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The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one describes reproduction with different phenotypes. Linear stability analysis of the homogeneous in space stationary solution is carried out. Existence of travelling waves is proved in the case of narrow kernels of the integrals. Periodic travelling waves are observed in numerical simulations. Existence of stationary solutions in the form of pulses is shown, and transition from periodic waves to pulses is studied. In the applications to the speciation theory, the results of this work signify that new species can emerge only if they do not have common offsprings. Thus, it is shown how Darwin's definition of species as groups of morphologically similar individuals is related to Mayr's definition as groups of individuals that can breed only among themselves., Comment: 15 pages, 4 figures

An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau -Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam (FPU) problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries (mKdV) equation. This model has application from laboratory to astrophysical plasmas as well as biological systems., Comment: 5 pages, 2 figures

Recently we showed that while the tensor force plays an important role in nuclear matter saturation in non-relativistic studies, it does not do so in relativistic studies. The reason behind this is the role of $M^*$, the sum of nucleon mass and its attractive self-energy in nuclear matter. Yet nonrelativistic calculations at a certain level of approximation are far less difficult than comparative relativistic calculation. Naturally the question arises if one can modify a nonrelativistic method, say, the lowest order Brueckner theory (LOBT), to reproduce approximately the results of a relativistic calculation. While a many body effect, the role of $M^*$ is intrinsically relativistic. It cannot be simulated by adding multi-body forces in a nonrelativistic calculation. Instead, we examine if adding a set of recipes to LOBT can be useful for the purpose. We point out that the differences in the results arise principally from two reasons - first, the role of $M^*$ and second, the disappearance in a relativistic treatment of the gap in the hole and particle energy spectra, present in LOBT. In this paper we show that LOBT, modified by {\it recipes} to remove these two reasons, generates results quite close to those of Dirac-Brueckner theory., Comment: 8 pages, revtex

The recent determination of the charged $\pi NN$ coupling constant, $g_{\pi^\pm}$, by the Uppsala Neutron Research Group implies that there may be considerable charge-splitting of the pion coupling constant. We investigate the consequences of this for the charge-independence breaking (CIB) of the $^1S_0$ scattering length, $\Delta a_{CIB}$. We find that $\Delta a_{CIB}$ depends sensitively on the difference between $g_{\pi^\pm}$ and the neutral $\pi NN$ coupling constant, $g_{\pi^0}$. Moreover, if $g^2_{\pi^\pm}$ is only about 3% larger than $g^2_{\pi^0}$, then the established theoretical explanation of $\Delta a_{CIB}$ (in terms of pion mass splitting) is completely wiped out., Comment: 9 pages, fbs styles, 1 figure; dedicated to Walter Gl\"ockle on the occasion of his 60th birthday

We calculate the leading direct-instanton contributions to the operator product expansion of the nucleon correlator in a magnetic background field and set up improved QCD sum rules for the nucleon magnetic moments. Remarkably, the instanton contributions are found to affect only those sum rules which had previously been considered unstable. The new sum rules show good stability and reproduce the experimental values of the nucleon magnetic moments with values of $\chi$, the quark condensate magnetic susceptibility, consistent with other estimates., Comment: 15 pages, 2 figures

In this two part series a chiral confining model of baryons is used to describe low--lying negative parity resonances $N^*$, $\Delta^*$, $\Lambda^*$ and $\Sigma^*$ in the mean field approximation. A physical baryon in this model consists of interacting valence quarks, mesons and a color and chiral singlet hybrid field coexisting inside a dynamically generated confining region. This first paper presents the quark contribution to the masses and wave functions of negative parity baryons calculated with an effective spin--isospin dependent instanton induced interaction. It does not include meson exchanges between quarks. The three--quark wave functions are used to calculate meson--excited baryon vertex functions to lowest order in meson--quark coupling. When the baryons are on mass--shell each of these vertex functions is a product of a coupling constant and a form factor. As examples, quark contributions to $N^*$ hadronic form factors as well as axial coupling constants are extracted from the vertex functions and problems with the analytical behaviour of the model form factors are discussed. The second paper will examine the mesonic corrections to excited baryon properties in the heavy baryon and one--loop approximations., Comment: ReVTeX, 29 pages, 3 Postscript figures, Submitted to Phys. Rev. C

