    2013-01-01

    We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

  5. General renormalized statistical approach with finite cross-field correlations

    International Nuclear Information System (INIS)

    Vakulenko, M.O.

    1992-01-01

    The renormalized statistical approach is proposed, accounting for finite correlations of potential and magnetic fluctuations. It may be used for analysis of a wide class of nonlinear model equations describing the cross-correlated plasma states. The influence of a cross spectrum on stationary potential and magnetic ones is investigated. 10 refs. (author)

  6. Pairing renormalization and regularization within the local density approximation

    International Nuclear Information System (INIS)

    Borycki, P.J.; Dobaczewski, J.; Nazarewicz, W.; Stoitsov, M.V.

    2006-01-01

    We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications

  7. Rota-Baxter algebras and the Hopf algebra of renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Ebrahimi-Fard, K.

    2006-06-15

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  8. Updated RENORM/MBR Predictions for Diffraction at the LHC

    CERN Document Server

    Goulianos, K

    2015-01-01

    Updated RENORM/MBR-model predictions of diffractive, total, and total-inelastic cross sections at the LHC are presented and compared with experimental results and predictions from other models. In addition, expectations for diffraction at the upcoming LHC run at √s = 13 TeV are discussed.

  9. Renormalization constants for 2-twist operators in twisted mass QCD

    International Nuclear Information System (INIS)

    Alexandrou, C.; Constantinou, M.; Panagopoulos, H.; Stylianou, F.; Korzec, T.

    2011-01-01

    Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to β=3.9, 4.05, 4.20. Subtraction of O(a 2 ) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a 2 ). The renormalization conditions are defined in the RI ' -MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS at 2 GeV using 3-loop perturbative results for the conversion factors.

  10. Renormalization group invariance in the presence of an instanton

    International Nuclear Information System (INIS)

    Ross, D.A.

    1987-01-01

    A pure Yang-Mills theory which admits an instanton is under discussion. n=1 supersymmetric (SU-2) Yang-Mills theory, both in the Wess-zumino gauge and in manifestly supersymmetric supergauge is considered. Two-loop vacuum graphs are calculated. The way a renormalization group invariance works under conditions of fermionic zero mode elimination is shown

  11. Dynamic mass generation and renormalizations in quantum field theories

    International Nuclear Information System (INIS)

    Miransky, V.A.

    1979-01-01

    It is shown that the dynamic mass generation can destroy the multiplicative renormalization relations and lead to new type divergences in the massive phase. To remove these divergences the values of the bare coupling constants must be fixed. The phase diagrams of gauge theories are discussed

  12. Rota-Baxter algebras and the Hopf algebra of renormalization

    International Nuclear Information System (INIS)

    Ebrahimi-Fard, K.

    2006-06-01

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  13. On Newton-Cartan local renormalization group and anomalies

    International Nuclear Information System (INIS)

    Auzzi, Roberto; Baiguera, Stefano; Filippini, Francesco; Nardelli, Giuseppe

    2016-01-01

    Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.

  14. Real-space renormalization group approach to driven diffusive systems

    Energy Technology Data Exchange (ETDEWEB)

    Hanney, T [SUPA and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ (United Kingdom); Stinchcombe, R B [Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP (United Kingdom)

    2006-11-24

    We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase.

  15. Equation-free dynamic renormalization in a glassy compaction model

    International Nuclear Information System (INIS)

    Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.

    2006-01-01

    Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena

  16. Equation-free dynamic renormalization in a glassy compaction model

    Science.gov (United States)

    Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.

    2006-07-01

    Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.

  17. Real-space renormalization group approach to driven diffusive systems

    International Nuclear Information System (INIS)

    Hanney, T; Stinchcombe, R B

    2006-01-01

    We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase

  18. Pade expansion and the renormalization of nucleon-nucleon scattering

    International Nuclear Information System (INIS)

    Yang Jifeng; Huang Jianhua; Liu Dan

    2006-01-01

    The importance of imposing physical boundary conditions on the T-matrix to remove to nonperturbative renormalization prescription dependence is stressed and demonstrated in two diagonal channels 1 P 1 and 1 D 2 , with the help of Pade expansion. (authors)

  19. Migdal-Kadanoff renormalization group for the Z(5) model

    International Nuclear Information System (INIS)

    Baltar, V.L.V.; Carneiro, G.M.; Pol, M.E.; Zagury, N.

    1984-01-01

    The Migdal-Kadanoff renormalization group methods is used to calculate the phase diagram of the AF Z(5) model. It is found that this scheme simulates a fixed line which it is interpreted as the locus of attraction of a critical phase. This result is in reasonable agreement with the predictions of Monte Carlo simulations. (Author) [pt

  20. First drop dissimilarity in drop-on-demand inkjet devices

    International Nuclear Information System (INIS)

    Famili, Amin; Palkar, Saurabh A.; Baldy, William J. Jr.

    2011-01-01

    As inkjet printing technology is increasingly applied in a broader array of applications, careful characterization of its method of use is critical due to its inherent sensitivity. A common operational mode in inkjet technology known as drop-on-demand ejection is used as a way to deliver a controlled quantity of material to a precise location on a target. This method of operation allows ejection of individual or a sequence (burst) of drops based on a timed trigger event. This work presents an examination of sequences of drops as they are ejected, indicating a number of phenomena that must be considered when designing a drop-on-demand inkjet system. These phenomena appear to be driven by differences between the first ejected drop in a burst and those that follow it and result in a break-down of the linear relationship expected between driving amplitude and drop mass. This first drop, as quantified by high-speed videography and subsequent image analysis, can be different in morphology, trajectory, velocity, and volume from subsequent drops within a burst. These findings were confirmed orthogonally by both volume and mass measurement techniques which allowed quantitation down to single drops.

  1. Satellite Formation during Coalescence of Unequal Size Drops

    KAUST Repository

    Zhang, F. H.

    2009-03-12

    The coalescence of a drop with a flat liquid surface pinches off a satellite from its top, in the well-known coalescence cascade, whereas the coalescence of two equally sized drops does not appear to leave such a satellite. Herein we perform experiments to identify the critical diameter ratio of two drops, above which a satellite is produced during their coalescence. We find that the critical parent ratio is as small as 1.55, but grows monotonically with the Ohnesorge number. The daughter size is typically about 50% of the mother drop. However, we have identified novel pinch-off dynamics close to the critical size ratio, where the satellite does not fully separate, but rather goes directly into a second stage of the coalescence cascade, thus generating a much smaller satellite droplet.

  2. Satellite Formation during Coalescence of Unequal Size Drops

    KAUST Repository

    Zhang, F. H.; Li, E. Q.; Thoroddsen, Sigurdur T

    2009-01-01

    The coalescence of a drop with a flat liquid surface pinches off a satellite from its top, in the well-known coalescence cascade, whereas the coalescence of two equally sized drops does not appear to leave such a satellite. Herein we perform experiments to identify the critical diameter ratio of two drops, above which a satellite is produced during their coalescence. We find that the critical parent ratio is as small as 1.55, but grows monotonically with the Ohnesorge number. The daughter size is typically about 50% of the mother drop. However, we have identified novel pinch-off dynamics close to the critical size ratio, where the satellite does not fully separate, but rather goes directly into a second stage of the coalescence cascade, thus generating a much smaller satellite droplet.

  3. Numerical modeling of aerosol particles scavenging by drops as a process of air depollution

    OpenAIRE

    Cherrier , Gaël

    2017-01-01

    This PhD-Thesis is dedicated to the numerical modeling of aerosol particles scavenging by drops. Investigated situations are about aerosol particles of aerodynamic diameter ranging from 1 nm to 100 µm captured in the air by water drops of diameter varying between 80 µm and 600 µm, with corresponding droplet Reynolds number ranging between 1 and 100. This air depollution modeling is achieved in two steps. The first step consists in obtaining a scavenging kernel predicting the flow rate of aero...

  4. A comprehensive coordinate space renormalization of quantum electrodynamics to two-loop order

    International Nuclear Information System (INIS)

    Haagensen, P.E.; Latorre, J.I.

    1993-01-01

    We develop a coordinate space renormalization of massless quantum electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all one- and two-loop 1PI diagrams, run renormalization group equations on them. and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle γ 5 problems

  5. Effect of particle diameter of porous media on flow and heat transfer in a mixing tee

    International Nuclear Information System (INIS)

    Wang, Yongwei; Lu, Tao; Wang, Kuisheng

    2012-01-01

    Highlights: ► Three particle diameter cases of 28 mm, 14 mm and 7 mm were simulated by LES. ► With the diameter decreasing, mixing scale tends to decrease in the mixing tee. ► With the diameter decreasing, thermal mixing is weakened. ► With the diameter decreasing, the thermal stratification is obvious. ► When the particle diameter ratio is 4:2:1, pressure drop ratio is 1:2:4. -- Abstract: Numerical simulations have been carried out to investigate flow and heat transfer in a mixing tee filled with periodic sintered copper spheres. Three particle diameter cases of 28 mm, 14 mm and 7 mm with the array of 4 × 4, 8 × 8 and 16 × 16 at the same porosity of 0.3 have been calculated using large-eddy simulations and the Smagorinsky–Lilly sub-grid scale model. With the particle diameter decreasing, the mixture scale of hot and cold fluid tends to decrease in the mixing tee; the pressure drop of fluid flow through porous media increases. When the particle diameter ratios are 4:2:1 and the specific surface ratios are 1:2:4, the pressure drop ratios are 1:2:4; the thermal mixing in porous media is weakened because the temperature fluctuation decreases and the stratification of hot and cold fluids is observed.

  6. Hanging drop crystal growth apparatus

    Science.gov (United States)

    Naumann, Robert J. (Inventor); Witherow, William K. (Inventor); Carter, Daniel C. (Inventor); Bugg, Charles E. (Inventor); Suddath, Fred L. (Inventor)

    1990-01-01

    This invention relates generally to control systems for controlling crystal growth, and more particularly to such a system which uses a beam of light refracted by the fluid in which crystals are growing to detect concentration of solutes in the liquid. In a hanging drop apparatus, a laser beam is directed onto drop which refracts the laser light into primary and secondary bows, respectively, which in turn fall upon linear diode detector arrays. As concentration of solutes in drop increases due to solvent removal, these bows move farther apart on the arrays, with the relative separation being detected by arrays and used by a computer to adjust solvent vapor transport from the drop. A forward scattering detector is used to detect crystal nucleation in drop, and a humidity detector is used, in one embodiment, to detect relative humidity in the enclosure wherein drop is suspended. The novelty of this invention lies in utilizing angular variance of light refracted from drop to infer, by a computer algorithm, concentration of solutes therein. Additional novelty is believed to lie in using a forward scattering detector to detect nucleating crystallites in drop.

  7. Renormalization Group scale-setting in astrophysical systems

    Science.gov (United States)

    Domazet, Silvije; Štefančić, Hrvoje

    2011-09-01

    A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

  8. Renormalization Group scale-setting in astrophysical systems

    International Nuclear Information System (INIS)

    Domazet, Silvije; Stefancic, Hrvoje

    2011-01-01

    A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

  9. Matrix product density operators: Renormalization fixed points and boundary theories

    Energy Technology Data Exchange (ETDEWEB)

    Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)

    2017-03-15

    We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).

  10. E-cigarette marketing and older smokers: road to renormalization.

    Science.gov (United States)

    Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

    2015-05-01

    To describe older smokers' perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking.

  11. Renormalization group procedure for potential −g/r2

    Directory of Open Access Journals (Sweden)

    S.M. Dawid

    2018-02-01

    Full Text Available Schrödinger equation with potential −g/r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r=0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

  12. Renormalization group approach to causal bulk viscous cosmological models

    International Nuclear Information System (INIS)

    Belinchon, J A; Harko, T; Mak, M K

    2002-01-01

    The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor

  13. Computing the effective action with the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)

    2016-04-15

    The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 0} can be obtained by integrating the flow equation from an ultraviolet scale k = Λ down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. (orig.)

  14. Renormalization-group study of the four-body problem

    International Nuclear Information System (INIS)

    Schmidt, Richard; Moroz, Sergej

    2010-01-01

    We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.

  15. Strong-Weak CP Hierarchy from Non-Renormalization Theorems

    Energy Technology Data Exchange (ETDEWEB)

    Hiller, Gudrun

    2002-01-28

    We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.

  16. Scaling algebras and renormalization group in algebraic quantum field theory

    International Nuclear Information System (INIS)

    Buchholz, D.; Verch, R.

    1995-01-01

    For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)

  17. The density-matrix renormalization group: a short introduction.

    Science.gov (United States)

    Schollwöck, Ulrich

    2011-07-13

    The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

  18. E-cigarette Marketing and Older Smokers: Road to Renormalization

    Science.gov (United States)

    Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

    2015-01-01

    Objectives To describe older smokers’ perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Methods Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Results Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. Conclusions To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking. PMID:25741681

  19. Two-loop renormalization of quantum gravity simplified

    Science.gov (United States)

    Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex

    2017-02-01

    The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

  20. One-loop renormalization of Lee-Wick gauge theory

    International Nuclear Information System (INIS)

    Grinstein, Benjamin; O'Connell, Donal

    2008-01-01

    We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theory than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.

  1. On the renormalization of operator products: the scalar gluonic case

    International Nuclear Information System (INIS)

    Zoller, Max F.

    2016-01-01

    In this paper we study the renormalization of the product of two operators O 1 =−(1/4)G μν G μν in QCD. An insertion of two such operators O 1 (x)O 1 (0) into a Greens function produces divergent contact terms for x→0. In the course of the computation of the operator product expansion (OPE) of the correlator of two such operators i∫ d 4 x e iqx T{ O 1 (x)O 1 (0)} to three-loop order http://dx.doi.org/10.1007/JHEP12(2012)119; http://dx.doi.org/10.1007/JHEP10(2014)169 we discovered that divergent contact terms remain not only in the leading Wilson coefficient C 0 , which is just the VEV of the correlator, but also in the Wilson coefficient C 1 in front of O 1 . As this correlator plays an important role for example in QCD sum rules a full understanding of its renormalization is desireable. This work explains how the divergences encountered in higher orders of an OPE of this correlator should be absorbed in counterterms and derives an additive renormalization constant for C 1 from first principles and to all orders in perturnbation theory. The method to derive the renormalization of this operator product is an extension of the ideas of V. Spiridonov, Anomalous dimension of g μν 2 and β-function, Preprint IYAI-P-0378 (1984). and can be generalized to other cases.

