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Showing papers in "Physical Review A in 1986"


Journal ArticleDOI
TL;DR: In this paper, the mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction.
Abstract: The mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction. An N logN algorithm for calculating I is presented. As proposed by Shaw, a minimum in I is found to be a good criterion for the choice of time delay in phase-portrait reconstruction from time-series data. This criterion is shown to be far superior to choosing a zero of the autocorrelation function.

4,160 citations


Journal ArticleDOI
TL;DR: A description of normalized distributions (measures) lying upon possibly fractal sets; for example those arising in dynamical systems theory, focusing upon the scaling properties of such measures, which are characterized by two indices: \ensuremath{\alpha}, which determines the strength of their singularities; and f, which describes how densely they are distributed.
Abstract: We propose a description of normalized distributions (measures) lying upon possibly fractal sets; for example those arising in dynamical systems theory. We focus upon the scaling properties of such measures, by considering their singularities, which are characterized by two indices: \ensuremath{\alpha}, which determines the strength of their singularities; and f, which describes how densely they are distributed. The spectrum of singularities is described by giving the possible range of \ensuremath{\alpha} values and the function f(\ensuremath{\alpha}). We apply this formalism to the ${2}^{\ensuremath{\infty}}$ cycle of period doubling, to the devil's staircase of mode locking, and to trajectories on 2-tori with golden-mean winding numbers. In all cases the new formalism allows an introduction of smooth functions to characterize the measures. We believe that this formalism is readily applicable to experiments and should result in new tests of global universality.

2,696 citations


Journal ArticleDOI
TL;DR: It is found that correlation contribution and relativistic effects are nonadditive in the MRD-CI method.
Abstract: A no-pair formalism employing external-field projection operators correct to second order in the potential is used to calculate the 1s energies of one-electron atoms and ground-state properties of the bromine and silver atoms in the framework of the multireference double-excitation configuration-interaction (MRD-CI) method. It is found that the relativistic two-component method that has been used reproduces the one-particle energies of the Dirac equation to order (Z\ensuremath{\alpha}${)}^{3}$. The operator is bounded from below and can be used variationally in relativistic electron-structure calculations of many-electron atoms and molecules. The relativistic correction to the total energy recovers 97% of the relativistic correction of the Dirac-Hartree-Fock (DHF) result in the case of the bromine atom and more than 99% in the case of the silver atom. The relativistic correction of the ionization potential of silver has been calculated to be 0.47 eV at the CI level, in good agreement with DHF results, the correlation contribution in the relativistic case being 0.42 eV. The remaining discrepancy of the absolute value of 6.85 eV (DHF 6.34 eV) to experiment (7.57 eV) is attributed to basis-set deficiencies. The corresponding CI value of the electron affinity (relativistic CI value 1.05 eV, nonrelativistic 0.90 eV) is in much better agreement with experiment (1.30 eV). It is found that correlation contribution and relativistic effects are nonadditive.

2,112 citations


Journal ArticleDOI
Gary S. Grest1, Kurt Kremer1
TL;DR: An efficient and general algorithm for simulating polymers, which can be used for single, large chains as well as many-chain systems, and confirmed two theoretical results, namely the anomalous behavior of S(q) for rings and the ${t}^{0.54}$ power law for the motion of a monomer in a self-avoiding chain undergoing Rouse relaxation.
Abstract: We describe an efficient and general algorithm for simulating polymers, which can be used for single, large chains as well as many-chain systems. It allows us to distinguish solvent effects from interchain effects on the dynamics of the chains. The method is tested for linear and cyclic chains of 50 to 200 monomers. We have confirmed two theoretical results which have not been observed numerically or experimentally, namely the anomalous behavior of S(q) for rings and the ${t}^{0.54}$ power law for the motion of a monomer in a self-avoiding chain undergoing Rouse relaxation.

