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It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrodinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of l (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.

While several papers deal with effects of truncation techniques on the total radiance there is a lack of such studies concerning polarized radiance. We present our first results obtained in studying the impact of phase matrix truncation on the accuracy of polarized radiance. Like for the total radiance, the single scattering (TMS) correction is crucial and efficient in case of the polarized radiance. We show that there is a systematic error on polarized radiance that increases with truncation factor and optical depth. This error is not induced by the restitution of the phase matrix angular dependency as a function of the number of terms in the Legendre polynomials expansion. Given a truncation factor, this error reaches a maximum asymptotic value for optical depth corresponding to the saturation of polarization. For the cloud droplet that we use in our study, the maximum error is 4.5% at λ=412nm. It raises the question of whether the condition for scale invariance of the scalar radiative transfer equation...

We show that the Modified Newtonian Dynamics (MOND) regime can be fully recovered as the weak-field limit of a particular theory of gravity formulated in the metric approach. This is possible when Milgrom's acceleration constant is taken as a fundamental quantity which couples to the theory in a very consistent manner. As a consequence, the scale invariance of the gravitational interaction is naturally broken. In this sense, Newtonian gravity is the weak-field limit of general relativity and MOND is the weak-field limit of that particular extended theory of gravity., To appear in the proceedings of the 2011 Spanish Relativity Meeting (ERE2011) held in Madrid, Spain, 4 pages

The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.

The correspondence between theories in anti-de Sitter space and field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. These equations, for both mesons and baryons, give a very good representation of the observed hadronic spectrum, including a zero mass pion. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. The meson and baryon wavefunctions derived from light-front holography and AdS/QCD also have remarkable phenomenological features, including predictions for the electromagnetic form factors and decay constants. The approach can be systematically improved using light-front Hamiltonian methods. Some novel features of QCD for baryon physics are also discussed., Presented by SJB at the International Conference on the Structure of Baryons, BARYONS'10, December 7-11, 2010, Osaka, Japan

In this paper, the problem of inhomogeneous plane symmetric metric is investigated in Wesson's scale invariant theory of gravitation with the matter field in the form of perfect fluid. The gauge function depends on time coordinate only (Dirac gauge). The cosmological model corresponding to stiff fluid is constructed and its properties are discussed.

Many dynamical systems from different areas of knowledge can be studied within the theoretical framework of time series, where the system can be considered as a black box, that only needs to be “listened” to. In this framework, non‐correlated series (white noise) and strongly correlated series (brownian noise or periodic series) constitute two extremes. Certain dynamical systems auto‐organize in a critical state that is characterized by 1/f or flicker noise. The family of fβ noises (β≤0) is fractal because fragments of the series are statistically identical to the original time series. 1/f noise (β = −1) is critical because it maximizes important complexity‐related quantities as memory, information content, efficiency and fractality. 1/f noise has been observed in classical systems, but also in quantum systems, and could possibly offer a unifying bridge of understanding between the macroscopic and the quantum world. In the present article, we will discuss some examples from both worlds.

We review some aspects of the backreaction problem. In a first part, using an averaging scheme generalized to arbitrary frames, we quantify the effect in the Poisson gauge of perturbation theory up to second order. The main result is the definition of a scale of homogeneity above which the backreaction effect becomes scale invariant. In a second part we present results about the structure of the effective lightcone in averaged cosmologies and show that a non‐trivial structure due to the backreaction may allow to test the relevance of the backreaction effect as a solution to the dark energy conundrum with future data.

A robust multiscale analysis of high‐frequency magnetic field measurements from the Cluster spacecraft is presented using complimentary measurements from the magnetometer and search‐coil instruments; in a stationary interval of fast ambient solar wind. We show a surprising and novel result: that for time‐scales smaller than the ion‐gyro period the magnetic field fluctuations exhibit non‐Gaussian monoscaling i.e. are globally scale invariant and can be characterized by a single scaling exponent and thus a single universal scaling function for the probability density. This presents new questions, as well as theoretical constraints, for determining how magnetic turbulent energy is dissipated in collisionless plasmas.

Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale l, where the fragments are subsequently allowed to settle under gravity. If this fragmentation‐reagglomeration cycle is repeated sufficiently often, the powder develops a fractal substructure with robust statistical properties. The structural evolution is discussed for two different models: The first one is an off‐lattice model, in which a fragment does not stick to the surface of other fragments that have already settled, but rolls down until it finds a locally stable position. The second one is a simpler lattice model, in which a fragment sticks at first contact with the agglomerate of fragments that have already settled. Results for the fragment size distribution are shown as well. One can distinguish scale invariant dust and fragments of a characteristic size. Their role in the process of structure formation will be addressed.