  2. Quasi-renormalization of the axial vector model

    International Nuclear Information System (INIS)

    Schweda, M.

    1979-01-01

    Using the regulator-free BPHZL renormalization scheme the problem of anomalies in a massive axial vector meson model is reinvestigated. The Adler-Bardeen-Bell-Jackiw anomaly introduces some impressive modifications: the nontrivial self-energy and the counterterm of the longitudinal part of the axial vector field depend on the anomaly via the anomalous Ward identity. The investigations are based on a Fermi-type gauge. (author)

  3. Fierz transformations and renormalization schemes for fourquark operators

    Directory of Open Access Journals (Sweden)

    Garron Nicolas

    2018-01-01

    Full Text Available It has been shown that the choice of renormalization scheme is crucial for four-quark operators, in particular for neutral kaon mixing beyond the Standard Model. In the context of SMOM schemes, the choice of projector is not unique and is part of the definition of the renormalisation scheme. I present the non-diagonal Fierz relations which relate some of these projectors.

  4. Evaluation of spectral zeta-functions with the renormalization group

    International Nuclear Information System (INIS)

    Boettcher, Stefan; Li, Shanshan

    2017-01-01

    We evaluate spectral zeta-functions of certain network Laplacians that can be treated exactly with the renormalization group. As specific examples we consider a class of Hanoi networks and those hierarchical networks obtained by the Migdal–Kadanoff bond moving scheme from regular lattices. As possible applications of these results we mention quantum search algorithms as well as synchronization, which we discuss in more detail. (paper)

  5. Disordered systems and the functional renormalization group, a pedagogical introduction

    International Nuclear Information System (INIS)

    Wiese, K.J.

    2002-01-01

    In this article, we review basic facts about disordered systems, especially the existence of many metastable states and and the resulting failure of dimensional reduction. Besides techniques based on the Gaussian variational method and replica-symmetry breaking (RSB), the functional renormalization group (FRG) is the only general method capable of attacking strongly disordered systems. We explain the basic ideas of the latter method and why it is difficult to implement. We finally review current progress for elastic manifolds in disorder (Author)

  6. Nonthermal fixed points and the functional renormalization group

    International Nuclear Information System (INIS)

    Berges, Juergen; Hoffmeister, Gabriele

    2009-01-01

    Nonthermal fixed points represent basic properties of quantum field theories, in addition to vacuum or thermal equilibrium fixed points. The functional renormalization group on a closed real-time path provides a common framework for their description. For the example of an O(N) symmetric scalar theory it reveals a hierarchy of fixed point solutions, with increasing complexity from vacuum and thermal equilibrium to nonequilibrium

  7. Renormalization group, principle of invariance and functional automodelity

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    1981-01-01

    There exists a remarkable identity of functional equations describing the property of functional automodelity in diverse branches of physics: renormalization group equations in quantum field theory, functional equations of the invariance principle of the one-dimensional transport theory and some others. The origin of this identity is investigated. It is shown that the structure of these equations reflects the simple and general property of transitivity with respect to the way of fixatio of initial on effective degrees of freedom [ru

  8. Renormalization of the δ expansion in curved space-time

    International Nuclear Information System (INIS)

    Cho, H.T.

    1991-01-01

    Renormalization of a recently proposed δ expansion for a self-interacting scalar field theory in curved space-time is examined. The explicit calculation is carried out up to order δ 2 , which indicates that the expansion is renormalizable, but reduces to essentially the λφ 4 theory when the cutoff is removed. A similar conclusion has been reached in a previous paper where the case of flat space-time is considered

  9. Tadpole renormalization and relativistic corrections in lattice NRQCD

    Science.gov (United States)

    Shakespeare, Norman H.; Trottier, Howard D.

    1998-08-01

    We make a detailed comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. We renormalize improved gauge-field and NRQCD actions using the mean-link u0,L in the Landau gauge, and using the fourth root of the average plaquette u0,P. Simulations are done for the three quarkonium systems cc¯, bc¯, and bb¯. The hyperfine splittings are computed both at leading [O(MQv4)] and at next-to-leading [O(MQv6)] order in the relativistic expansion, where MQ is the renormalized quark mass, and v2 is the mean-squared velocity. Results are obtained at a large number of lattice spacings, in the range of about 0.14-0.38 fm. A number of features emerge, all of which favor tadpole renormalization using u0,L. This includes a much better scaling behavior of the hyperfine splittings in the three quarkonium systems when u0,L is used. We also find that relativistic corrections to the spin splittings are smaller when u0,L is used, particularly for the cc¯ and bc¯ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about 1 in lattice units. Simulations with u0,L also appear to be better behaved in this context: the bare quark masses turn out to be larger when u0,L is used, compared to when u0,P is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.

  10. Renormalization analysis of catalytic Wright-Fisher diffusions

    Czech Academy of Sciences Publication Activity Database

    Swart, Jan M.; Fleischmann, K.

    2006-01-01

    Roč. 2006, č. 11 (2006), s. 585-654 ISSN 1083-6489 R&D Projects: GA ČR GA201/06/1323 Institutional research plan: CEZ:AV0Z10750506 Keywords : renormalization * catalytic Wright-Fisher diffusion * embedded particle system * extinction * unbounded growth * interacting diffusions * universality Subject RIV: BA - General Mathematics Impact factor: 0.676, year: 2006

  11. The Bogolyubov renormalization group in theoretical and mathematical physics

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    1999-01-01

    This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part I) partially overlaps with corresponding text of my previous commemorative paper - see Ref. [6] in the list. At the same time the second part includes some fresh results in QFT (Sect. 2.1.) and summarizes (Sect. 2.4) an impressive recent progress of the 'QFT renormalization group' application in mathematical physics

  12. Renormalization-group flows and charge transmutation in string theory

    International Nuclear Information System (INIS)

    Orlando, D.; Petropoulos, P.M.; Sfetsos, K.

    2006-01-01

    We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an attractor from both the target-space and world-sheet points of view. We also address the question of instabilities created by the presence of closed time-like curves in string backgrounds. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  13. Renormalization, unstable manifolds, and the fractal structure of mode locking

    International Nuclear Information System (INIS)

    Cvitanovic, P.; Jensen, M.H.; Kadanoff, L.P.; Procaccia, I.

    1985-01-01

    The apparent universality of the fractal dimension of the set of quasiperiodic windings at the onset of chaos in a wide class of circle maps is described by construction of a universal one-parameter family of maps which lies along the unstable manifold of the renormalization group. The manifold generates a universal ''devil's staircase'' whose dimension agrees with direct numerical calculations. Applications to experiments are discussed

  14. Real space renormalization group for spectra and density of states

    International Nuclear Information System (INIS)

    Wiecko, C.; Roman, E.

    1984-09-01

    We discuss the implementation of the Real Space Renormalization Group Decimation Technique for 1-d tight-binding models with long range interactions with or without disorder and for the 2-d regular square lattice. The procedure follows the ideas developed by Southern et al. Some new explicit formulae are included. The purpose of this study is to calculate spectra and densities of states following the procedure developed in our previous work. (author)

  15. BPHZ renormalization in configuration space for the A4-model

    Science.gov (United States)

    Pottel, Steffen

    2018-02-01

    Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.

  16. Temperature renormalization group approach to spontaneous symmetry breaking

    International Nuclear Information System (INIS)

    Manesis, E.; Sakakibara, S.

    1985-01-01

    We apply renormalization group equations that describe the finite-temperature behavior of Green's functions to investigate thermal properties of spontaneous symmetry breaking. Specifically, in the O(N).O(N) symmetric model we study the change of symmetry breaking patterns with temperature, and show that there always exists the unbroken symmetry phase at high temperature, modifying the naive result of leading order in finite-temperature perturbation theory. (orig.)

  17. Using acoustics to study and stimulate the coalescence of oil drops surrounded by water

    Energy Technology Data Exchange (ETDEWEB)

    Gardner, E.A.; Apfel, R.E. (Yale Univ., New Haven, CT (United States). Dept. of Mechanical Engineering)

    1993-08-01

    The coalescence of oil drops in water is studied using acoustic levitation and stimulated with acoustic cavitation. Unlike most earlier studies, which investigate the coalescence of a single drop with an initially planar interface, the use of acoustic radiation forces allows two drops to be brought into contact and allowed to coalesce. The acoustic technique has the advantage over other drop-drop coalescence systems in that the drops remain in contact until they coalesce without the use of solid supports to control them. Additionally, acoustic cavitation is observed to deposit sufficient energy in the oil-water interface to trigger the coalescence of a pair of 2-mm-diameter drops. This stimulation mechanism could have application to emulsion breaking. Some of the factors that affect spontaneous and stimulated coalescence are investigated.

  18. Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

    Science.gov (United States)

    Panagopoulos, Haralambos; Spanoudes, Gregoris

    2018-03-01

    In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet (Σfψ¯fΓψf', f : flavor index) and nonsinglet (ψ¯f1Γψf2,f1 ≠ f2) bilinear quark operators (where Γ = 𝟙, γ5, γ µ, γ5 γ µ, γ5 σµv on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D [1].

  19. Can renormalization group flow end in a Big Mess?

    International Nuclear Information System (INIS)

    Morozov, Alexei; Niemi, Antti J.

    2003-01-01

    The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. This could lead to Big Mess scenarios in applications to multiphase systems, from spin-glasses and neural networks to fundamental string (M?) theory. We consider various general aspects of such chaotic flows. We argue that they pose no obvious contradictions with the known properties of effective actions, the existence of dissipative Lyapunov functions, and even the strong version of the c-theorem. We also explain the difficulties encountered when constructing effective actions with chaotic renormalization group flows and observe that they have many common virtues with realistic field theory effective actions. We conclude that if chaotic renormalization group flows are to be excluded, conceptually novel no-go theorems must be developed

  20. Physical renormalization schemes and asymptotic safety in quantum gravity

    Science.gov (United States)

    Falls, Kevin

    2017-12-01

    The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.

  1. One-loop renormalization of a gravity-scalar system

    Energy Technology Data Exchange (ETDEWEB)

    Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)

    2017-05-15

    Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

  2. Renormalization group fixed points of foliated gravity-matter systems

    Energy Technology Data Exchange (ETDEWEB)

    Biemans, Jorn [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Platania, Alessia [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Department of Physics and Astronomy, University of Catania,Via S. Sofia 63, 95123 Catania (Italy); INFN, Catania section,Via S. Sofia 64, 95123, Catania (Italy); INAF, Catania Astrophysical Observatory,Via S. Sofia 78, 95123, Catania (Italy); Saueressig, Frank [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands)

    2017-05-17

    We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) “time”-direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton’s constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d{sub g}, d{sub λ}. We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

  3. One-loop renormalization of a gravity-scalar system

    International Nuclear Information System (INIS)

    Park, I.Y.

    2017-01-01

    Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

  4. One-loop renormalization of a gravity-scalar system

    Science.gov (United States)

    Park, I. Y.

    2017-05-01

    Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the "mass" term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information.

  5. 45-FOOT HIGH DROP TOWER

    Data.gov (United States)

    Federal Laboratory Consortium — The Drop Tower is used to simulate and measure the impact shocks that are exerted on parachute loads when they hit the ground. It is also used for HSL static lift to...

  6. Quantum renormalization group approach to quantum coherence and multipartite entanglement in an XXZ spin chain

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)

    2017-01-30

    We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.

  7. Investigation of water and saline solution drops evaporation on a solid substrate

    Directory of Open Access Journals (Sweden)

    Orlova Evgenija G.

    2014-01-01

    Full Text Available Experimental investigation water and saline solution drops evaporation on a solid substrate made of anodized aluminum is presented in the paper. Parameters characterizing drop profile have been obtained (contact angle, contact diameter, height. The specific evaporation rate has been calculated from obtained values. It was found that water and saline solution drops with concentration up to 9.1% evaporate in the pinning mode. However, with increasing the salt concentration in the solution up to 16.7% spreading mode was observed. Two stages of drop evaporation depending on change of the evaporation rate have been separated.

  8. Renormalized trajectory for non-linear sigma model and improved scaling behaviour

    International Nuclear Information System (INIS)

    Guha, A.; Okawa, M.; Zuber, J.B.

    1984-01-01

    We apply the block-spin renormalization group method to the O(N) Heisenberg spin model. Extending a previous work of Hirsch and Shenker, we find the renormalized trajectory for O(infinite) in two dimensions. Four finite N models, we choose a four-parameter action near the large-N renormalized trajectory and demonstrate a remarkable improvement in the approach to continuum limit by performing Monte Carlo simulation of O(3) and O(4) models. (orig.)

  9. Space-time versus world-sheet renormalization group equation in string theory

    International Nuclear Information System (INIS)

    Brustein, R.; Roland, K.

    1991-05-01

    We discuss the relation between space-time renormalization group equation for closed string field theory and world-sheet renormalization group equation for first-quantized strings. Restricting our attention to massless states we argue that there is a one-to-one correspondence between the fixed point solutions of the two renormalization group equations. In particular, we show how to extract the Fischler-Susskind mechanism from the string field theory equation in the case of the bosonic string. (orig.)

  10. Effects of renormalizing the chiral SU(2) quark-meson model

    Science.gov (United States)

    Zacchi, Andreas; Schaffner-Bielich, Jürgen

    2018-04-01

    We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

  11. Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)

    1983-04-28

    We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

  12. The fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

    International Nuclear Information System (INIS)

    Foda, O.E.

    1983-01-01

    We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes. (orig.)

  13. Renormalization of the new trajectory in the unitarized conventional dual model

    International Nuclear Information System (INIS)

    Quiros, M.