1,548 citations


Journal ArticleDOI
TL;DR: In this paper, a Lie-group-theoretical approach to the analysis of interferometers is presented, which can achieve phase sensitivity Δo approaching 1/N, where N is the total number of quanta entering the interferometer, provided that the light entering the input ports is prepared in a suitable quantum state.
Abstract: A Lie-group-theoretical approach to the analysis of interferometers is presented. Conventional interferometers such as the Mach-Zehnder and Fabry-Perot can be characterized by SU(2). We introduce a class of interferometers characterized by SU(1,1). These interferometers employ active elements such as four-wave mixers or degenerate-parametric amplifiers in their construction. Both the SU(2) and SU(1,1) interferometers can in principle achieve a phase sensitivity Δo approaching 1/N, where N is the total number of quanta entering the interferometer, provided that the light entering the input ports is prepared in a suitable quantum state. SU(1,1) interferometers can achieve this sensitivity with fewer optical elements.

951 citations


Journal ArticleDOI
TL;DR: In this paper, an algorithm for measuring the dimension of a strange attractor from a time series is applied both to autocorrelated Gaussian noise and to a dynamical system.
Abstract: An algorithm devised for measuring the dimension of a strange attractor from a time series is applied both to autocorrelated Gaussian noise and to a dynamical system. It is analytically shown that a finite sequence of stochastic data---where by ``finite'' it is meant that N2${\ensuremath{\tau}}^{m/2}$, where N is the number of points in the sequence, \ensuremath{\tau} is the autocorrelation time (in units of sampling period), and m is the embedding dimension---exhibits anomalous structure in its correlation integral. The anomaly is seen numerically in both stochastic and dynamical data. Unrecognized, it can lead to unnecessarily inaccurate and possibly spurious estimates of dimension. We propose a slight modification of the standard algorithm which eliminates this difficulty.

942 citations


Journal ArticleDOI
TL;DR: An algorithm for computing Liapunov exponents from an experimental time series is analyzed and a hydrodynamic experiment is investigated.
Abstract: We analyze in detail an algorithm for computing Liapunov exponents from an experimental time series. As an application, a hydrodynamic experiment is investigated.

860 citations


Journal ArticleDOI
TL;DR: Some of the differences among several alternative formulations of constant-pressure molecular dynamics are described, which all agree in the large-system limit, but differ for small systems.
Abstract: Some of the differences among several alternative formulations of constant-pressure molecular dynamics are described. The formulations all agree in the large-system limit, but differ for small systems.

807 citations


Journal ArticleDOI
TL;DR: The ballistic aggregation model, in which particles are added to a growing structure via linear (ballistic) trajectories, is the most fundamental of these models and has been studied intensively.
Abstract: In recent years considerable interest has developed In the formation of random structures under non-equilibrium conditions. Much of our understanding of the geometry of these structures and its relationship to their formation mechanism has come from the study of simple models by means of both computer simulation and theoretical methods. One of the most fundamental of these models is the ballistic aggregation model in which particles are added to a growing structure via linear (ballistic) trajectories. Other simple models which have been studied intensively include the Eden1 model, diffusion limited aggregation2 (DLA) and diffusion limited cluster-cluster aggregation.3,4

418 citations


Journal ArticleDOI
Shin-Tson Wu1
TL;DR: T theory on the quantitative birefringence dispersions of liquid crystals was developed and found to have excellent agreement with experimental results throughout the entire visible and infrared spectral regions.
Abstract: The origins of liquid-crystal birefringence were investigated. Theory on the quantitative birefringence dispersions of liquid crystals was developed and found to have excellent agreement with experimental results throughout the entire visible and infrared spectral regions. New guidelines for selecting or synthesizing the liquid crystals with the desired birefringence are established. Novel applications of liquid crystals in the infrared region are foreseeable.

418 citations


Journal ArticleDOI
TL;DR: A method by which a quantum-mechanical partition function can be approximated from below by an effective classical partition function and the associated potential is obtained by a simple smearing procedure.
Abstract: We present a method by which a quantum-mechanical partition function can be approximated from below by an effective classical partition function. The associated potential is obtained by a simple smearing procedure. For a strongly anharmonic oscillator and a double-well potential, the lowest approximation gives a free energy which is accurate to a few percent, even at zero temperature.