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.

The analysis of the scaling properties in deep‐inelastic processes using the “Quality Factor” (QF) method is summarised. Data from HERA and fixed target experiments with x

We present an approach for scale invariant 3D object detection based on phase Fourier transform (PhFT). Three‐dimensionality is expressed in terms of range images. The PhFT of a range image gives information about the orientations of the surfaces in the 3D object. When the 3D object is scaled, the PhFT becomes a distribution multiplied by a constant factor. So, scale invariant 3D pattern recognition is converted into illumination invariant 2D pattern recognition.

A canonical formalism is developed for implementing the dilatation symmetry to the Fokker‐Planck equation. A condition is derived, under which the equation admits a nonstationary scale‐invariant solution.

The dark matter distribution is arguably scale invariant in a range of scales, so that it has a fractal geometry, observable in the clustering of galaxies and in cosmic voids. We review evidence of fractal geometry in recent observations, which shows, in particular, that a simple fractal model is not sufficient. Therefore, we propose a multifractal model of the dark matter distribution realized on fractal halo populations, in which voids appear naturally.

Ubiquitous non‐Gaussianity of the probability density of (time‐series) fluctuations in many real world phenomena has been known and modelled extensively in recent years. Similarly, the analysis of (multi)scaling properties of (fluctuations in) complex systems has become a standard way of addressing unknown complexity. Yet the combined analysis and modelling of multiscale behaviour of probability density — multiscale PDF analysis — has only recently been proposed for the analysis of time series arising in complex systems, such as the cardiac neuro‐regulatory system, financial markets or hydrodynamic turbulence. This relatively new technique has helped significantly to expand the previously obtained insights into the phenomena addressed. In particular, it has helped to identify a novel class of scale invariant behaviour of the multiscale PDF in healthy heart rate regulation during daily activity and in a market system undergoing crash dynamics. This kind of invariance reflects invariance of the system under...

New methods of solutions of the DGLAP equation and their implementation through NNLO in QCD are briefly reviewed. We organize the perturbative expansion that describes in $x$-space the evolved parton distributions in terms of scale invariant functions, which are determined recursively, and logarithms of the ratio of the running couplings at the initial and final evolution scales. Resummed solutions are constructed within the same approach and involve logarithms of more complex functions, which are given in the non-singlet case. Differences in the evolution schemes are shown to be numerically sizeable and intrinsic to perturbation theory. We illustrate these points in the case of Drell-Yan lepton pair production near the Z resonance, analysis that can be extended to searches of extra $Z^{\prime}$. We show that the reduction of the NNLO cross section compared to the NLO prediction may be attributed to the NNLO evolution., 5 pages, 2 figures. Talk given at QCD@work 2007, Martina Franca, Italy, 16-20 June 2007. To be published in the American Institute of Physics (AIP) conference proceedings

Lie group analysis is applied to the nonlinear bubble dynamics accounting both distortion and breathing modes according to the perfect‐liquid model. The Hamiltonian formulation of the problem has been presented and the closed form of the Hamiltonian as a functional of canonical variables has been obtained. The equations of the prolongation theory have been derived and particular solutions corresponding subgroups of the full symmetry group have been determined. The availability of certain continuous group of symmetry generally offers a possibility of reducing the order of the corresponding differential equation. It appears possible to describe analytically the nonlinear dynamics of a bubble driven by an external perturbation in the conditions ensuring the scale invariance. The efficiency of bubble extension under the action of a periodically prolonged scale‐invariant external acoustic field has been studied.

The outstanding feature of healthy human heart rate is the robust scale invariance in the non‐Gaussian probability density function (PDF), which is preserved not only in a quiescent condition, but also in a dynamic state during waking hours [K. Kiyono et al. Phys. Rev. Lett. 93 (2004)]. Together with 1/f like scaling, this characteristic is a strong indication of far‐from‐equilibrium, critical‐like dynamics of heart rate regulation. Our results suggest that healthy human heart rate departs from a critical state‐like operation during sleeping hours, at a rate which is heterogeneous with respect to sleep stages annotated according to traditional techniques. We study specific contributions of sleep stages to the relative departure from criticality through the analysis of sleep stage dependence of the root mean square of multiscale local energy and the multiscale PDF. There is a possibility that the involvement of cortical activity may be important for a critical state‐like operation.