    1978-08-01

    The contribution of one-loop planar diagrams to the two-reggeon two-particle amplitude is derived. Its regge limit splits into two separate contributions which must be interpreted as renormalization effects, to order g 2 , of the α and β trajectories. It is shown that the Neveu-Scherk renormalization prescription is able to render finite both contributions. The intercept of the β trajectory is shifted from its bare value by the renormalization procedure, whereas that of the α trajectrory is not renormalized as it was required by the gauge invariance of dual theories

  14. Unique determination of the effective potential in terms of renormalization group functions

    International Nuclear Information System (INIS)

    Chishtie, F. A.; Hanif, T.; McKeon, D. G. C.; Steele, T. G.

    2008-01-01

    The perturbative effective potential V in the massless λφ 4 model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition (d 4 V/dφ 4 )| φ=μ =λ is used, where μ represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal-subtraction (MS) renormalization group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading-logarithm, next-to-leading-logarithm, and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the renormalization group functions from the MS scheme to the Coleman-Weinberg scheme requires the use of multiscale renormalization group methods.

  15. Transformation of renormalization groups in 2N-component fermion hierarchical model

    International Nuclear Information System (INIS)

    Stepanov, R.G.

    2006-01-01

    The 2N-component fermion model on the hierarchical lattice is studied. The explicit formulae for renormalization groups transformation in the space of coefficients setting the Grassmannian-significant density of the free measure are presented. The inverse transformation of the renormalization group is calculated. The definition of immovable points of renormalization groups is reduced to solving the set of algebraic equations. The interesting connection between renormalization group transformations in boson and fermion hierarchical models is found out. It is shown that one transformation is obtained from other one by the substitution of N on -N [ru

  16. Renormalization of the γ-ray strength functions of light nuclei

    International Nuclear Information System (INIS)

    Canbula, B.; Ersan, S.; Babacan, H.

    2015-01-01

    γ-ray strength function is the key input for the photonuclear reactions, which have a special astrophysical importance, and should be renormalized by using the nuclear level density for calculating the theoretical average radiative capture width, but performing such renormalization is challenging for light nuclei. With this motivation, recently introduced level density parameter formula including collective effects is used to calculate the average radiative capture width of light nuclei, and therefore to renormalize their γ-ray strength functions. Obtained normalization factors are tested in (n, γ) reactions for the necessity of renormalization for light nuclei. (author)

  17. Renormalization group flow of scalar models in gravity

    International Nuclear Information System (INIS)

    Guarnieri, Filippo

    2014-01-01

    In this Ph.D. thesis we study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Horava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson's renormalization group. In particular we quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω=0 in the local potential approximation. Finally, we investigate, using a perturbative RG scheme, the asymptotic freedom of the Horava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton's constant to a marginal coupling and explicitly preserves unitarity. In particular we evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.

  18. Drop Spreading with Random Viscosity

    Science.gov (United States)

    Xu, Feng; Jensen, Oliver

    2016-11-01

    Airway mucus acts as a barrier to protect the lung. However as a biological material, its physical properties are known imperfectly and can be spatially heterogeneous. In this study we assess the impact of these uncertainties on the rate of spreading of a drop (representing an inhaled aerosol) over a mucus film. We model the film as Newtonian, having a viscosity that depends linearly on the concentration of a passive solute (a crude proxy for mucin proteins). Given an initial random solute (and hence viscosity) distribution, described as a Gaussian random field with a given correlation structure, we seek to quantify the uncertainties in outcomes as the drop spreads. Using lubrication theory, we describe the spreading of the drop in terms of a system of coupled nonlinear PDEs governing the evolution of film height and the vertically-averaged solute concentration. We perform Monte Carlo simulations to predict the variability in the drop centre location and width (1D) or area (2D). We show how simulation results are well described (at much lower computational cost) by a low-order model using a weak disorder expansion. Our results show for example how variability in the drop location is a non-monotonic function of the solute correlation length increases. Engineering and Physical Sciences Research Council.

  19. Thermocapillary reorientation of Janus drops

    Science.gov (United States)

    Rosales, Rodolfo; Saenz, Pedro

    2017-11-01

    Janus drops, named after the Ancient Roman two-faced god, are liquid drops formed from two immiscible fluids. Experimental observations indicate that a Janus drop may re-orientate in response to an applied external thermal gradient due to the Marangoni effect. Depending on the angle between the interior interface and the direction of the temperature gradient, disparities in the physical properties of the constituent liquids may lead to asymmetries in the thermocapillary flow. As a result, the drop will move along a curved path until a torque-free configuration is achieved, point after which it will continue on a straight trajectory. Here, we present the results of a theoretical investigation of this realignment phenomenon in the Stokes regime and in the limit of non-deformable interfaces. A 3D semi-analytical method in terms of polar spherical harmonics is developed to characterize and rationalize the hydrodynamic response (forces and torques), flow (velocity and temperature distribution) and trajectory of a Janus drop moving during the temperature-driven reorientation process. Furthermore, we discuss how this phenomenon may be exploited to develop dynamically reconfigurable micro-lenses. This work was partially supported by the US National Science Foundation through Grants DMS-1614043 and DMS-1719637.

  20. Non-renormalization theorems andN=2 supersymmetric backgrounds

    International Nuclear Information System (INIS)

    Butter, Daniel; Wit, Bernard de; Lodato, Ivano

    2014-01-01

    The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed

  1. Studies in the renormalization-prescription dependence of perturbative calculations

    International Nuclear Information System (INIS)

    Celmaster, W.; Sivers, D.

    1981-01-01

    Now that the quantitative testing of perturbative quantum chromodynamics (QCD) has become a major experimental and theoretical effort, it is important to understand the renormalization-prescription dependence of perturbative calculations. We stress the phenomenological importance of finding a definition of the QCD expansion parameter which reduces the magnitude of high-order corrections. We give explicit arguments suggesting that a choice of coupling based on momentum-space subtraction can be phenomenologically useful. Examples from QCD and QED are used to illustrate these arguments, and we also discuss possibilities for refining them

  2. On the renormalization group flow in two dimensional superconformal models

    International Nuclear Information System (INIS)

    Ahn, Changrim; Stanishkov, Marian

    2014-01-01

    We extend the results on the RG flow in the next to leading order to the case of the supersymmetric minimal models SM p for p≫1. We explain how to compute the NS and Ramond fields conformal blocks in the leading order in 1/p and follow the renormalization scheme proposed in [1]. As a result we obtained the anomalous dimensions of certain NS and Ramond fields. It turns out that the linear combination expressing the infrared limit of these fields in term of the IR theory SM p−2 is exactly the same as those of the nonsupersymmetric minimal theory

  3. Renormalization group approach to Sudakov resummation in prompt photon production

    International Nuclear Information System (INIS)

    Bolzoni, Paolo; Forte, Stefano; Ridolfi, Giovanni

    2005-01-01

    We prove the all-order exponentiation of soft logarithmic corrections to prompt photon production in hadronic collisions, by generalizing an approach previously developed in the context of Drell-Yan production and deep-inelastic scattering. We show that all large logs in the soft limit can be expressed in terms of two dimensionful variables, and we use the renormalization group to resum them. The resummed results that we obtain are more general though less predictive than those proposed by other groups, in that they can accommodate for violations of Sudakov factorization

  4. Renormalization and applications of baryon distribution amplitudes QCD

    Energy Technology Data Exchange (ETDEWEB)

    Rohrwild, Juergen Holger

    2009-07-17

    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N{sup *} distribution amplitudes. (orig.)

  5. Renormalization and applications of baryon distribution amplitudes in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Rohrwild, Juergen Holger

    2009-07-17

    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N* distribution amplitudes. (orig.)

  6. Renormalization-group analysis of the Kobayashi-Maskawa matrix

    International Nuclear Information System (INIS)

    Babu, K.S.

    1987-01-01

    The one-loop renormalization-group equations for the quark mixing (Kobayashi-Maskawa) matrix V are derived, independent of one's weak interaction basis, in the standard model as well as in its two Higgs and supersymmetric extensions, and their numerical solutions are presented. While the mixing angles vertical strokeV ub vertical stroke, vertical strokeV cb vertical stroke, vertical strokeV td vertical stroke and the phase-invariant measure of CP nonconservation J all vary slowly with momentum, in the standard model they are predicted to increase in clear contrast to the two Higgs and supersymmetric extensions where they decrease with momentum. (orig.)

  7. Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds

    International Nuclear Information System (INIS)

    Asorey, M.; Berredo-Peixoto, G. de; Shapiro, I. L.

    2006-01-01

    We analyze the problem of the existing ambiguities in the conformal anomaly in theories with an external scalar field in curved backgrounds. In particular, we consider the anomaly of a self-interacting massive scalar field theory and of a Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of local nonminimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise

  8. Renormalizing the kinetic energy operator in elementary quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Coutinho, F A B [Faculdade de Medicina, Universidade de Sao Paulo e LIM 01-HCFMUSP, 05405-000 Sao Paulo (Brazil); Amaku, M [Faculdade de Medicina Veterinaria e Zootecnia, Universidade de Sao Paulo, 05508-970 Sao Paulo (Brazil)], E-mail: coutinho@dim.fm.usp.br

    2009-09-15

    In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form {psi}(r) = u(r)/r, where u(0) {ne} 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

  9. Exact renormalization group equation for the Lifshitz critical point

    Science.gov (United States)

    Bervillier, C.

    2004-10-01

    An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

  10. Invariant renormalization method for nonlinear realizations of dynamical symmetries

    International Nuclear Information System (INIS)

    Kazakov, D.I.; Pervushin, V.N.; Pushkin, S.V.

    1977-01-01

    The structure of ultraviolet divergences is investigated for the field theoretical models with nonlinear realization of the arbitrary semisimple Lie group, with spontaneously broken symmetry of vacuum. An invariant formulation of the background field method of renormalization is proposed which gives the manifest invariant counterterms off mass shell. A simple algorithm for construction of counterterms is developed. It is based on invariants of the group of dynamical symmetry in terms of the Cartan forms. The results of one-loop and two-loop calculations are reported

  11. Renormalization and applications of baryon distribution amplitudes in QCD

    International Nuclear Information System (INIS)

    Rohrwild, Juergen Holger

    2009-01-01

    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N * (1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N* distribution amplitudes. (orig.)

  12. Renormalization and applications of baryon distribution amplitudes QCD

    International Nuclear Information System (INIS)

    Rohrwild, Juergen Holger

    2009-01-01

    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N * (1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N * distribution amplitudes. (orig.)

  13. Potts ferromagnet correlation length in hypercubic lattices: Renormalization - group approach

    International Nuclear Information System (INIS)

    Curado, E.M.F.; Hauser, P.R.

    1984-01-01

    Through a real space renormalization group approach, the q-state Potts ferromagnet correlation length on hierarchical lattices is calculated. These hierarchical lattices are build in order to simulate hypercubic lattices. The high-and-low temperature correlation length asymptotic behaviours tend (in the Ising case) to the Bravais lattice correlation length ones when the size of the hierarchical lattice cells tends to infinity. It is conjectured that the asymptotic behaviours several values of q and d (dimensionality) so obtained are correct. Numerical results are obtained for the full temperature range of the correlation length. (Author) [pt

  14. Renormalization group equations in the stochastic quantization scheme

    International Nuclear Information System (INIS)

    Pugnetti, S.

    1987-01-01

    We show that there exists a remarkable link between the stochastic quantization and the theory of critical phenomena and dynamical statistical systems. In the stochastic quantization of a field theory, the stochastic Green functions coverge to the quantum ones when the frictious time goes to infinity. We therefore use the typical techniques of the Renormalization Group equations developed in the framework of critical phenomena to discuss some features of the convergence of the stochastic theory. We are also able, in this way, to compute some dynamical critical exponents and give new numerical valuations for them. (orig.)

  15. Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence

    Science.gov (United States)

    Rubinstein, Robert

    1994-01-01

    Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

  16. Renormalizing the kinetic energy operator in elementary quantum mechanics

    International Nuclear Information System (INIS)

    Coutinho, F A B; Amaku, M

    2009-01-01

    In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form ψ(r) = u(r)/r, where u(0) ≠ 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

  17. Entanglement renormalization, quantum error correction, and bulk causality

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Isaac H. [IBM T.J. Watson Research Center,1101 Kitchawan Rd., Yorktown Heights, NY (United States); Kastoryano, Michael J. [NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen (Denmark)

    2017-04-07

    Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

  18. Renormalized thermodynamic entropy of black holes in higher dimensions

    International Nuclear Information System (INIS)

    Kim, S.P.; Kim, S.K.; Soh, K.; Yee, J.H.

    1997-01-01

    We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstroem black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. copyright 1997 The American Physical Society

  19. Tensor renormalization group with randomized singular value decomposition

    Science.gov (United States)

    Morita, Satoshi; Igarashi, Ryo; Zhao, Hui-Hai; Kawashima, Naoki

    2018-03-01

    An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.

  20. Interfacial Instabilities in Evaporating Drops

    Science.gov (United States)

    Moffat, Ross; Sefiane, Khellil; Matar, Omar

    2007-11-01

    We study the effect of substrate thermal properties on the evaporation of sessile drops of various liquids. An infra-red imaging technique was used to record the interfacial temperature. This technique illustrates the non-uniformity in interfacial temperature distribution that characterises the evaporation process. Our results also demonstrate that the evaporation of methanol droplets is accompanied by the formation of wave-trains in the interfacial temperature field; similar patterns, however, were not observed in the case of water droplets. More complex patterns are observed for FC-72 refrigerant drops. The effect of substrate thermal conductivity on the structure of the complex pattern formation is also elucidated.

  1. Combining spray nozzle simulators with meshes: characterization of rainfall intensity and drop properties

    Science.gov (United States)

    Carvalho, Sílvia C. P.; de Lima, João L. M. P.; de Lima, M. Isabel P.