Journal ArticleDOI
TL;DR: The theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity is presented.
Abstract: We present the theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity. Both a microscopic theory and a heuristic Fokker-Planck approach are presented. We show that the micromaser exhibits a number of novel features that are averaged out in usual masers and lasers. First, the field is in general sub-Poissonian, which reflects the quantization of both the field and its sources. Second, the onset of maser oscillations may be followed by a succession of abrupt transitions in the state of the field. Finally, as the atomic flux through the resonator is increased, the maser threshold acquires characteristics of a continuous phase transition, whereas the subsequent changes in the field distribution become analogous to first-order phase transitions.



Journal ArticleDOI
TL;DR: In this paper, the output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty.
Abstract: The output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty. This interferometer includes an optical Kerr medium in one arm with a coherent-state input. Unusual ``crescent''-shaped squeezing which preserves photon number is revealed in the unitary evolution associated with a self-phase-modulation in the Kerr medium. Photon-number uncertainty 〈\ensuremath{\Delta}n${^}^{2}$〉 can be reduced by interference with a coherent-state reference wave. It can be minimized to 〈n^${〉}^{1/3}$, far below the limit 〈n^${〉}^{2/3}$ achieved by an ordinary squeezed state. The increased phase uncertainty due to self-phase-modulation and the reduced photon-number uncertainty still preserve the minimum-uncertainty product 〈\ensuremath{\Delta}n${^}^{2}$〉〈\ensuremath{\Delta}\ensuremath{\Phi}${^}^{2}$〉\ensuremath{\sim}(1/4). .AE

Journal ArticleDOI
TL;DR: Comparisons with available experimental data show that new theoretical results are clearly superior to earlier calculations based on linear theory for stopping power and effective charge based on nonlinear density-functional calculations.
Abstract: Theoretical calculations of the stopping power of the electron gas for slow ions, v${v}_{F}$, are reviewed. New results are presented for stopping power and effective charge based on nonlinear density-functional calculations. Extensive comparisons with available experimental data show that these new theoretical results are clearly superior to earlier calculations based on linear theory.

Journal ArticleDOI
TL;DR: The Nose oscillator is a borderline case, not sufficiently chaotic for a fully statistical description, and it is suggested that the behavior of only slightly more complicated systems is considerably simpler and in accord with statistical mechanics.
Abstract: Nos\'e has developed many-body equations of motion designed to reproduce Gibbs's canonical phase-space distribution. These equations of motion have a Hamiltonian basis and are accordingly time reversible and deterministic. They include thermodynamic temperature control through a single deterministic friction coefficient, which can be thought of as a control variable or as a memory function. We apply Nos\'e's ideas to a single classical one-dimensional harmonic oscillator. This relatively simple system exhibits both regular and chaotic dynamical trajectories, depending on the initial conditions. We explore here the nature of these solutions by estimating their fractal dimensionality and Lyapunov instability. The Nos\'e oscillator is a borderline case, not sufficiently chaotic for a fully statistical description. We suggest that the behavior of only slightly more complicated systems is considerably simpler and in accord with statistical mechanics.


Journal ArticleDOI
TL;DR: The connection between stochastic differential equations and associated Fokker-Planck equations is elucidated by the full functional calculus and leads to a mean first-passage-time formula in quantitative agreement with the results of numerical simulation and in contrast with earlier theoretical conclusions.
Abstract: The connection between stochastic differential equations and associated Fokker-Planck equations is elucidated by the full functional calculus. One-variable equations with either additive or multiplicative noise are considered. The central focus is on approximate Fokker-Planck equations which describe the consequences of using ``colored'' noise, which has an exponential correlation function and a correlation time \ensuremath{\tau}. To leading order in \ensuremath{\tau}, the functional-calculus approach generalizes the \ensuremath{\tau}-expansion result and produces an approximate Fokker-Planck equation free from certain difficulties which have plagued the less general approximations. Mean first-passage-time behavior for bistable potentials, an additive case, is discussed in detail. The new result presented here leads to a mean first-passage-time formula in quantitative agreement with the results of numerical simulation and in contrast with earlier theoretical conclusions. The theory provides new results for the multiplicative case as well.

