983 resultados para eventually positive solution
Resumo:
Recent theoretical developments in the reggeization of inelastic processes involving particles with high spin are incorporated into a model of vector meson production. A number of features of experimental differential cross sections and density matrices are interpreted in terms of this model.
The method chosen for reggeization of helicity amplitudes first separates kinematic zeros and singularities from the parity-conserving amplitudes and then applies results of Freedman and Wang on daughter trajectories to the remaining factors. Kinematic constraints on helicity amplitudes at t = 0 and t = (M – MΔ)2 are also considered.
It is found that data for reactions of types πN→VN and πN→VΔ are consistent with a model of this type in which all kinematic constraints at t = 0 are satisfied by evasion (vanishing of residue functions). As a quantitative test of the parametrization, experimental differential cross sections of vector meson production reactions dominated by pion trajectory exchange are compared with the theory. It is found that reduced residue functions are approximately constant, once the kinematic behavior near t = (M – MΔ)2 has been removed.
The alternative possibility of conspiracy between amplitudes is also discussed; and it is shown that unless conspiracy is present, some amplitudes allowed by angular momentum conservation will not contribute with full strength in the forward direction. An example, γp→π+n in which the data for dσ/dt indicate conspiracy, is studied in detail.
Resumo:
The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:
1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.
2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.
3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.
These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10-3 sec-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.
New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.
Resumo:
In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.
We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).
In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m3. However, it may be possible to solve the factorized SU(2) problem with this model.
The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.
Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.
Resumo:
Steady-state procedures, of their very nature, cannot deal with dynamic situations. Statistical models require extensive calibration, and predictions often have to be made for environmental conditions which are often outside the original calibration conditions. In addition, the calibration requirement makes them difficult to transfer to other lakes. To date, no computer programs have been developed which will successfully predict changes in species of algae. The obvious solution to these limitations is to apply our limnological knowledge to the problem and develop functional models, so reducing the requirement for such rigorous calibration. Reynolds has proposed a model, based on fundamental principles of algal response to environmental events, which has successfully recreated the maximum observed biomass, the timing of events and a fair simulation of the species succession in several lakes. A forerunner of this model was developed jointly with Welsh Water under contract to Messrs. Wallace Evans and Partners, for use in the Cardiff Bay Barrage study. In this paper the authors test a much developed form of this original model against a more complex data-set and, using a simple example, show how it can be applied as an aid in the choice of management strategy for the reduction of problems caused by eutrophication. Some further developments of the model are indicated.
Resumo:
We are concerned with the class ∏n of nxn complex matrices A for which the Hermitian part H(A) = A+A*/2 is positive definite.
Various connections are established with other classes such as the stable, D-stable and dominant diagonal matrices. For instance it is proved that if there exist positive diagonal matrices D, E such that DAE is either row dominant or column dominant and has positive diagonal entries, then there is a positive diagonal F such that FA ϵ ∏n.
Powers are investigated and it is found that the only matrices A for which Am ϵ ∏n for all integers m are the Hermitian elements of ∏n. Products and sums are considered and criteria are developed for AB to be in ∏n.
Since ∏n n is closed under inversion, relations between H(A)-1 and H(A-1) are studied and a dichotomy observed between the real and complex cases. In the real case more can be said and the initial result is that for A ϵ ∏n, the difference H(adjA) - adjH(A) ≥ 0 always and is ˃ 0 if and only if S(A) = A-A*/2 has more than one pair of conjugate non-zero characteristic roots. This is refined to characterize real c for which cH(A-1) - H(A)-1 is positive definite.
The cramped (characteristic roots on an arc of less than 180°) unitary matrices are linked to ∏n and characterized in several ways via products of the form A -1A*.
Classical inequalities for Hermitian positive definite matrices are studied in ∏n and for Hadamard's inequality two types of generalizations are given. In the first a large subclass of ∏n in which the precise statement of Hadamardis inequality holds is isolated while in another large subclass its reverse is shown to hold. In the second Hadamard's inequality is weakened in such a way that it holds throughout ∏n. Both approaches contain the original Hadamard inequality as a special case.
Solar flare particle propagation--comparison of a new analytic solution with spacecraft measurements
Resumo:
A new analytic solution has been obtained to the complete Fokker-Planck equation for solar flare particle propagation including the effects of convection, energy-change, corotation, and diffusion with ĸr = constant and ĸƟ ∝ r2. It is assumed that the particles are injected impulsively at a single point in space, and that a boundary exists beyond which the particles are free to escape. Several solar flare particle events have been observed with the Caltech Solar and Galactic Cosmic Ray Experiment aboard OGO-6. Detailed comparisons of the predictions of the new solution with these observations of 1-70 MeV protons show that the model adequately describes both the rise and decay times, indicating that ĸr = constant is a better description of conditions inside 1 AU than is ĸr ∝ r. With an outer boundary at 2.7 AU, a solar wind velocity of 400 km/sec, and a radial diffusion coefficient ĸr ≈ 2-8 x 1020 cm2/sec, the model gives reasonable fits to the time-profile of 1-10 MeV protons from "classical" flare-associated events. It is not necessary to invoke a scatter-free region near the sun in order to reproduce the fast rise times observed for directly-connected events. The new solution also yields a time-evolution for the vector anisotropy which agrees well with previously reported observations.
In addition, the new solution predicts that, during the decay phase, a typical convex spectral feature initially at energy To will move to lower energies at an exponential rate given by TKINK = Toexp(-t/ƬKINK). Assuming adiabatic deceleration and a boundary at 2.7 AU, the solution yields ƬKINK ≈ 100h, which is faster than the measured ~200h time constant and slower than the adiabatic rate of ~78h at 1 AU. Two possible explanations are that the boundary is at ~5 AU or that some other energy-change process is operative.
Resumo:
Recent advances in our knowledge of the genetic structure of human caliciviruses (HuCVs) and small round-structured viruses (SRSVs) have led to the development of polymerase chain reaction (PCR)-based molecular tests specific for these viruses. These methods have been developed to detect a number of human pathogenic viruses in environmental samples including water, sewage and shellfish. HuCVs and SRSVs are not culturable, and no animal model is currently available. Therefore there is no convenient method of preparing viruses for study or for reagent production. One problem facing those attempting to use PCR-based methods for the detection of HuCVs and SRSVs is the lack of a suitable positive control substrate. This is particularly important when screening complex samples in which the levels of inhibitors present may significantly interfere with amplificiation. Regions within the RNA polymerase regions of two genetically distinct human caliciviruses have been amplified and used to produce recombinant baculoviruses which express RNA corresponding to the calicivirus polymerase. This RNA is being investigated as a positive control substrate for PCR testing, using current diagnostic primer sets. Recombinant baculovirus technology will enable efficient and cost-effective production of large quantities of positive control RNA with a specific known genotype. We consider the development of these systems as essential for successful screening and monitoring applications.
Resumo:
Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. n = root epsilon mu, in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as epsilon = epsilon(r) + i(epsilon i) and mu = mu(r) + i mu(i). The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability epsilon(i) > 0 and mu(i) > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability epsilon(i) < 0 and mu(i) < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters epsilon(r), mu(r), epsilon(i), and mu(i), in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re {Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously epsilon < 0 and mu < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for epsilon(r) < 0, mu(r) > 0, epsilon(i) > 0, and mu(i) > 0, the refractive index is negative n < 0 provided mu(i)/epsilon(i) > mu(r)/vertical bar epsilon(r)vertical bar. (c) 2006 Elsevier B.V. All rights reserved.