    2013-04-01

    Rainfall simulators can be a powerful tool to increase our understanding of hydrological and geomorphological processes. Nevertheless, rainfall simulators' design and operation might be rather demanding, for achieving specific rainfall intensity distributions and drop characteristics. The pressurized simulators have some advantages over the non-pressurized simulators: drops do not rely on gravity to reach terminal velocity, but are sprayed out under pressure; pressurized simulators also yield a broad range of drop sizes in comparison with drop-formers simulators. The main purpose of this study was to explore in the laboratory the potential of combining spray nozzle simulators with meshes in order to change rainfall characteristics (rainfall intensity and diameters and fall speed of drops). Different types of spray nozzles were tested, such as single full-cone and multiple full-cone nozzles. The impact of the meshes on the simulated rain was studied by testing different materials (i.e. plastic and steel meshes), square apertures and wire thicknesses, and different vertical distances between the nozzle and the meshes underneath. The diameter and fall speed of the rain drops were measured using a Laser Precipitation Monitor (Thies Clima). The rainfall intensity range and coefficients of uniformity of the sprays and the drop size distribution, fall speed and kinetic energy were analysed. Results show that when meshes intercept drop trajectories the spatial distribution of rainfall intensity and the drop size distribution are affected. As the spray nozzles generate typically small drop sizes and narrow drop size distributions, meshes can be used to promote the formation of bigger drops and random their landing positions.

  2. Communication: Random phase approximation renormalized many-body perturbation theory

    International Nuclear Information System (INIS)

    Bates, Jefferson E.; Furche, Filipp

    2013-01-01

    We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations

  3. Source Localization by Entropic Inference and Backward Renormalization Group Priors

    Directory of Open Access Journals (Sweden)

    Nestor Caticha

    2015-04-01

    Full Text Available A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible.

  4. Dynamical renormalization group resummation of finite temperature infrared divergences

    International Nuclear Information System (INIS)

    Boyanovsky, D.; Vega, H.J. de; Boyanovsky, D.; Simionato, M.; Holman, R.; Simionato, M.

    1999-01-01

    We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and apply it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form e -αampersandhthinsp;Tampersandhthinsp;tampersandhthinsp;ln[t/t 0 ] for hard momentum charged excitations. This is in contrast with the usual quasiparticle interpretation of charged collective excitations at finite temperature in the sense of exponential relaxation of a narrow width resonance for which the width is the imaginary part of the self-energy on shell. In the case of narrow resonances away from thresholds, this approach leads to the usual exponential relaxation. The hard thermal loop resummation program is incorporated consistently into the dynamical renormalization group yielding a picture of relaxation and damping phenomena in a plasma in real time that transcends the conceptual limitations of the quasiparticle picture and other types of resummation schemes. copyright 1999 The American Physical Society

  5. Renormalization group flow of entanglement entropy on spheres

    Energy Technology Data Exchange (ETDEWEB)

    Ben-Ami, Omer; Carmi, Dean [Raymond and Beverly Sackler Faculty of Exact Sciences School of Physics and Astronomy,Tel-Aviv University, Ramat-Aviv 69978 (Israel); Smolkin, Michael [Center for Theoretical Physics and Department of Physics,University of California, Berkeley, CA 94720 (United States)

    2015-08-12

    We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the bare couplings and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in d=2,3,4. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal ‘area law’ for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.

  6. Holographic renormalization group and cosmology in theories with quasilocalized gravity

    International Nuclear Information System (INIS)

    Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John

    2001-01-01

    We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations

  7. The renormalized action principle in quantum field theory

    International Nuclear Information System (INIS)

    Balasin, H.

    1990-03-01

    The renormalized action principle holds a central position in field theory, since it offers a variety of applications. The main concern of this work is the proof of the action principle within the so-called BPHZ-scheme of renormalization. Following the classical proof given by Lam and Lowenstein, some loopholes are detected and closed. The second part of the work deals with the application of the action principle to pure Yang-Mills-theories within the axial gauge (n 2 ≠ 0). With the help of the action principle we investigate the decoupling of the Faddeev-Popov-ghost-fields from the gauge field. The consistency of this procedure, suggested by three-graph approximation, is proven to survive quantization. Finally we deal with the breaking of Lorentz-symmetry caused by the presence of the gauge-direction n. Using BRST-like techniques and the semi-simplicity of the Lorentz-group, it is shown that no new breakings arise from quantization. Again the main step of the proof is provided by the action principle. (Author, shortened by G.Q.)

  8. Effective field renormalization group approach for Ising lattice spin systems

    Science.gov (United States)

    Fittipaldi, Ivon P.

    1994-03-01

    A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

  9. Renormalized sum rules for structure functions of heavy meson decays

    International Nuclear Information System (INIS)

    Grozin, A.G.; Korchemsky, G.P.

    1996-01-01

    We consider the properties of the structure functions of inclusive heavy meson decays B→X c and treat the c quark mass as a free parameter. We show that in two extreme cases of heavy and light c quarks the structure functions of heavy-heavy and heavy-light transitions are given by a Fourier transform of the matrix elements of Wilson lines containing a timelike and a lightlike segment, correspondingly. Using the renormalization properties of Wilson lines we find the dependence of the structure functions on the factorization scale, the structure function of the heavy-heavy transition is renormalized multiplicatively, while that of the heavy-light transition obeys the GLAP-type evolution equation. We propose a generalization of the sum rules for the moments of the structure functions (Bjorken, Voloshin, and the open-quote open-quote third close-quote close-quote sum rules) with a soft exponential factorization cutoff, which correctly incorporates both perturbative and nonperturbative effects. We analyze nonperturbative corrections by first considering infrared renormalon contributions to the Wilson lines. Uncertainties induced by the leading renormalon pole at u=1/2 are exactly canceled by a similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at u=1 are parametrized by the matrix element μ π 2 which is proportional to the heavy quark kinetic energy. copyright 1996 The American Physical Society

  10. Dynamical renormalization group approach to relaxation in quantum field theory

    International Nuclear Information System (INIS)

    Boyanovsky, D.; Vega, H.J. de

    2003-01-01

    The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths

  11. A non-renormalization theorem for conformal anomalies

    International Nuclear Information System (INIS)

    Petkou, Anastasios; Skenderis, Kostas

    1999-01-01

    We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields

  12. Phase structure of NJL model with weak renormalization group

    Science.gov (United States)

    Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

    2018-06-01

    We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

  13. Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian

    Science.gov (United States)

    Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.

    2018-03-01

    Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.

  14. Green's functions for theories with massless particles (in perturbation theory). [Growth properties, momentum space, mass renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)

    1975-01-01

    With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.

  15. Renormalization group improved Yennie-Frautschi-Suura theory for Z0 physics

    International Nuclear Information System (INIS)

    Ward, B.F.L.

    1987-06-01

    Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z 0 physics at the SLC and LEP

  16. Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System

    Science.gov (United States)

    Kim, Chungku

    2018-06-01

    We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.

  17. Application of 't Hooft's renormalization scheme to two-loop calculations 230

    International Nuclear Information System (INIS)

    Vladimirov, A.A.

    1975-01-01

    The advantages of the Hooft scheme for asymptotic calculations in the renormalization group have been demonstrated. Two-loop calculations have been carried out in three renormalized models: in scalar electrodynamics, in a pseudoscalar Yukawa theory and in the Weiss-Zumino supersymmetrical model [ru

  18. Fluid flow in drying drops

    NARCIS (Netherlands)

    Gelderblom, Hanneke

    2013-01-01

    When a suspension drop evaporates, it leaves behind a drying stain. Examples of these drying stains encountered in daily life are coffee or tea stains on a table top, mineral rings on glassware that comes out of the dishwasher, or the salt deposits on the streets in winter. Drying stains are also

  19. Pressure drop in contraction flow

    DEFF Research Database (Denmark)

    Rasmussen, Henrik Koblitz

    This note is a supplement to Dynamic of Polymeric Liquids (DPL) page 178. DPL gives an equation for the pressure drop in a tapered (and circular) contraction, valid only at low angles. Here the general definition of contraction flow (the Bagley correction) and a more general method to find...

  20. Two-loop renormalization in the standard model, part I. Prolegomena

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)

    2006-12-15

    In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)

  1. Renormalization in self-consistent approximation schemes at finite temperature I: theory

    International Nuclear Information System (INIS)

    Hees, H. van; Knoll, J.

    2001-07-01

    Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)

  2. Thermal imaging of levitated fresh and salt water drops during laser irradiation

    Science.gov (United States)

    Brownell, Cody; Biggs, Harrison

    2017-11-01

    Simulation of high energy laser propagation and scattering in the maritime environment is problematic, due to the high likelihood of turbulence, fog, and rain or sea spray within the beam path. Considering large water drops (diameters of approximately 1-mm), such as those found in a light rain, an incident high energy laser will lead to rapid evaporation of the water drop as it traverses the beam path. In this work we present surface temperature measurements of a water drop obtained using a FLIR IR camera. The drop is acoustically levitated, and subject to a continuous wave laser with a wavelength of 1070-nm and a mean irradiance of approximately 800 W/cm2. These measurements show that the steady-state surface temperature of the drop is well below the saturation temperature, and for pure substances the equilibrium temperature decreases with decreasing drop volume similar to observations with smaller aqueous aerosols. Temperature non-uniformity within the drop is also assessed from statistics of the surface temperature fluctuations. Preliminary results from irradiated salt water drops show notably different behavior from fresh water drops, including temperature spikes as the drop volume decreases and occasional nucleate boiling. Acknowledge support from ONR #N00014-17-WX-00031.

  3. Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions

    DEFF Research Database (Denmark)

    Altenkamp, Lukas; Dittmaier, Stefan; Rzehak, Heidi

    2017-01-01

    We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on M S ¯ prescriptions for th...

  4. Rain drop size densities over land and over sea

    Science.gov (United States)

    Bumke, Karl

    2010-05-01

    A detailed knowledge of rain drop size densities is an essential presumption with respect to remote sensing of precipitation. Since maritime and continental aerosol is significantly different yielding to differences in cloud drop size densities, maritime and continental rain drop size densities may be different, too. In fact only a little is known about differences in rain drop size densities between land and sea due to a lack of suitable data over the sea. To fill in this gap measurements were performed during the recent 10 years at different locations in Germany and on board of research vessels over the Baltic Sea, the North Sea, Atlantic, Indian, and Pacific Ocean. Measurements were done by using an optical disdrometer (ODM 470, Großklaus et al., 1998), which is designed especially to perform precipitation measurements on moving ships and under high wind speeds. Temporal resolution of measurements is generally 1 minute, total number of time series is about 220000. To investigate differences in drop size densities over land and over sea measurements have been divided into four classes on the basis of prevailing continental or maritime influence: land measurements, coastal measurements, measurements in areas of semi-enclosed seas, and open sea measurements. In general differences in drop size densities are small between different areas. A Kolmogoroff Smirnoff test does not give any significant difference between drop size densities over land, coastal areas, semi-enclosed, and open seas at an error rate of 5%. Thus, it can be concluded that there are no systematic differences between maritime and continental drop size densities. The best fit of drop size densities is an exponential decay curve, N(D ) = 6510m -3mm -1mm0.14h- 0.14×R-0.14×exp(- 4.4mm0.25h-0.25×R- 0.25×D mm -1), it is estimated by using the method of least squares. N(D) is the drop size density normalized by the resolution of the optical disdrometer, D the diameter of rain drops in mm, and R the

  5. Functional renormalization group study of fluctuation effects in fermionic superfluids

    Energy Technology Data Exchange (ETDEWEB)

    Eberlein, Andreas

    2013-03-22

    This thesis is concerned with ground state properties of two-dimensional fermionic superfluids. In such systems, fluctuation effects are particularly strong and lead for example to a renormalization of the order parameter and to infrared singularities. In the first part of this thesis, the fermionic two-particle vertex is analysed and the fermionic renormalization group is used to derive flow equations for a decomposition of the vertex in charge, magnetic and pairing channels. In the second part, the channel-decomposition scheme is applied to various model systems. In the superfluid state, the fermionic two-particle vertex develops rich and singular dependences on momentum and frequency. After simplifying its structure by exploiting symmetries, a parametrization of the vertex in terms of boson-exchange interactions in the particle-hole and particle-particle channels is formulated, which provides an efficient description of the singular momentum and frequency dependences. Based on this decomposition of the vertex, flow equations for the effective interactions are derived on one- and two-loop level, extending existing channel-decomposition schemes to (i) the description of symmetry breaking in the Cooper channel and (ii) the inclusion of those two-loop renormalization contributions to the vertex that are neglected in the Katanin scheme. In the second part, the superfluid ground state of various model systems is studied using the channel-decomposition scheme for the vertex and the flow equations. A reduced model with interactions in the pairing and forward scattering channels is solved exactly, yielding insights into the singularity structure of the vertex. For the attractive Hubbard model at weak coupling, the momentum and frequency dependence of the two-particle vertex and the frequency dependence of the self-energy are determined on one- and two-loop level. Results for the suppression of the superfluid gap by fluctuations are in good agreement with the literature

  6. The effect of dropping impact on bruising pomegranate fruit

    Directory of Open Access Journals (Sweden)

    M Mohammad Shafie

    2016-04-01

    Full Text Available Introduction: The pomegranate journey from orchard to supermarket is very complex and pomegranates are subjected to the variety of static and dynamic loads that could result in this damage and bruise occurring. Bruise area and bruise volume are the most important parameters to evaluate fruit damage occurred in harvest and postharvest stages. The bruising is defined as damage to fruit flesh usually with no abrasion of the peel. The two different types of dynamic loading which can physically cause fruit bruising are impact and vibration. The impact and vibration loadings may occur during picking or sorting as the pomegranates are dropped into storage bins and during transportation. The focus of this work was on the impact loading as this appeared to be the most prevalent. In view of the limitations of conventional testing methods (ASTM D3332 Standard Test Methods for Mechanical Shock Fragility of Products, the method and procedure for determining dropping bruise boundary of fruit were also established by adapting free-fall dropping tests. Materials and Methods: After the ‘Malas-e-Saveh’ pomegranates had been selected, they were numbered, and the weight and dimension of each sample were measured and recorded. Firmness in cheek region of each fruit was also measured. Fruit firmness was determined by measuring the maximum force during perforating the sample to a depth of 10 mm at a velocity of 100 mm min-1 with an 8 mm diameter cylindrical penetrometer mounted onto a STM-5 Universal Testing Machine (SANTAM, Design CO. LTD., England. Free-fall dropping tests with a series of drop heights (6, 7, 10, 15, 30 and 60 cm were conducted on fresh ‘Malas-e-Saveh’ pomegranates. Three samples were used for each dropping height, and each sample was subjected to impact on two different positions. Before the test was started, it was necessary to control the sample's drop position. The cheek of sample was placed on the fruit holder. An aluminum plate mounted

  7. Pressure drop in two-phase He I natural circulation loop at low vapour quality

    International Nuclear Information System (INIS)

    Baudouy, B.