Journal ArticleDOI
TL;DR: A recommended set of cross sections for these levels has been deduced from a comparison of all the measured values of the excitation rate coefficients with those calculated from the Boltzmann analysis.
Abstract: Excitation rate coefficients for the 1${s}_{5}$, 1${s}_{4}$, 1${s}_{3}$, and 1${s}_{2}$ levels of argon by collisions with low-energy electrons have been measured using a drift-tube technique. Time dependences of the absolute population densities of the excited levels were measured by an absorption method with a tunable diode laser as a light source. The absorption data were analyzed according to the rate equations for these levels and the excitation rate coefficient per unit length of electron drift and per argon-atom density was obtained for each level as a function of the electric field to gas density ratio E/N. The values for the 1${s}_{5}$ level vary from 2.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ to 2.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ ${\mathrm{cm}}^{2}$ as E/N increases from 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ V ${\mathrm{cm}}^{2}$. In comparison with these values, those for the 1${s}_{3}$ level are about one-fifth, those for the 1${s}_{4}$ level are about the same, and those for the 1${s}_{2}$ level are slightly larger in respective measured E/N ranges. In order to estimate the cascading effects from the higher-lying levels, excitation rate coefficients for the 2p and 3p levels have also been measured from absolute intensities of the line emissions. From a comparison of all the measured values of the excitation rate coefficients with those calculated from the Boltzmann analysis, a recommended set of cross sections for these levels has been deduced.

Journal ArticleDOI
TL;DR: The non-positive-definite second-order terms in the quantum evolution equation are responsible for quantum recurrences and prevent the appearance of fine-scale-structure ‘‘whorls’’ predicted in a classical description.
Abstract: We consider the dynamics of a quantum joint phase-space probability density in an exactly solvable model. The density is defined to be a true (i.e., positive) probability distribution for approximate (and thus simultaneously measurable) position and momentum variables. The dynamics of the quantum density is governed by a second-order partial-differential equation with non-positive-definite second-order coefficients. The quantum dynamics is contrasted with the dynamics of a similar joint density in a classical description. The non-positive-definite second-order terms in the quantum evolution equation, not present in the classical case, are responsible for quantum recurrences and prevent the appearance of fine-scale-structure ‘‘whorls’’ predicted in a classical description. The generation of ‘‘squeezing’’ in the model is also discussed.

Journal ArticleDOI
TL;DR: It is suggested that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level.
Abstract: This paper clarifies the origins of the standard quantum limit for the amplitude noise of a laser-oscillator outgoing field. The amplitude noise within the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\le}\ensuremath{\omega}/Q, is ultimately caused by the pump amplitude fluctuation, while that above the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\ge}\ensuremath{\omega}/Q, is due to the field zero-point fluctuation. The uncertainty product of the amplitude- and phase-noise spectra at an extremely high pumping level is still larger than the Heisenberg minimum-uncertainty product because of the presence of nonstationary phase-diffusion noise. In this sense, an ordinary laser oscillator is not a quantum-limited device. This paper suggests that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level. The paper discusses possible schemes for suppressing pump fluctuation, commutator bracket preservation without pump fluctuation, and resulting amplitude and phase spectra. The similarity of and difference between a pump-noise-suppressed laser and a cavity degenerate parametric amplifier are delineated.