Due to the internal structure of the nucleon, we should expect, in general, that the effective meson nucleon parameters may change in nuclear medium. We study such changes by using a chiral confining model of the nucleon. We use density-dependent masses for all mesons except the pion. Within a Dirac-Brueckner analysis, based on the relativistic covariant structure of the NN amplitude, we show that the effect of such a density dependence in the NN interaction on the saturation properties of nuclear matter, while not large, is quite significant. Due to the density dependence of the $g_{\sigma NN}$, as predicted by the chiral confining model, we find, in particular, a looping behavior of the binding energy at saturation as a function of the saturation density. A simple model is described, which exhibits looping and which is shown to be mainly caused by the presence of a peak in the density dependence of the medium modified $\sigma N$ coupling constant at low density. The effect of density dependence of the coupling constants and the meson masses tends to improve the results for $E/A$ and density of nuclear matter at saturation. From the present study we see that the relationship between binding energy and saturation density may not be as universal as found in nonrelativistic studies and that more model dependence is exhibited once medium modifications of the basic nuclear interactions are considered., Comment: Acknowledgements have been modified. 34 pages, revtex, uuencoded gz-compressed tar file

We present the results for the electric dipole amplitude for $\gamma N \to \pi^0 N$ at threshold at the $O(p^2)$ level in SU$_f$(3) chiral perturbation theory. We find that the SU$_f$(3) results differ only slightly from the SU$_f$(2) results. At the $O(p^3)$ level one encounters new, unknown counterterms to fix which one is likely to need the threshold photoproduction data themselves, thus losing predictive power. We suggest, instead, that the {\it difference} between the proton and neutron $\pi^0$ photoproduction amplitudes may provide a test of the convergence properties of the $\chi$PT in the present context. We urge that the neutron's electric dipole amplitude be measured., Comment: Revised version with corrected value of the Kaon loop contribution

The paper deals with two issues. First, we explore the quantitiative importance of higher multiplets for properties of the $\Delta$ decuplet in chiral perturbation theory. In particular, it is found that the lowest order one--loop contributions from the Roper octet to the decuplet masses and magnetic moments are substantial. The relevance of these results to the chiral expansion in general is discussed. The exact values of the magnetic moments depend upon delicate cancellations involving ill--determined coupling constants. Second, we present new relations between the magnetic moments of the $\Delta$ decuplet that are independent of all couplings. They are exact at the order of the chiral expansion used in this paper., Comment: 7 pages of double column revtex, no figures

Baryon masses are calculated in chiral perturbation theory at the one--loop-${\cal O}(p^3)$ level in the chiral expansion and to leading order in the heavy baryon expansion. Ultraviolet divergences occur requiring the introduction of counter--terms. Despite this neccessity, no knowledge of the counter terms is required to determine the violations to the Gell--Mann Okubo mass relation for the baryon octet or to the decuplet equal mass--spacing rule, as all divergences cancel {\it exactly} at this order. For the same reason all reference to an arbitrary scale $\mu$ is absent. Neither of these features continue to higher--powers in the chiral expansion. We also discuss critically the absolute neccessity of simultaneously going beyond the leading order heavy baryon expansion, if one goes beyond the one-loop-${\cal O}(p^3)$ level. We point out that these corrections in $1/M_B$ generate new divergences $\propto m^4/M_{10}$. These divergences together with the divergences occuring in one-loop-${\cal O}(p^4)$ graphs of chiral perturbation theory are taken care of by the same set of counter--terms. Because of these unknown counter--terms one cannot predict the baryon mass splittings at the one-loop-${\cal O}(p^4)$ level. We point out another serious problem of going to the one-loop-${\cal O}(p^4)$ level. When the decuplet is off its mass--shell there are additional $\pi N\Delta$ and $\pi\Delta\Delta$ interaction terms. These interactions contribute not only to the divergent terms $\propto (m^4/M_{10})$, but also to nonanalytic terms such as $\propto (m^4/M_{10}){\rm ln}(m/M_{10})$. Thus without a knowledge of the coupling constants appearing in these interactions one cannot carry out a consistent one-loop-${\cal O}(p^4)$ level calculation., Comment: 10 revtex pages, 3 ps figures. Extended version with modified presentation to incorporate new results on 1/M corrections; reference list has also been expanded