    2003-01-01

    Steady state pressure drop in a two-phase He I natural circulation loop has been measured at atmospheric pressure. Results are obtained up to 0.2 exit vapor quality for a 14-mm diameter copper tube heated over a length of 1.2 m. Pressure drop assessment, done with the momentum balance equation including subcooling, reveals that the homogeneous model and Friedel's friction multiplier associated with Huq and Loth's void fraction correlations predict data within 15%. (author)

  8. From nuclei to liquid drops

    Energy Technology Data Exchange (ETDEWEB)

    Menchaca-Rocha, A.; Huidobro, F.; Michaelian, K.; Perez, A.; Rodriguez, V. [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Fisica; Carjan, N. [Bordeaux-1 Univ., 33 - Gradignan (France). Centre d`Etudes Nucleaires

    1995-12-31

    Collisions of symmetric mercury-drop pairs have been studied experimentally as a function of impact parameter, in a relative-velocity range going from a coalescence-dominated region to interactions yielding several residues. The experiments are compared with predictions of a dynamical model used in nuclear physics. The time evolution of the shapes is well reproduced by the simulation. (authors). 8 refs., 3 figs.

  9. The dynamics of Leidenfrost drops

    OpenAIRE

    van Limbeek, Michiel Antonius Jacobus

    2017-01-01

    Temperature control is omnipresent in today’s life: from keeping your fridge cold, maintaining a room at a pleasant temperature or preventing your computer from overheating. Efficient ways of heat transfer are often based on phase change, making use of the high latent heat of evaporation. In the context of spray cooling, liquid drops are impacting a hot plate to ensure a rapid cooling. At some temperature however, no contact occurs between the liquid and the plate, and the heat transfer rate ...

  10. Topological field theory: zero-modes and renormalization

    International Nuclear Information System (INIS)

    Ouvry, S.; Thompson, G.

    1989-09-01

    We address the issue of the non-triviality of the observables in various Topological Field Theories by means of the explicit introduction of the zero-modes into the BRST algebra. Supersymmetric quantum mechanics and Topological Yang-Mills theory are dealt with in detail. It is shown that due to the presence of fermionic zero-modes the BRST algebra may be dynamically broken leading to non trivial observables albeit the local cohomology being trivial. However the metric and coupling constant independence of the observables are still valid. A renormalization procedure is given that correctly incorporates the zero-modes. Particular attention is given to the conventional gauge fixing in Topological Yang-Mills theories, with emphasis on the geometrical character of the fields and their role in the non-triviality of the observables

  11. Perturbative renormalization and effective Langrangians in Φ44

    International Nuclear Information System (INIS)

    Keller, G.; Salmhofer, M.; Kopper, C.

    1992-01-01

    Polchinski's proof of the perturbative renormalizability of massive Euclidean Φ 4 4 is considerably simplified, in some respects clarified and extended to general renormalization conditions and Green's functions with arbitrary external momenta. Φ 3 4 and Φ 2 4 are also dealt with. Moreover we show that adding e.g. Φ≥ 5 type interactions to the bare Lagrangian, with coupling constants vanishing at least as some inverse power of the UV-cutoff, does not alter the Green's functions in the limit where the UV-cutoff is removed. Establishing the validity of the action principle in this formalism has not yet been possible, but some partial results are obtained. (orig.)

  12. The renormalized theory of beam-beam interaction

    International Nuclear Information System (INIS)

    Chin, Yong Ho.

    1988-06-01

    A new approach to calculate analytically the particle distribution in the presence of beam-beam interaction and synchrotron radiation effects for an electron-positron colliding beam storage ring is presented. The method is based on correct calculation of the Green's function which includes the full effect of the beam-beam force on the distortion of particle orbits, borrowing the renormalization technique of quantum field therory. By this way, the theory is applicable to any level of beam-beam interaction, no matter whether chaos ensues in phase space or not. This paper is devoted mostly to verificaiton of the theory by comparison with the results of computer simulations. Fairly good agreements are obtained. 5 refs., 3 figs

  13. Numerical renormalization group method for entanglement negativity at finite temperature

    Science.gov (United States)

    Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.

    2018-04-01

    We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.

  14. Momentum-subtraction renormalization techniques in curved space-time

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.

    1987-10-01

    Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.

  15. Momentum-subtraction renormalization techniques in curved space-time

    International Nuclear Information System (INIS)

    Foda, O.

    1987-01-01

    Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should

  16. Gauge mediation scenario with hidden sector renormalization in MSSM

    International Nuclear Information System (INIS)

    Arai, Masato; Kawai, Shinsuke; Okada, Nobuchika

    2010-01-01

    We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5 minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.

  17. Gauge mediation scenario with hidden sector renormalization in MSSM

    Science.gov (United States)

    Arai, Masato; Kawai, Shinsuke; Okada, Nobuchika

    2010-02-01

    We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5¯ minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.

  18. High Precision Renormalization Group Study of the Roughening Transition

    CERN Document Server

    Hasenbusch, M; Pinn, K

    1994-01-01

    We confirm the Kosterlitz-Thouless scenario of the roughening transition for three different Solid-On-Solid models: the Discrete Gaussian model, the Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with standard (cosine) action. The method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are performed using efficient cluster algorithms. We obtain high precision estimates for the critical couplings and other non-universal quantities. For the XY model with cosine action our critical coupling estimate is $\\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and $K_R^{ASOS}=0.8061(3)$, respectively.

  19. Improved quasi parton distribution through Wilson line renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Jiunn-Wei [Department of Physics, Center for Theoretical Sciences, and Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 106, Taiwan (China); Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Ji, Xiangdong [INPAC, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China); Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Zhang, Jian-Hui, E-mail: jianhui.zhang@physik.uni-regensburg.de [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)

    2017-02-15

    Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV) power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a “mass” counterterm in the auxiliary z-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.

  20. Improved quasi parton distribution through Wilson line renormalization

    Directory of Open Access Journals (Sweden)

    Jiunn-Wei Chen

    2017-02-01

    Full Text Available Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a “mass” counterterm in the auxiliary z-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.

  1. Resummation and renormalization in effective theories of particle physics

    CERN Document Server

    Jakovac, Antal

    2015-01-01

    Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to vario...

  2. A geometric renormalization group in discrete quantum space-time

    International Nuclear Information System (INIS)

    Requardt, Manfred

    2003-01-01

    We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality

  3. Mutual information, neural networks and the renormalization group

    Science.gov (United States)

    Koch-Janusz, Maciej; Ringel, Zohar

    2018-06-01

    Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

  4. Renormalization group theory for percolation in time-varying networks.

    Science.gov (United States)

    Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M

    2018-05-22

    Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.

  5. Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory

    Directory of Open Access Journals (Sweden)

    Jutho Haegeman

    2018-01-01

    Full Text Available We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a “half-shift”: translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

  6. Irreversibility of world-sheet renormalization group flow

    International Nuclear Information System (INIS)

    Oliynyk, T.; Suneeta, V.; Woolgar, E.

    2005-01-01

    We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in α ' in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we give a proof by constructing an entropy that increases monotonically along the flow, based on Perelman's Ricci flow entropy. One consequence is the absence of periodic solutions, and we are able to give a second, direct proof of this. If the scalar curvature is everywhere positive, we instead construct a regularized volume to provide an entropy for the flow. Our results are, in a sense, the analogue of Zamolodchikov's c-theorem for world-sheet RG flows on noncompact spacetimes (though our entropy is not the Zamolodchikov C-function)

  7. Functional renormalization group study of the Anderson–Holstein model

    International Nuclear Information System (INIS)

    Laakso, M A; Kennes, D M; Jakobs, S G; Meden, V

    2014-01-01

    We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron–phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson–Holstein quantum dot and find clear signatures of the presence of the phonon mode. (paper)

  8. Higgs boson, renormalization group, and naturalness in cosmology

    International Nuclear Information System (INIS)

    Barvinsky, A.O.; Kamenshchik, A.Yu.; Kiefer, C.; Starobinsky, A.A.; Steinwachs, C.F.

    2012-01-01

    We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. At the one-loop level with the running of constants taken into account, it leads to a range of the Higgs mass that is entirely determined by the lower WMAP bound on the cosmic microwave background (CMB) spectral index. We find that the SM phenomenology is sensitive to current cosmological data, which suggests to perform more precise CMB measurements as a SM test complementary to the LHC program. By using the concept of a field-dependent cutoff, we show the naturalness of the gradient and curvature expansion in this model within the conventional perturbation theory range of the SM. We also discuss the relation of these results to two-loop calculations and the limitations of the latter caused by parametrization and gauge dependence problems. (orig.)

  9. Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters

    International Nuclear Information System (INIS)

    Golterman, Maarten; Shamir, Yigal

    2010-01-01

    It is usually believed that there are no perturbative anomalies in supersymmetric gauge theories beyond the well-known chiral anomaly. In this paper we revisit this issue, because previously given arguments are incomplete. Specifically, we rule out the existence of soft anomalies, i.e., quantum violations of supersymmetric Ward identities proportional to a mass parameter in a classically supersymmetric theory. We do this by combining a previously proven theorem on the absence of hard anomalies with a spurion analysis, using the methods of algebraic renormalization. We work in the on-shell component formalism throughout. In order to deal with the nonlinearity of on-shell supersymmetry transformations, we take the spurions to be dynamical, and show how they nevertheless can be decoupled.

  10. Fermi-edge singularity and the functional renormalization group

    Science.gov (United States)

    Kugler, Fabian B.; von Delft, Jan

    2018-05-01

    We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

  11. Device for making liquid drops

    International Nuclear Information System (INIS)

    Yamada, Masao; Fukuda, Fumito; Nishikawa, Masana; Ishii, Takeshi.

    1976-01-01

    Object: To provide a device for producing liquid drops in the form of liquefied gases indispensable to make deuterium and tritium ice pellets used as a fusion fuel in a tokamak type fusion reactor. Structure: First, pressure P 1 at the upper surface of liquefied gas in a container and outlet pressure P 2 of a nozzle disposed at the lower part of the container are adjusted into the state of P 1 >= P 2 , and it is preset so that even under such conditions, the liquefied gas from the nozzle is not naturally flown out. Next, a vibration plate disposed within the container is rapidly downwardly advanced toward the nozzle through a predetermined distance. As a result, pressure of the liquefied gas within a depression under the vibration plate rises instantaneously or in a pulse fashion to dissatisfy the aforesaid set condition whereby the liquefied gas may be flown out from the nozzle in the form of liquid drops. In accordance with the present device, it is possible to produce a suitable number of drops at a suitable point. (Yoshihara, H.)

  12. Diameter-speed relation of sprite streamers

    International Nuclear Information System (INIS)

    Kanmae, T; Stenbaek-Nielsen, H C; McHarg, M G; Haaland, R K

    2012-01-01

    Propagation and splitting of sprite streamers has been observed at high temporal and spatial resolution using two intensified high-speed CMOS cameras recording at 10 000 and 16 000 frames per second. Concurrent video recordings from a remote site provided data for triangulation allowing us to determine accurate altitude scales for the sprites. Diameters and speeds of the sprite streamers were measured from the high-speed images, and the diameters were scaled to the reduced diameters based on the triangulated locations. The sprite streamers with larger reduced diameter move faster than those with smaller diameter; the relation between the reduced diameter and speed is roughly linear. The reduced diameters at ≈65-70 km altitude are larger than streamer diameters measured at ground pressure in laboratory discharges indicating a deviation from the similarity law possibly due to the effects of the photoionization and an expansion of the streamer head along its propagation over a long distance. The reduced diameter and speed of the sprite streamers agree well with the diameter-velocity relation proposed by Naidis (2009 Phys. Rev. E 79 057401), and the peak electric field of the sprite streamers is estimated to be approximately 3-5 times the breakdown threshold field. (paper)

  13. The renormalization group of relativistic quantum field theory as a set of generalized, spontaneously broken, symmetry transformations

    International Nuclear Information System (INIS)

    Maris, Th.A.J.

    1976-01-01

    The renormalization group theory has a natural place in a general framework of symmetries in quantum field theories. Seen in this way, a 'renormalization group' is a one-parametric subset of the direct product of dilatation and renormalization groups. This subset of spontaneously broken symmetry transformations connects the inequivalent solutions generated by a parameter-dependent regularization procedure, as occurs in renormalized perturbation theory. By considering the global, rather than the infinitesimal, transformations, an expression for general vertices is directly obtained, which is the formal solution of exact renormalization group equations [pt

  14. Renormalization-scheme-invariant QCD and QED: The method of effective charges

    International Nuclear Information System (INIS)

    Grunberg, G.

    1984-01-01

    We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding Stueckelberg--Peterman--Gell-Mann--Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter Λ, even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass m is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales

  15. Experimental research of pressure drop in packed beds of monosized spheres a novel correlation for pressure drop calculation

    Directory of Open Access Journals (Sweden)

    Stamenić Mirjana S.