Journal ArticleDOI
TL;DR: The origins and viability of the nonlinear density feedback mechanism first identified by Leutheusser as a source of the liquid-glass transition are investigated and it is found that there is no sharp transition, but there is evidence for a rounded version of the transition.
Abstract: We study the fluctuating nonlinear hydrodynamics of compressible fluids. Development of the appropriate field-theoretical description for this problem requires treatment of nonlinearities which arise through the relationship g=\ensuremath{\rho}V, where g is the momentum density, \ensuremath{\rho} is the mass density, and V is the velocity field. We show how this constraint can be naturally included in a field theory of the Martin-Siggia-Rose type. We analyze the structure of the resulting field theory using the available fluctuation-dissipation theorem. We also develop the perturbation-theory expansion in powers of the temperature and evaluate the contributions from the nonlinearities to one-loop order. We show that the theory is renormalizable in the hydrodynamic limit. This field-theoretical model is used to systematically investigate the origins and viability of the nonlinear density feedback mechanism first identified by Leutheusser as a source of the liquid-glass transition. While we find that the nonlinear couplings driving this mechanism are present, we also find contributions, arising from the nonlinear constraint relating g, \ensuremath{\rho}, and V, which cut off the mechanism. The cutoff arises from a nonhydrodynamic correction not treated in previous work. While we find that there is no sharp transition, we do find evidence for a rounded version of the transition.

Journal ArticleDOI
TL;DR: The acceleration of trapped electrons in the relativistic plasma waves (wake fields) produced by specially shaped charged-particle beams is described by physical, analytic, and two-dimensional simulation models.
Abstract: The acceleration of trapped electrons in the relativistic plasma waves (wake fields) produced by specially shaped charged-particle beams is described by physical, analytic, and two-dimensional simulation models. The effects of competing instabilities, imperfect bunch shapes, transverse dynamics, and dephasing of trapped particles are considered.

Journal ArticleDOI
TL;DR: It is demonstrated that the revivals of atomic excitation which are the signature of the quantum nature of the evolution are strongly affected by field dissipation even when the damping hardly affects the underlying Rabi oscillations.
Abstract: The fully quantum-electrodynamical model of a two-level atom interacting with a single-cavity mode predicts an atomic evolution whose form is dictated by the discrete nature of the field energy and its statistical distribution. We demonstrate that the revivals of atomic excitation which are the signature of the quantum nature of the evolution are strongly affected by field dissipation even when the damping hardly affects the underlying Rabi oscillations.

Journal ArticleDOI
TL;DR: In this article, the percolation models of immiscible displacement in porous media are discussed, with emphasis on the critical behavior, including fractal nature of the nonwetting fluid configuration at breakthrough in drainage, and the size distribution of the residual non-wetting clusters in imbibition.
Abstract: The observable consequences of percolation models of immiscible displacement in porous media are discussed, with emphasis on the critical behavior. At the microscopic level, these include the fractal nature of the nonwetting fluid configuration at breakthrough in drainage, and the size distribution of the residual nonwetting clusters in imbibition. At the macroscopic level, it is suggested that percolation ideas are consistent with the usual multiphase Darcy equations, and critical behaviors of the relative permeability and capillary pressure curves are obtained. By using these results, predictions are made for the shape of the fluid saturation profiles near the percolation thresholds in the presence of buoyancy or viscous pressure gradients. Finally, it is pointed out that very close to the percolation thresholds, the diverging correlation length requires these macroscopic ideas to be modified. A simple way of doing this is suggested.

Journal ArticleDOI
G. C. Lie1, Enrico Clementi1
TL;DR: The Matsuoka-Clementi-Yoshimine configuration interaction potential for rigid water-water interactions has been extended to include the intramolecular vibrations and the simulated high-frequency sound mode seems to support the results and interpretation of a recent coherent inelastic neutron scattering experiment.
Abstract: The Matsuoka-Clementi-Yoshimine (MCY) configuration interaction potential for rigid water-water interactions has been extended to include the intramolecular vibrations The extended potential (MCYL), using no empirical parameters other than the atomic masses, electron charge, and Planck constant, is used in a molecular-dynamics simulation study of the static and dynamic properties of liquid water Among the properties studied are internal energy, heat capacity, pressure, radial distribution functions, dielectric constant, static structure factor, velocity autocorrelation functions, self-diffusion coefficients, dipole autocorrelation function, and density and current fluctuations Comparison with experiments is made whenever possible Most of these properties are found to improve slightly relative to the MCY model The simulated high-frequency sound mode seems to support the results and interpretation of a recent coherent inelastic neutron scattering experiment