We study numerically the statistical properties of a modified Bak‐Tang‐Wiesenfeld sand pile model by introducing a non‐zero driving rate, and time‐dependent avalanche propagation on a two‐dimensional lattice. When we consider a very small driving rate, this model approaches the original BTW model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)]. As the driving rate increases, the model exhibits a continuous phase transition. At the critical point, the variation in the sand flux, the amount of moving grains, exhibits long‐range temporal correlations with a 1/f power spectrum. Moreover, the critical fluctuations show scale invariance of the non‐Gaussian probability density function. We will discuss how the characteristics in this system depend on the driving rate.

During the last decade, the outcome of self‐affine geometrical properties of many growing aggregates, originated in a width variety of processes, has been well characterized. However, little progress has been achieved in the search of an unified description of the underlying dynamics. Extensive numerical evidences are given showing that the bulk of aggregates formed upon ballistic aggregation and random deposition with surface relaxation processes, can be break down into a set of infinite scale invariant structures called “trees”. These two types of aggregates have been selected because it has been established that they belong to different universality classes: those of Kardar‐Parisi‐Zhang and Edward‐Wilkinson, respectively. Exponents describing the spatial and temporal scale invariance of the trees can be related to the classical exponents describing the self‐affine nature of the growing interface. Furthermore, those exponents allows to distinguish on either the compact or non‐compact nature of the growi...

In this paper we propose a method for restoring gammagraphic images. The method is based on a Bayesian estimator containing a compound regularizer. This method allows to take into account all gammagraphic image characteristics (such as positive radio-isotope distribution blurred by photon scattering and degraded by Poisson noise). Moreover the compound regularizer is constructed so that the estimator satisfies several desirable analytical and computational properties including uniqueness, stability, scale invariance and efficient implementation.

An alternative methodology to monitor the heartbeat is presented. The new technique is based on a low power laser beam focused reflected off by a living heart and detected with a linear response photodiode that serves to plot cardiac movements. In order to prove the laser technique an invertebrate, an oyster, was chosen. Three sets of measurements of the heartbeat were done with five oysters changing ambiental salinity, time of data acquisition, and sampling frequency. In all the experiments the temperature was (23±1) °C. Typical “laser-cardiograms” clearly show cardiac signals superposed to the motions of other organs like the gills and the valves. Analysis of the data is done using two methods: Traditional Fast Fourier Transformation to find the principal frequencies of motion and Detrended Fluctuation Analysis to study the nonlinear fluctuation of the interbeat. This algorithm developed handles very well the nonstationarities of biological signals and predicts the level of time scale invariance of the ...

A review is given of various aspects of scale invariant systems in order to accentuate the similarity of the phenomena shown by a wide variety of such systems. A scale invariant system shows the same appearance if the time or frequency scales are altered in size. Many natural and human systems show scale invariance and this can be revealed by various ranking or correlation plots as well as noise with a power law spectrum. The basic reason for the scale invariance is different for each system but each implies a wide range of characteristic times. The wide range often results from processes derived from the multiplication of several steps, rather than the addition or from a process governed by a variable which has a wide distribution and occurs as an exponent. Various ways that a 1/f spectrum have been derived from scale invariant processes in electronic systems are reviewed.

In this general talk, we offer an overview of some problems of interest to biophysicists, medical physicists, and econophysicists. These include DNA sequences, brain plaques in Alzheimer patients, heartbeat intervals, and time series giving price fluctuations in economics. These problems have the common feature that they exhibit features that appear to be scale invariant. Particularly vexing is the problem that some of these scale invariant phenomena are not stationary-their statistical properties vary from one time interval to the next or form one position to the next. We will discuss methods, such as wavelet methods and multifractal methods, to cope with these problems.

I review here some works done in collaboration with G. Brown, D.-P. Min and M. Rho. With a simple Brown-Rho (BR) scaled chiral model Lagrangian we discuss how BR scaling can be applied to nuclear matter and connected with relativistic Landau Fermi-liquid theory.

S-dualities in scale invariant N=2 supersymmetric field theories are derived by embedding those theories in asymptotically free theories with higher rank gauge groups. S-duality transformations on the couplings of the scale invariant theory follow from the geometry of the embedding of the scale invariant theory in the Coulomb branch of the asymptotically free theory.

Under healthy conditions, the normal cardiac (sinus) interbeat interval fluctuates in a complex manner. Quantitative analysis using techniques adapted from statistical physics reveals the presence of long‐range power‐law correlations extending over thousands of heartbeats. This scale‐invariant (fractal) behavior suggests that the regulatory system generating these fluctuations is operating far from equilibrium. In contrast, we find that for subjects at high risk of sudden death (e.g. congestive heart failure patients) these long‐range correlations break down. Application of fractal scaling analysis and related techniques provides new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as motivating development of novel physiological models of systems that appear to be ‘‘hetero‐dynamic’’ rather than ‘‘homeo‐static.’’