    2017-01-01

    Full Text Available Flow through packed beds of spheres is a complex phenomenon and it has been extensively studied. Although, there is many different correlations there is still no reliable universal equation for prediction of pressure drop. The paper presents the results of experimental research of pressure drop in packed bed of monosized spheres of three different diameters, 8, 11, and 13 mm set within cylindrical vessel of diameter dk = 74 mm, and two different heights of packed bed, hs = 300 and 400 mm. It has been proposed modification of widely used Ergun’s equation in the form of fp = [150+1.3•(Rep/(1-ε]•(1-ε2/(ε3×Rep and new correlation fp = 1/[(27.4-25700•dh/Rep+0.545+6.85•dh] for pressure drop calculation in simple and convenient form for hand and computer calculations. For total number of 362 experimental runs the correlation ratio of the modified Ergun’s relation was CR = 99.3%, and standard deviation SD = 12.2%, while novel relation has CR = 93.7% and SD = 5.4%. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 33049

  16. Visualization, granulometry and evaporation of drops and sprays - Study in close and pressurized atmosphere

    International Nuclear Information System (INIS)

    Lassauce, Aurelia

    2011-01-01

    The objective of this thesis is to determine the influence of ambient pressure between 100 and 600 KPa on the evaporation of a drop, and on the evaporation of a spray in the same conditions. The first step is to study the influence of ambient pressure on the evolution of the shape, the diameter, the speed and the evaporation rate of a drop of liquid in free fall. Then, an optical measurement technique has been used and a methodology was developed to calibrate this measurement technique and minimize measurement errors on the particle size. In parallel, an analytical model of evaporation of falling drops has been developed: a particular attention was paid to the determination of an appropriate correlation for the drag coefficient to take into account changes in the shape of drops during their fall. This model of evaporation of drop is compared with a spray evaporation model (taking into account the training of air, the vapor concentration away from the drop and the influence of the pressure to show the limits of this drop evaporation model when applied to the evaporation of a spray. The second phase of the study was to apply the measurement techniques and analysis developed previously to study the drop size of a spray to characterize the influence of three parameters: ambient pressure, injection pressure of the liquid and nature of the liquid. The analysis of the results allowed developing a statistical model to determine the size of the drops of these sprays [fr

  17. g-Boson renormalization effects in the interacting Boson model for nondegenerate orbits

    Science.gov (United States)

    Duval, P. D.; Pittel, S.; Barrett, B. R.; Druce, C. H.

    1983-09-01

    A nonperturbative model-space truncation procedure is utilized to include the effects of a single g boson on the parameters of the neutron-proton Interacting Boson Model in the realistic case of nondegenerate single-particle orbits. Particular emphasis is given to the single-boson energies ɛdϱ (ϱ = v, π), with numerical results presented for the even isotopes of Hg. Only part of the observed renormalization is obtained. Possible sources of further renormalizations to ɛdϱ are discussed. Results are also presented for the renormalizations of the boson quadrupole parameters κ and χϱ.

  18. The Kadanoff lower-bound variational renormalization group applied to an SU(2) lattice spin model

    International Nuclear Information System (INIS)

    Thorleifsson, G.; Damgaard, P.H.

    1990-07-01

    We apply the variational lower-bound Renormalization Group transformation of Kadanoff to an SU(2) lattice spin model in 2 and 3 dimensions. Even in the one-hypercube framework of this renormalization group transformation the present model is characterised by having an infinite basis of fundamental operators. We investigate whether the lower-bound variational renormalization group transformation yields results stable under truncations of this operator basis. Our results show that for this particular spin model this is not the case. (orig.)

  19. Strong renormalization scheme dependence in τ-lepton decay: Fact or fiction?

    International Nuclear Information System (INIS)

    Chyla, J.

    1995-01-01

    The question of the renormalization scheme dependence of the τ semileptonic decay rate is examined in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this dependence and the actual selection of a subset of ''acceptable'' renormalization schemes. It is pointed out that this criticism is valid only within a particular definition of the ''strength'' of the renormalization scheme dependence and should not discourage further attempts to use the semileptonic τ decay rate for quantitative tests of perturbative QCD

  20. Renormalization of the nonlinear O(3) model with θ-term

    Energy Technology Data Exchange (ETDEWEB)

    Flore, Raphael, E-mail: raphael.flore@uni-jena.de [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)

    2013-05-11

    The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.

  1. Renormalization-group theory for the eddy viscosity in subgrid modeling

    Science.gov (United States)

    Zhou, YE; Vahala, George; Hossain, Murshed

    1988-01-01

    Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

  2. Pressure drop and He II flow through fine mesh screens

    Science.gov (United States)

    Maddocks, J. R.; van Sciver, S. W.

    1989-05-01

    Fluid acquisition systems for He II transfer devices will utilize gallery arms to ensure that the fluid encounters the pump inlet. In near term experiments such as Superfluid Helium on Orbit Transfer (SHOOT), the preferred configuration consists of several rectangular channels which have one side made from a Dutch weave stainless steel screen having 325 x 2300 wires per inch. The effective pore diameter for this screen is about 5 microns. The present paper reports on measurements of pressure drop across a screen when it is subjected to a flow of liquid helium. The experiment measures the time rate of change of the level in two different helium reservoirs connected by a screen-blocked channel. Results with normal helium are compared with predictions based on the Armour-Cannon (1968) equations. The He II data show considerable deviation from the classical result. A discussion of the He II pressure drop results in terms of two fluid hydrodynamics is included.

  3. Vortex flow in acoustically levitated drops

    Energy Technology Data Exchange (ETDEWEB)

    Yan, Z.L.; Xie, W.J. [Department of Applied Physics, Northwestern Polytechnical University, Xi' an 710072 (China); Wei, B., E-mail: bbwei@nwpu.edu.cn [Department of Applied Physics, Northwestern Polytechnical University, Xi' an 710072 (China)

    2011-08-29

    The internal flow of acoustically levitated water drops is investigated experimentally. This study reveals a kind of vortex flow which rotates in the meridional plane of the levitated drop. The magnitude of fluid velocity is nearly vanishing at the drop center, whereas it increases toward the free surface of a levitated drop until the maximum value of about 80 mm/s. A transition of streamline shapes from concentric circles to ellipses takes place at the distance of about 1.2 mm from the drop center. The fluid velocity distribution is plotted as a function of polar angle for seven characteristic streamlines. -- Highlights: → We experimentally observe the internal flow of acoustically levitated water drops. → We present a fascinating structure of vortex flow inside the levitated water drop. → This vortex flow rotates around the drop center in the meridional plane. → Velocity distribution information of this vortex flow is quantitatively analyzed.

  4. Vortex flow in acoustically levitated drops

    International Nuclear Information System (INIS)

    Yan, Z.L.; Xie, W.J.; Wei, B.

    2011-01-01

    The internal flow of acoustically levitated water drops is investigated experimentally. This study reveals a kind of vortex flow which rotates in the meridional plane of the levitated drop. The magnitude of fluid velocity is nearly vanishing at the drop center, whereas it increases toward the free surface of a levitated drop until the maximum value of about 80 mm/s. A transition of streamline shapes from concentric circles to ellipses takes place at the distance of about 1.2 mm from the drop center. The fluid velocity distribution is plotted as a function of polar angle for seven characteristic streamlines. -- Highlights: → We experimentally observe the internal flow of acoustically levitated water drops. → We present a fascinating structure of vortex flow inside the levitated water drop. → This vortex flow rotates around the drop center in the meridional plane. → Velocity distribution information of this vortex flow is quantitatively analyzed.

  5. Drag and drop display & builder

    Energy Technology Data Exchange (ETDEWEB)

    Bolshakov, Timofei B.; Petrov, Andrey D.; /Fermilab

    2007-12-01

    The Drag and Drop (DnD) Display & Builder is a component-oriented system that allows users to create visual representations of data received from data acquisition systems. It is an upgrade of a Synoptic Display mechanism used at Fermilab since 2002. Components can be graphically arranged and logically interconnected in the web-startable Project Builder. Projects can be either lightweight AJAX- and SVG-based web pages, or they can be started as Java applications. The new version was initiated as a response to discussions between the LHC Controls Group and Fermilab.

  6. CANFLEX fuel bundle junction pressure drop

    International Nuclear Information System (INIS)

    Chung, H. J.; Chung, C. H.; Jun, J. S.; Hong, S. D.; Chang, S. K.; Kim, B. D.

    1996-11-01

    This report describes the junction pressure drop test results which are to used to determine the alignment angle between bundles to achieve the most probable fuel string pressure drop for randomly aligned bundles for use in the fuel string total pressure drop test. (author). 4 tabs., 17 figs

  7. CANFLEX fuel bundle junction pressure drop

    Energy Technology Data Exchange (ETDEWEB)

    Chung, H. J.; Chung, C. H.; Jun, J. S.; Hong, S. D.; Chang, S. K.; Kim, B. D.

    1996-11-01

    This report describes the junction pressure drop test results which are to used to determine the alignment angle between bundles to achieve the most probable fuel string pressure drop for randomly aligned bundles for use in the fuel string total pressure drop test. (author). 4 tabs., 17 figs.

  8. 49 CFR 178.603 - Drop test.

    Science.gov (United States)

    2010-10-01

    ... used for the hydrostatic pressure or stacking test. Exceptions for the number of steel and aluminum..., non-resilient, flat and horizontal surface. (e) Drop height. Drop heights, measured as the vertical... than flat drops, the center of gravity of the test packaging must be vertically over the point of...

  9. 7 CFR 51.320 - Diameter.

    Science.gov (United States)

    2010-01-01

    ... Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE REGULATIONS AND STANDARDS UNDER THE AGRICULTURAL MARKETING ACT OF 1946... Standards for Grades of Apples Definitions § 51.320 Diameter. When measuring for minimum size, “diameter...

  10. Drop Characteristics of non-Newtonian Impinging Jets at High Generalized Bird-Carreau Jet Reynolds Numbers

    Science.gov (United States)

    Sojka, Paul E.; Rodrigues, Neil S.

    2015-11-01

    The current study investigates the drop characteristics of three Carboxymethylcellulose (CMC) sprays produced by the impingement of two liquid jets. The three water-based solutions used in this work (0.5 wt.-% CMC-7MF, 0.8 wt.-% CMC-7MF, and 1.4 wt.-% CMC-7MF) exhibited strong shear-thinning, non-Newtonian behavior - characterized by the Bird-Carreau rheological model. A generalized Bird-Carreau jet Reynolds number was used as the primary parameter to characterize the drop size and the drop velocity, which were measured using Phase Doppler Anemometry (PDA). PDA optical configuration enabled a drop size measurement range of approximately 2.3 to 116.2 μm. 50,000 drops were measured at each test condition to ensure statistical significance. The arithmetic mean diameter (D10) , Sauter mean diameter (D32) , and mass median diameter (MMD) were used as representative diameters to characterize drop size. The mean axial drop velocity Uz -mean along with its root-mean square Uz -rms were used to characterize drop velocity. Incredibly, measurements for all three CMC liquids and reference DI water sprays seemed to follow a single curve for D32 and MMD drop diameters in the high generalized Bird-Carreau jet Reynolds number range considered in this work (9.21E +03

  11. The Implementation of the Renormalized Complex MSSM in FeynArts and FormCalc

    CERN Document Server

    Fritzsche, T; Heinemeyer, S; Rzehak, H; Schappacher, C

    2014-01-01

    We describe the implementation of the renormalized complex MSSM (cMSSM) in the diagram generator FeynArts and the calculational tool FormCalc. This extension allows to perform UV-finite one-loop calculations of cMSSM processes almost fully automatically. The Feynman rules for the cMSSM with counterterms are available as a new model file for FeynArts. Also included are default definitions of the renormalization constants; this fixes the renormalization scheme. Beyond that all model parameters are generic, e.g. we do not impose any relations to restrict the number of input parameters. The model file has been tested extensively for several non-trivial decays and scattering reactions. Our renormalization scheme has been shown to give stable results over large parts of the cMSSM parameter space.

  12. Comment on non-renormalization theorem in the four dimensional superstrings

    International Nuclear Information System (INIS)

    Soda, Jiro; Nakazawa, Naohito; Sakai, Kenji; Ojima, Shuichi.

    1987-10-01

    We discuss non-renormalization theorem in the context of the four dimensional superstrings. We explicitly demonstrate that the graviton 3-point one-loop amplitude does not vanish in contrast to the ten dimensional superstring theories. (author)

  13. Introduction to the renormalization group study in relativistic quantum field theory

    International Nuclear Information System (INIS)

    Mignaco, J.A.; Roditi, I.

    1985-01-01

    An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.) [pt

  14. Two-and three-dimension Potts magnetism in the renormalization group approximation

    International Nuclear Information System (INIS)

    Silva, L.R. da.

    1985-01-01

    Through a real space Renormalization Group (RG) technique we discuss the criticality of various physical systems, calculate order parameters for geometrical problems and analyse convergence aspects of the RG theory. (author) [pt

  15. Renormalization theory of stationary homogeneous strong turbulence in a collisionless plasma

    International Nuclear Information System (INIS)

    Zhang, Y.Z.

    1984-01-01

    A renormalization procedure for the perturbation expansion of the Vlasov-Poisson equation is presented to describe stationary homogeneous turbulence. By using the diagramatic scheme the theory is shown to be renormalizable to any order. The expressions for the renormalized propagator, the renormalized dielectric function, and the intrinsically incoherent source are given. The renormalization leads to a complete separation of the fluctuating distribution function f/sub k/ into two parts, the coherent part, which is proved to represent the dielectric effect of the medium, and the intrinsically incoherent part, which represents the effect of nonlinear source. The turbulent collisional operator in the transport equation is proved equal to GAMMA 0 , the frequency broadening when k = 0

  16. How to resolve the factorization- and the renormalization-scheme ambiguities simultaneously

    International Nuclear Information System (INIS)

    Nakkagawa, H.; Niegawa, A.

    1982-01-01

    A combined investigation of both the factorization- and renormalization-scheme dependences of perturbative QCD calculations is reported. Applyong Stevenson's optimization method, we get a remarkable result, which forces us to exponentiate 'everything' with uncorrected subprocess cross sections. (orig.)