Journal ArticleDOI
TL;DR: The theory of neural networks is extended to include a static noise as well as nonlinear updating of synapses by learning, which may modify the energy surface and lead to interesting new computational capabilities in an unsaturated network.
Abstract: The theory of neural networks is extended to include a static noise as well as nonlinear updating of synapses by learning. The noise appears either in the form of spin-glass interactions, which are independent of the learning process, or as a random decaying of synapses. In an unsaturated network, the nonlinear learning algorithms may modify the energy surface and lead to interesting new computational capabilities. Close to saturation, they act as an additional source of a static noise. The effect of the noise on memory storage is calculated.

Journal ArticleDOI
TL;DR: In this article, it was shown that quantum perturbation theory must fail, for chaotic systems, in the semiclassical limit ε ≥ 0, for two arbitrarily close Hamiltonians with different sets of eigenvectors.
Abstract: When a quantum system has a chaotic classical analog, its matrix elements in the energy representation are closely related to various microcanonical averages of the classical system. The diagonal matrix elements cluster around the classical expectation values, with fluctuations similar to the values of the off-diagonal matrix elements. The latter in turn are related to the classical autocorrelations. These results imply that quantum perturbation theory must fail, for chaotic systems, in the semiclassical limit \ensuremath{\Elzxh}\ensuremath{\rightarrow}0: Two arbitrarily close Hamiltonians have, in general, completely different sets of eigenvectors.

Journal ArticleDOI
TL;DR: In this paper, the authors measured the cross section of the excited-state photoionization cross section for the 3p, 2p and 2p transition in atomic oxygen using two-photon excited fluorescence.
Abstract: The technique of two-photon excited fluorescence has been used to measure the cross section for the 3p ${\mathrm{}}^{3}$${P}_{2}$,1,0\ensuremath{\leftarrow}2p ${\mathrm{}}^{3}$${\mathrm{P}}_{2}$ transition in atomic oxygen. Excitation was monitored by observing fluorescence at 845 nm from the 3p ${\mathrm{}}^{3}$${P}_{2}$,1,0\ensuremath{\rightarrow}3s ${\mathrm{}}^{3}$${\mathrm{S}}_{1}$ transition. Spontaneous Raman scattering from ${\mathrm{H}}_{2}$ was used to calibrate the fluorescence collection system. The spatial and temporal profiles of the exciting dye-laser pulses were carefully measured in a mildly focused excitation geometry, allowing the integrated two-photon absorption coefficient to be measured absolutely. The integrated absorption coefficient is the product of an atomic quantity, ${\mathcal{J}}_{J\mathcal{'}}$${\ensuremath{\sigma}}_{0}^{(2)}$(J'\ensuremath{\leftarrow}2), and the second-order correlation function of the laser field, ${G}^{(2)}$. The experimental value of this coefficient is ${\mathcal{J}}_{\mathrm{J}\mathcal{'}}$${\mathrm{\ensuremath{\sigma}}}_{0}^{(2)}$(J'\ensuremath{\leftarrow}2)${\mathrm{G}}^{(2)}$ =(2.66\ifmmode\pm\else\textpm\fi{}0.80)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}35}$ ${\mathrm{cm}}^{4}$. If chaotic photon statistics are assumed (i.e., ${G}^{(2)}$=2), excellent agreement with the calculations presented in the companion paper is obtained. The cross section for photoionization by a third, identical 226-nm photon has been determined by measuring the absolute number of ions produced per laser pulse. The excited-state photoionization cross section is ${\ensuremath{\sigma}}_{\mathrm{pi}=(5.3\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}{10}^{\mathrm{\ensuremath{-}}19}}$ ${\mathrm{cm}}^{2}$.