The major features of transport and relaxation in disordered systems are shown to be due to the occurrence of long‐tailed distributions of rate‐limiting event times. The mean‐time of this distribution is divergent, and hence there is no intrinsic time scale associated with the dynamic response of the system. The lack of time scale is manifest in the film‐thickness dependence of the transit time of a single carrier and in the occurence of stretched‐exponential time dependence of the relaxation.

The power spectra of the X-ray variable AGN are typically scale invariant with no characteristic timescale. The one strong exception to this is NGC6814, where the EXOSAT data showed evidence for a periodic component at 12200 plus or minus 100 seconds. The power spectra of a GINGA lightcurve from this source, found using simulation techniques to account for the uneven sampling, also cannot be well fit by a single power law. A folded light curve analysis of the GINGA data shows a strong peak in the variance, indicative of a periodic component, at 12130.9 plus or minus 0.6 seconds. A second GINGA observation of this source taken one year later is consistent with the periodicity maintaining phase coherence for 7 periods in the range of 12110-12145 seconds. Including the limits from the folding selects a period of 12130.39 plus or minus 0.05 seconds. Phase coherence is not maintained between this and the EXOSAT observations, as the structure of the folded light curves is very different. Thus the periodicity is long lived and stable, but phase coherence is only maintained on timescales of approximately 1 year.

An isotemporal model of cosmological structure in a strictly geometric sense, whether shaped primarily by a fragmenting or aggregating process, must coherently accomodate the apparent incongruence of the extreme isotropy of the cosmic microwave background radiation (CMBR) with the large scale anisotropy of scale invariant structure. The extreme isotropy of the CMBR also would indicate that, beyond some maximum scale, the distribution of matter transitions to homogeneity; however, this scale has not yet been established. In defining the possible relative proportions of such a scale, considerations for an ideal model exhibiting these properties are discussed.

The deviation of galactic rotation curves from their expected Keplerian falloff with distance as based on the observed distribution of light, has prompted the suggestion, by a small number of authors, that this phenomenon signifies a drastic departure of certain laws of physics at large scales from their smaller scale forms. A number of proposals is reviewed with particular attention being given to a locally scale invariant theory of gravity proposed by the authors. This latter theory and several of its consequences and comparisons to observation are presented.

The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power law spectra for n from -2 to 1. We place an upper bound on the quadrupole anisotropy of DeltaT/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of our modeling of the Galaxy could yield a significant reduction of these upper bounds.

A review of existing data on nucleus‐nucleus collisions at Bevatron‐Bevalac energies (few GeV/nucleon) is given to test to what extent such collisions can be compared to nucleon‐nucleon studies performed at NAL and ISR energies. Data are examined for such phenomena as limiting fragmentation, scaling and factorization of cross‐sections. A brief discussion of experiments—either in progress or about to start, which bear on the question of testing high‐energy interactions models—is included.

Some recent developments have been made in the study of phase transitions in grand unified theories (GUTs) in which radiatively induced corrections to the effective potential play an important role (e.g. Coleman‐Weinberg models). The course of the phase transition is shown to depend sensitively on the choice of parameters of the theory. A restricted class of parameters, excluding the simplest SU(5) GUT model, is found to lead to an inflationary Universe. An heuristic argument is given to show that the spectrum of fluctuations in such models (on observable scales) is scale invariant and a dimensional argument is proposed to explain the amplitude of the resultant fluctuations. Only a much more restricted class of GUT models is found to yield an inflationary Universe with fluctuations that are not so big as to be inconsistent with the isotropy and homogeneity in the observable Universe.

We review Landau's hydrodynamic description of multiparticle processes and show how to calculate single particle inclusive distribution functions in terms of the collective variables of such a description. In the scaling regime, we solve analytically the hydrodynamic equations for simple initial conditions expected to be appropriate in pp collisions and in e+ e− annihilation into hadrons. We then discuss how these scaling solutions relate to more exact numerical calculations of EdN/d3p obtained for comparison with present accelerator data.

A survey of recent results on deep inelastic inclusive reaction with beams of electrons, muons, and neutrinos is presented. Tests of scaling, the spin of the constituents, and the relationship between electron/muon and neutrino scattering is discussed.

A review of recent results for both deep inelastic electroproduction and neutrino scattering is presented.

We present a summary of results obtained during the last few months from the 30‐inch hydrogen bubble chamber at National Accelerator Laboratory.