  17. Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

    Science.gov (United States)

    Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

    2012-07-01

    We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

  18. Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik

    2007-06-15

    We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)

  19. Diameter-dependent coloration of silver nanowires

    International Nuclear Information System (INIS)

    Stewart, Mindy S; Qiu Chao; Jiang Chaoyang; Kattumenu, Ramesh; Singamaneni, Srikanth

    2011-01-01

    Silver nanowires were synthesized with a green method and characterized with microscopic and diffractometric methods. The correlation between the colors of the nanowires deposited on a solid substrate and their diameters was explored. Silver nanowires that appear similar in color in the optical micrographs have very similar diameters as determined by atomic force microscopy. We have summarized the diameter-dependent coloration for these silver nanowires. An optical interference model was applied to explain such correlation. In addition, microreflectance spectra were obtained from individual nanowires and the observed spectra can be explained with the optical interference theory. This work provides a cheap, quick and simple screening method for studying the diameter distribution of silver nanowires, as well as the diameter variations of individual silver nanowires, without complicated sample preparation.

  20. Electrohydrodynamics of a viscous drop with inertia.

    Science.gov (United States)

    Nganguia, H; Young, Y-N; Layton, A T; Lai, M-C; Hu, W-F

    2016-05-01

    Most of the existing numerical and theoretical investigations on the electrohydrodynamics of a viscous drop have focused on the creeping Stokes flow regime, where nonlinear inertia effects are neglected. In this work we study the inertia effects on the electrodeformation of a viscous drop under a DC electric field using a novel second-order immersed interface method. The inertia effects are quantified by the Ohnesorge number Oh, and the electric field is characterized by an electric capillary number Ca_{E}. Below the critical Ca_{E}, small to moderate electric field strength gives rise to steady equilibrium drop shapes. We found that, at a fixed Ca_{E}, inertia effects induce larger deformation for an oblate drop than a prolate drop, consistent with previous results in the literature. Moreover, our simulations results indicate that inertia effects on the equilibrium drop deformation are dictated by the direction of normal electric stress on the drop interface: Larger drop deformation is found when the normal electric stress points outward, and smaller drop deformation is found otherwise. To our knowledge, such inertia effects on the equilibrium drop deformation has not been reported in the literature. Above the critical Ca_{E}, no steady equilibrium drop deformation can be found, and often the drop breaks up into a number of daughter droplets. In particular, our Navier-Stokes simulations show that, for the parameters we use, (1) daughter droplets are larger in the presence of inertia, (2) the drop deformation evolves more rapidly compared to creeping flow, and (3) complex distribution of electric stresses for drops with inertia effects. Our results suggest that normal electric pressure may be a useful tool in predicting drop pinch-off in oblate deformations.

  1. Alternating chain with Hubbard-type interactions: renormalization group analysis

    International Nuclear Information System (INIS)

    Buzatu, F. D.; Jackeli, G.

    1998-01-01

    A large amount of work has been devoted to the study of alternating chains for a better understanding of the high-T c superconductivity mechanism. The same phenomenon renewed the interest in the Hubbard model and in its one-dimensional extensions. In this work we investigate, using the Renormalization Group (RG) method, the effect of the Hubbard-type interactions on the ground-state properties of a chain with alternating on-site atomic energies. The one-particle Hamiltonian in the tight binding approximation corresponding to an alternating chain with two nonequivalent sites per unit cell can be diagonalized by a canonical transformation; one gets a two band model. The Hubbard-type interactions give rise to both intra- and inter-band couplings; however, if the gap between the two bands is sufficiently large and the system is more than half-filled, as for the CuO 3 chain occurring in high-T c superconductors, the last ones can be neglected in describing the low energy physics. We restrict our considerations to the Hubbard-type interactions (upper band) in the particular case of alternating on-site energies and equal hopping amplitudes. The standard RG analysis (second order) is done in terms of the g-constants describing the elementary processes of forward, backward and Umklapp scatterings: their expressions are obtained by evaluating the Hubbard-type interactions (upper band) at the Fermi points. Using the scaling to the exact soluble models Tomonaga-Luttinger and Luther-Emery, we can predict the low energy physics of our system. The ground-state phase diagrams in terms of the model parameters and at arbitrary band filling are determined, where four types of instabilities have been considered: Charge Density Waves (CDW), Spin Density Waves (SDW), Singlet Superconductivity (SS) and Triplet Superconductivity (TS). The 3/4-filled case in terms of some renormalized Hubbard constants is presented. The relevance of our analysis to the case of the undistorted 3/4-filled Cu

  2. A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

    OpenAIRE

    SASAKURA, NAOKI

    2010-01-01

    Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

  3. Renormalization group treatment for spin waves in the randomly disordered Heisenberg chain

    International Nuclear Information System (INIS)

    Chaves, C.M.; Koiller, B.

    1983-03-01

    Local densities of states in the randomly disordered binary quantum Heisenberg chain using a generalization of a recently developed approach based on renormalization group ideas are calculated. It envolves decimating alternate apins along the chain in such a way as to obtain recursion relations to describe the renormalized set of Green's function equations of motion. The densities of states are richly structured, indicating that the method takes into account compositional fluctuations of arbitrary range. (Author) [pt

  4. Application of the renormalization group to the study of structure function in the deep inelastic scattering

    International Nuclear Information System (INIS)

    Dias, S.A.

    1985-01-01

    The transformation law of truncated pertubation theory observables under changes of renormalization scheme is deduced. Based on this, a criticism of the calculus of the moments of structure functions in deep inelastic scattering, obtaining that the A 2 coefficient not renormalization group invariant is done. The PMS criterion is used to optimize the perturbative productions of the moments, truncated to 2nd order. (author) [pt

  5. Experimental test of renormalization group theory on the uniaxial, dipolar coupled ferromagnet LiTbf4

    DEFF Research Database (Denmark)

    Als-Nielsen, Jens Aage

    1976-01-01

    The transverse correlation range ξ and the susceptibility in the critical region has been measured by neutron scattering. A special technique required to resolve the superdiverging longitudinal correlation range has been utilized. The results for ξ together with existing specific-heat data are in...... are in remarkable agreement with the renormalization group theory of systems with marginal dimensionality. The ratio between the susceptibility amplitudes above and below Tc was found to be 2 in accordance with renormalization-group and meanfield theory....

  6. Renormalization group and relations between scattering amplitudes in a theory with different mass scales

    International Nuclear Information System (INIS)

    Gulov, A.V.; Skalozub, V.V.

    2000-01-01

    In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives possibility to reduce the problem to the scattering of light particles on the external field substituting a heavy virtual state. Applications of the results to problem of searching new physics beyond the Standard Model are discussed [ru

  7. Full counting statistics of level renormalization in electron transport through double quantum dots

    International Nuclear Information System (INIS)

    Luo Junyan; Shen Yu; Cen Gang; He Xiaoling; Wang Changrong; Jiao Hujun

    2011-01-01

    We examine the full counting statistics of electron transport through double quantum dots coupled in series, with particular attention being paid to the unique features originating from level renormalization. It is clearly illustrated that the energy renormalization gives rise to a dynamic charge blockade mechanism, which eventually results in super-Poissonian noise. Coupling of the double dots to an external heat bath leads to dephasing and relaxation mechanisms, which are demonstrated to suppress the noise in a unique way.

  8. Renormalized perturbation theory: Vlasov-Poisson System, weak turbulence limit and gyrokinetics

    International Nuclear Information System (INIS)

    Zhang, Y.Z.; Mahajan, S.M.

    1987-10-01

    The Self-consistency of the renormalized perturbation theory is demonstrated by applying it to the Vlasov-Poisson System and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-β gyrokinetic system. Comparison of our theory with other current theories is presented. 22 refs

  9. Quark-mixing renormalization effects on the W-boson partial decay widths

    International Nuclear Information System (INIS)

    Almasy, A.A.; Kniehl, B.A.; Sirlin, A.

    2008-10-01

    We briefly review existing proposals for the renormalization of the Cabibbo- Kobayashi-Maskawa matrix and study their numerical effects on the W-boson partial decay widths. The differences between the decay widths predicted by the various renormalization schemes are generally negligible, while their deviations from the MS results are very small, except for W + → u anti b and W + →c anti b, where they reach approximately 4%. (orig.)

  10. Renormalization-group decimation technique for spectra, wave-functions and density of states

    International Nuclear Information System (INIS)

    Wiecko, C.; Roman, E.

    1983-09-01

    The Renormalization Group decimation technique is very useful for problems described by 1-d nearest neighbour tight-binding model with or without translational invariance. We show how spectra, wave-functions and density of states can be calculated with little numerical work from the renormalized coefficients upon iteration. The results of this new procedure are verified using the model of Soukoulis and Economou. (author)

  11. Capillary Thinning of Particle-laden Drops

    Science.gov (United States)

    Wagoner, Brayden; Thete, Sumeet; Jahns, Matt; Doshi, Pankaj; Basaran, Osman

    2015-11-01

    Drop formation is central in many applications such as ink-jet printing, microfluidic devices, and atomization. During drop formation, a thinning filament is created between the about-to-form drop and the fluid hanging from the nozzle. Therefore, the physics of capillary thinning of filaments is key to understanding drop formation and has been thoroughly studied for pure Newtonian fluids. The thinning dynamics is, however, altered completely when the fluid contains particles, the physics of which is not well understood. In this work, we explore the impact of solid particles on filament thinning and drop formation by using a combination of experiments and numerical simulations.

  12. Vibration-Induced Climbing of Drops

    Science.gov (United States)

    Brunet, P.; Eggers, J.; Deegan, R. D.

    2007-10-01

    We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wetted by the drop. The frequency of vibrations ranges from 30 to 200 Hz, and, above a threshold in vibration acceleration, drops experience an upward motion. We attribute this surprising motion to the deformations of the drop, as a consequence of an up or down symmetry breaking induced by the presence of the substrate. We relate the direction of motion to contact angle measurements. This phenomenon can be used to move a drop along an arbitrary path in a plane, without special surface treatments or localized forcing.

  13. A complete non-perturbative renormalization prescription for quasi-PDFs

    Energy Technology Data Exchange (ETDEWEB)

    Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Constantinou, Martha [Temple Univ., Philadelphia, PA (United States). Dept. of Physics; Hadjiyiannakou, Kyriakos [The Cyprus Institute, Nicosia (Cyprus); Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Panagopoulos, Haralambos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Collaboration: European Twisted Mass Collaboration

    2017-06-15

    In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI{sup '} scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with N{sub f}=2+1+1 dynamical quarks, and a pion mass of around 375 MeV.

  14. Setting the renormalization scale in QCD: The principle of maximum conformality

    DEFF Research Database (Denmark)

    Brodsky, S. J.; Di Giustino, L.

    2012-01-01

    A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormali......A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when...... the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta...... = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit...

  15. All-order renormalization of propagator matrix for fermionic system with flavor mixing

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics

    2013-08-15

    We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.

  16. Structural impact on the eigenenergy renormalization for carbon and silicon allotropes and boron nitride polymorphs

    Science.gov (United States)

    Tutchton, Roxanne; Marchbanks, Christopher; Wu, Zhigang

    2018-05-01

    The phonon-induced renormalization of electronic band structures is investigated through first-principles calculations based on the density functional perturbation theory for nine materials with various crystal symmetries. Our results demonstrate that the magnitude of the zero-point renormalization (ZPR) of the electronic band structure is dependent on both crystal structure and material composition. We have performed analysis of the electron-phonon-coupling-induced renormalization for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Phonon dispersions of each material were computed, and our analysis indicates that materials with optical phonons at higher maximum frequencies, such as graphite and hexagonal BN, have larger absolute ZPRs, with the exception of graphene, which has a considerably smaller ZPR despite having phonon frequencies in the same range as graphite. Depending on the structure and material, renormalizations can be comparable to the GW many-body corrections to Kohn-Sham eigenenergies and, thus, need to be considered in electronic structure calculations. The temperature dependence of the renormalizations is also considered, and in all materials, the eigenenergy renormalization at the band gap and around the Fermi level increases with increasing temperature.

  17. Application of hydrochloric cyclopentolate eye drops in the mydriasis test and optometry for children with hyperopia

    Directory of Open Access Journals (Sweden)

    Hong-Ping Yin

    2016-02-01

    Full Text Available AIM:To observe and study the comprehensive application effect of hydrochloric cyclopentolate eye drops in the mydriasis test and optometry for children with hyperopia.METHODS:Eighty-four children with hyperopia who were intervened with mydriasis test and optometry in our hospital from February 2014 to March 2015 were selected as the research object,and they were intervened with mydriasis test and optometry by tropicamide or hydrochloric cyclopentolate eye drops. The diopter, pupil diameter and residual regulation before administration and at different time after administration of the two methods were compared,and the detected results of the two groups with different severity degree were compared too.RESULTS:The diopter, pupil diameter and residual regulation before administration of the two eye drops had no significant differences(all P>0.05,while the residual regulation after using hydrochloric cyclopentolate eye drops at 20, 40, 60min and 24h were all smaller than those after using tropicamide(all PP>0.05. The pupil diameter of the two groups at 48h after administration both had no significant differences to those before administration(all P>0.05.CONCLUSION:The comprehensive application effect of hydrochloric cyclopentolate eye drops in the mydriasis test and optometry of children with hyperopia is better,and its paralysis effect for ciliaris is obvious.

  18. Breaking generalized covariance, classical renormalization, and boundary conditions from superpotentials

    International Nuclear Information System (INIS)

    Livshits, Gideon I.

    2014-01-01

    Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson

  19. Renormalization group evolution of the universal theories EFT

    International Nuclear Information System (INIS)

    Wells, James D.; Zhang, Zhengkang

    2016-01-01

    The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.

  20. Phenomenological renormalization of free nucleon-nucleon interaction

    International Nuclear Information System (INIS)

    Prakash, M.; Waghmare, Y.R.; Mehrotra, I.

    1976-01-01

    Low-lying spectra of 6 Li, 18 F, 18 O, 42 Sc, 42 Ca, 58 Ni and 92 Zr are studied with Sussex matrix elements (SME) and their central, spin-orbit and tensor components. It is observed that major contribution to level energies comes from the central part, while the tensor part provides the finer details of spectra, particularly for T = 0 levels. The spin-orbit part does not make any appreciable contribution to level energies. A phenomenological renormalization fo the SME is carried out to improve the agreement with the experimental results. It turns out that some of the low-lying T = 0 levels can be satisfactorily described if the SME in the 3 S 1 relative state are made (1+α) times their bare interaction value, where α is a constant to be determined from a comparison with experimental level energies. Similarly, for T = 1 levels, better agreement with the experimental results is obtained if a delta-function-plus-quadrupole interaction is added to the SME. (orig.) [de

  1. Renormalization group method in the theory of dynamical systems

    International Nuclear Information System (INIS)

    Sinai, Y.G.; Khanin, K.M.

    1988-01-01

    One of the most important events in the theory of dynamical systems for the last decade has become a wide penetration of ideas and renormalization group methods (RG) into this traditional field of mathematical physics. RG-method has been one of the main tools in statistical physics and it has proved to be rather effective while solving problems of the theory of dynamical systems referring to new types of bifurcations (see further). As in statistical mechanics the application of the RG-method is of great interest in the neighborhood of the critical point concerning the order-chaos transition. First the RG-method was applied in the pioneering papers dedicated to the appearance of a stochastical regime as a result of infinite sequences of period doubling bifurcations. At present this stochasticity mechanism is the most studied one and many papers deal with it. The study of the so-called intermittency phenomenon was the next example of application of the RG-method, i.e. the study of such a situation where the domains of the stochastical and regular behavior do alternate along a trajectory of the dynamical system

  2. Renormalized multiple-scattering theory of photoelectron diffraction

    International Nuclear Information System (INIS)

    Biagini, M.

    1993-01-01

    The current multiple-scattering cluster techniques for the calculation of x-ray photoelectron and Auger-electron diffraction patterns consume much computer time in the intermediate-energy range (200--1000 eV); in fact, because of the large value of the electron mean free path and of the large forward-scattering amplitude at such energies, the electron samples a relatively large portion of the crystal, so that the number of paths to be considered becomes dramatically high. An alternative method is developed in the present paper: instead of calculating the individual contribution from each single path, the scattering matrix of each plane parallel to the surface is calculated with a renormalization process that calculates every scattering event in the plane up to infinite order. Similarly the scattering between two planes is calculated up to infinite order, and the double-plane scattering matrix is introduced. The process may then be applied to the calculation of a larger set of atomic layers. The advantage of the method is that a relatively small number of internuclear vectors have been used to obtain convergence in the calculation

  3. Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model

    Energy Technology Data Exchange (ETDEWEB)

    Friederich, Simon

    2010-12-08

    Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)

  4. Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model

    International Nuclear Information System (INIS)

    Friederich, Simon

    2010-01-01

    Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T c cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)

  5. Anatomy of the magnetic catalysis by renormalization-group method

    Science.gov (United States)

    Hattori, Koichi; Itakura, Kazunori; Ozaki, Sho

    2017-12-01

    We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu-Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

  6. Renormalization group approach to a p-wave superconducting model

    International Nuclear Information System (INIS)

    Continentino, Mucio A.; Deus, Fernanda; Caldas, Heron

    2014-01-01

    We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.

  7. Spectral functions and transport coefficients from the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Tripolt, Ralf-Arno

    2015-06-03

    In this thesis we present a new method to obtain real-time quantities like spectral functions and transport coefficients at finite temperature and density using the Functional Renormalization Group approach. Our non-perturbative method is thermodynamically consistent, symmetry preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations. We demonstrate the applicability of this method by calculating mesonic spectral functions as well as the shear viscosity for the quark-meson model. In particular, results are presented for the pion and sigma spectral function at finite temperature and chemical potential, with a focus on the regime near the critical endpoint in the phase diagram of the quark-meson model. Moreover, the different time-like and space-like processes, which give rise to a complex structure of the spectral functions, are discussed. Finally, based on the momentum dependence of the spectral functions, we calculate the shear viscosity and the shear viscosity to entropy density ratio using the corresponding Green-Kubo formula.

  8. Driven similarity renormalization group: Third-order multireference perturbation theory.

    Science.gov (United States)

    Li, Chenyang; Evangelista, Francesco A

    2017-03-28

    A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6 ) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2 , H 2 O 2 , C 2 H 6 , and N 2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST =E T -E S ) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol -1 , a value that is within 0.1 kcal mol -1 from multireference coupled cluster results.

  9. Interleaved numerical renormalization group as an efficient multiband impurity solver

    Science.gov (United States)

    Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.

    2016-06-01

    Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.

  10. Temperature dependent quasiparticle renormalization in nickel and iron

    Energy Technology Data Exchange (ETDEWEB)

    Ovsyannikov, Ruslan; Thirupathaiah, Setti; Sanchez-Barriga, Jaime; Fink, Joerg; Duerr, Hermann [Helmholtz Zentrum Berlin, BESSY II, Albert-Einstein-Strasse 15, D-12489 Berlin (Germany)

    2010-07-01

    One of the fundamental consequences of electron correlation effects is that the bare particles in solids become 'dressed' with an excitation cloud resulting in quasiparticles. Such a quasiparticle will carry the same spin and charge as the original particle, but will have a renormalized mass and a finite lifetime. The properties of many-body interactions are described with a complex function called self energy which is directly accessible to modern high-resolution angle resolved photoemission spectroscopy (ARPES). Ferromagnetic metals like nickel or iron offers the exciting possibility to study the spin dependence of quasiparticle coupling to bosonic modes. Utilizing the exchange split band structure as an intrinsic 'spin detector' it is possible to distinguish between electron-phonon and electron-magnon coupling phenomena. In this contribution we will report a systematic investigation of the k- and temperature dependence of the electron-boson coupling in nickel and iron metals as well as discuss origin of earlier observed anomalous lifetime broadening of majority spin states of nickel at Fermi level.

  11. Bogolyubov renormalization group and symmetry of solution in mathematical physics

    International Nuclear Information System (INIS)

    Shirkov, D.V.; Kovalev, V.F.

    2000-01-01

    Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparametrization one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of a new approach to solution for a problem of self-focusing laser beam in a nonlinear medium

  12. Anatomy of the magnetic catalysis by renormalization-group method

    Directory of Open Access Journals (Sweden)

    Koichi Hattori

    2017-12-01

    Full Text Available We first examine the scaling argument for a renormalization-group (RG analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger–Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu–Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

  13. Ultrasoft renormalization of the potentials in vNRQCD

    Energy Technology Data Exchange (ETDEWEB)

    Stahlhofen, Maximilian Horst

    2009-02-18

    The effective field theory vNRQCD allows to describe among others the production of top-antitop pairs in electron-positron collisions at threshold, i.e. with very small relative velocity {upsilon} << 1 of the quarks. Potentially large logarithms {proportional_to} ln {upsilon} are systematically summed up and lead to a scale dependence of the Wilson coefficients of the theory. The missing contributions to the cross section {sigma}(e{sup +}e{sup -} {yields} t anti t) in the resonance region at NNLL level are the so-called mixing contributions to the NNLL anomalous dimension of the S-wave production/annihilation current of the topquark pair. To calculate these one has to know the NLL renormalization group running of so-called potentials (4-quark operators). The dominant contributions to the anomalous dimension of these potentials come from vNRQCD diagrams with ultrasoft gluon loops. The aim of this thesis is to derive the complete ultrasoft NLL running of the relevant potentials. For that purpose the UV divergent parts of about 10{sup 4} two-loop diagrams are determined. Technical and conceptional issues are discussed. Some open questions related to the calculation of the non-Abelian two-loop diagrams arise. Preliminary results are analysed with regard to the consequences for the mentioned cross section and its theoretical uncertainty. (orig.)

  14. Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids

    International Nuclear Information System (INIS)

    Meden, V; Schoeller, H; Andergassen, S; Enss, T; Schoenhammer, K

    2008-01-01

    We compare two fermionic renormalization group (RG) methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor man's method set-up to resum 'leading-log' divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional RG (fRG) method and leads to a set of differential equations which can only for certain set-ups and in limiting cases be solved analytically, while in general it must be integrated numerically. Both methods are claimed to be applicable for inhomogeneities of arbitrary strength and to capture effects of the two-particle interaction, such as interaction dependent exponents, up to leading order. We critically review this for the simplest case of a single impurity. While on first glance the poor man's approach seems to describe the crossover from the 'perfect' to the 'open chain fixed point' we collect evidence that difficulties may arise close to the 'perfect chain fixed point'. Due to a subtle relation between the scaling dimensions of the two fixed points this becomes apparent only in a detailed analysis. In the fRG method the coupling of the different scattering channels is kept which leads to a better description of the underlying physics

  15. Who is dropping your course?

    Science.gov (United States)

    Storrs, Alex; Ghent, C.; Labattaglia, R.

    2011-01-01

    We present an analysis of pre and post instruction instruments in a basic astronomy course. This analysis is built on the Light and Spectroscopy Concept Inventory (LSCI, Bardar et al. 2007). In addition to assessing our student's gain in knowledge of this fundamental topic, we have added some demographic questions. While the primary purpose is to compare the gain in knowledge during a semester of instruction to changes in instruction, we also look at the demographics of students who take the pretest but not the posttest. These students are usually excluded from this type of analysis. We look for trends in the demographic information among students who drop the course, and suggest ways to make the course more palatable. References: Bardar et al., 2007: "Development and Validation of the Light and Spectroscopy Concept Inventory", Astr. Ed. Rev. 5(2), 103-113

  16. Magnetically focused liquid drop radiator

    Science.gov (United States)

    Botts, Thomas E.; Powell, James R.; Lenard, Roger

    1986-01-01

    A magnetically focused liquid drop radiator for application in rejecting rgy from a spacecraft, characterized by a magnetizable liquid or slurry disposed in operative relationship within the liquid droplet generator and its fluid delivery system, in combination with magnetic means disposed in operative relationship around a liquid droplet collector of the LDR. The magnetic means are effective to focus streams of droplets directed from the generator toward the collector, thereby to assure that essentially all of the droplets are directed into the collector, even though some of the streams may be misdirected as they leave the generator. The magnetic focusing means is also effective to suppress splashing of liquid when the droplets impinge on the collector.

  17. Two-phase flow boiling pressure drop in small channels

    International Nuclear Information System (INIS)

    Sardeshpande, Madhavi V.; Shastri, Parikshit; Ranade, Vivek V.

    2016-01-01

    Highlights: • Study of typical 19 mm steam generator tube has been undertaken in detail. • Study of two phase flow boiling pressure drop, flow instability and identification of flow regimes using pressure fluctuations is the main focus of present work. • Effect of heat and mass flux on pressure drop and void fraction was studied. • Flow regimes identified from pressure fluctuations data using FFT plots. • Homogeneous model predicted pressure drop well in agreement. - Abstract: Two-phase flow boiling in small channels finds a variety of applications in power and process industries. Heat transfer, boiling flow regimes, flow instabilities, pressure drop and dry out are some of the key issues related to two-phase flow boiling in channels. In this work, the focus is on pressure drop in two-phase flow boiling in tubes of 19 mm diameter. These tubes are typically used in steam generators. Relatively limited experimental database is available on 19 mm ID tube. Therefore, in the present work, the experimental set-up is designed for studying flow boiling in 19 mm ID tube in such a way that any of the different flow regimes occurring in a steam generator tube (from pre-heating of sub-cooled water to dry-out) can be investigated by varying inlet conditions. The reported results cover a reasonable range of heat and mass flux conditions such as 9–27 kW/m 2 and 2.9–5.9 kg/m 2 s respectively. In this paper, various existing correlations are assessed against experimental data for the pressure drop in a single, vertical channel during flow boiling of water at near-atmospheric pressure. A special feature of these experiments is that time-dependent pressures are measured at four locations along the channel. The steady-state pressure drop is estimated and the identification of boiling flow regimes is done with transient characteristics using time series analysis. Experimental data and corresponding results are compared with the reported correlations. The results will be

  18. Normal ureteral diameter in infancy and childhood

    International Nuclear Information System (INIS)

    Hellstroem, M.; Hjaelmaas, K.; Jacobsson, B.; Jodal, U.; Oden, A.; Oestra Sjukhuset, Goeteborg; Oestra Sjukhuset, Goeteborg; Goeteborg Univ.

    1985-01-01

    Ureteral diameters were estimated on films from intravenous urography in 194 children (100 boys and 94 girls) aged 0-16 years. Children with signs of urinary tract infection, calculi, obstruction, duplication or malformation were excluded. Films obtained without abdominal compression were used for measurements, including only ureters visualized over 50 per cent of their lengths. A good correlation was demonstrated between ureteral diameter and age and between ureteral diameter and the length of a segment of the lumbar spine. The widest part of the ureter was most often located just above the crossing of the iliac vessels. The right ureter was slightly wider than the left one. No difference between boys and girls was noted. The results are in good agreement with those of others obtained at autopsy. Bearing in mind the possible physiologic variations, it would seem that measuring the ureteral diameter can be of value for a more objective differentiation between dilated and non-dilated ureters. (orig.)

  19. SEX DETERMINATION FROM FEMORAL HEAD DIAMETERS IN ...

    African Journals Online (AJOL)

    hi-tech

    2000-03-01

    Mar 1, 2000 ... In medico-legal cases where sophisticated methods of sex determination is lacking, these ... scientific methods(3). Using the visual method ... between the sexes and the values of the right and left femoral head diameters.

  20. Effective diameters and corresponding states of fluids

    Science.gov (United States)

    Del Río, Fernando

    Effective hard-sphere diameters of fluids with purely repulsive interactions are derived from a generalized corresponding-states principle of Leland, Rowlinson and coworkers. Various alternative definitions are discussed and related. Virial expansions of the effective diameters and their corresponding volumes are obtained and compared with results of perturbation theory. Applications are made to inverse-power potentials, the repulsive part of the Lennard-Jones potential and hard spherocylinders and dumbells.