Solitons and kinks in a general car-following model

We study a car-following model of traffic flow which assumes only that a car's acceleration depends on its own speed, the headway ahead of it, and the rate of change of headway, with only minimal assumptions about the functional form of that dependence. The velocity of uniform steady flow is found implicitly from the acceleration function, and its linear stability criterion can be expressed simply in terms of it. Crucially, unlike in previously analyzed car-following models, the threshold of absolute stability does not generally coincide with an inflection point in the steady velocity function. The Burgers and KdV equations can be derived under the usual assumptions, but the mKdV equation arises only when absolute stability does coincide with an inflection point. Otherwise, the KdV equation applies near absolute stability, while near the inflection point one obtains the mKdV equation plus an extra, quadratic term. Corrections to the KdV equation "select" a single member of the one-parameter set of soliton solutions. In previous models this has always marked the threshold of a finite- amplitude instability of steady flow, but here it can alternatively be a stable, small-amplitude jam. That is, there can be a forward bifurcation from steady flow. The new, augmented mKdV equation which holds near an inflection point admits a continuous family of kink solutions, like the mKdV equation, and we derive the selection criterion arising from the corrections to this equation.Comment: 25 page

The Goldberger -- Treiman Relation, gAg_A and gπNNg_{\pi NN} at T≠0T\neq 0

The Goldberger-Treiman relation is shown to persist in the chiral limit at finite temperatures to order $O(T^2)$. The $T$ dependence of $g_A$ turns out to be the same as for $F_{\pi}$, $g_{A}(T)=g_{A}(0)(1-T^2/12F^2)$, while $g_{\pi NN}$ is temperature independent to this order. The baryon octet ${\cal D}$ and ${\cal F}$ couplings also behave as $F_{\pi}$ if only pions are massless in the pseudoscalar meson octet.Comment: 7p, NSF-ITP-93-145, BUTP-93/27, PUTP-1433, November 199

Electromagnetic corrections in hadronic processes

In quantum field theory, the splitting of the Hamiltonian into a strong and an electromagnetic part cannot be performed in a unique manner. We propose a convention for disentangling these two effects: one matches the parameters of two theories -- with and without electromagnetic interactions -- at a given scale mu_1, referred to as the matching scale. This procedure enables one to analyze the separation of strong and electromagnetic contributions in a transparent manner. We illustrate the method -- in the framework of the loop expansion -- in a Yukawa model, as well as in the linear sigma model, where we also investigate the corresponding low-energy effective theory.Comment: 19 pages (LaTex), 5 figures, published version. References in the introduction added, discussion shortened, 1 figure removed, conclusions unchange

The Mediterranean outflow water : transformations and pathways into the Gulf of Cádiz

The Mediterranean Outflow Water (MOW) is a dense (¿>1028.5 kg/m3), saline (38.5 g/kg) ocean stream originated in the evaporative Mediterranean basin flowing westward past Espartel Sill as a fast (>1 m/s) and often unstable (as indicated by its gradient Richardson number) gravity current. During its descense into the Gulf of Cadiz, the MOW entrains the overlying North Atlantic Central Water (NACW), until the density difference between both water masses vanishes, and reaches its equilibrium depth. Inertia, Coriolis and frictional forces (both internal and with the bottom), as well as pressure gradients (associated with both seafloor slope and density gradients), play varying roles throughout the MOW’s trajectory. In particular, bathymetric steering due to contouritic, turbiditic and diapiric structures controls the early trajectory of the outflow. Using both historic and current hydrographic data, and a new high-resolution bathymetry of a critical region west of Espartel Sill, we examine the hydrographic characteristics of the MOW and the mechanisms that set its pathway. Our study is complemented with the proposal of simple models that help explain pbservations of vertical mixing in the Strait of Gibraltar and the behavior of the MOW as a gravity current within the Gulf of Cádiz, as well as with a new tool, based on water tributaries methods, that assesses the relative impact of both seafloor slope and Coriolis force in steering the outflow.La sortida d'aigua mediterrània (MOW) és un corrent oceànic dens (¿>1028.5 kg/m3) i salí (38.5 lg/m3) originat en la conca evaporativa de la Mar Mediterrània que flueix passant la baixa d'Espartel en forma d'un corrent de gravetat molt ràpid (>1 m/s) i sovint inestable (tal i com indica el número de gradient de Richardson). Durant el seu descens al Golf de Cadis, la MOW incorpora les aigües atlàntiques (NACW) suprajacents fins que la diferència de densitat entre ambdues masses d'aigua desapareix i assoleix la fondària d'equilibri. Les forces d'inèrcia, Coriolis i de fricció (tan internes com amb el fons), així com els gradients de pressió (associats amb el pendent del fons i els gradients de densitat), juguen papers variables al llarg de la trajectòria del MOW. En particular, la canalització del flux gràcies a les estructures de tipus contourític, turbidites i diapirs controlen la trajectòria del corrent. Aquest treball examina les característiques hidrogràfiques del MOW i els mecanismes que determinen la seva trajectòria usant dades històriques i modernes, així com una nova batimetria d'alta resolució d'una regió critica a l'oest de la baixa d'Espartel. L'estudi es complementa amb les propostes de models senzills que ajuden a explicar les observacions de barreja vertical a l'Estret de Gibraltar i el comportament de la MOW com un corrent de gravetat al Golf de Cadis, així com una nova eina, basada en metodologies per aigües tributàries, que permet valorar la importància relativa del pendent del fons i la força de Coriolis en la conducció del flux

Energy level displacement of the excited nl state of pionic hydrogen

The energy level displacements of the excited nl states of pionic hydrogen and the contribution of the ns -> 1s transitions and the (pi^-p)_Coul -> 1s transitions of the pi^-p pair, coupled by the attractive Coulomb field in the S-wave state with a continuous energy spectrum, to the shift of the energy level of the ground state of pionic hydrogen, caused by strong low-energy interactions, are calculated within a quantum field theoretic, relativistic covariant and model-independent approach developed in nucl-th/0306047.Comment: 18 pages, no figures, latex, text is revised, references are adde

Critical Analysis of Baryon Masses and Sigma-Terms in Heavy Baryon Chiral Perturbation Theory

We present an analysis of the octet baryon masses and the $\pi N$ and $KN$ $\sigma$--terms in the framework of heavy baryon chiral perturbation theory. At next-to-leading order, ${\cal O}(q^3)$, knowledge of the baryon masses and $\sigma_{\pi N}(0)$ allows to determine the three corresponding finite low--energy constants and to predict the the two $KN$ $\sigma$--terms $\sigma^{(1,2)}_{KN} (0)$. We also include the spin-3/2 decuplet in the effective theory. The presence of the non--vanishing energy scale due to the octet--decuplet splitting shifts the average octet baryon mass by an infinite amount and leads to infinite renormalizations of the low--energy constants. The first observable effect of the decuplet intermediate states to the baryon masses starts out at order $q^4$. We argue that it is not sufficient to retain only these but no other higher order terms to achieve a consistent description of the three--flavor scalar sector of baryon CHPT. In addition, we critically discuss an SU(2) result which allows to explain the large shift of $\sigma_{\pi N}(2M_\pi^2) - \sigma_{\pi N}(0)$ via intermediate $\Delta (1232)$ states.Comment: 18 pp, TeX, BUTP-93/05 and CRN-93-0

Scalar form factors of light mesons

The scalar radius of the pion plays an important role in CHPT, because it is related to one of the basic effective coupling constants, viz. the one which controls the quark mass dependence of F_pi at one loop. In a recent paper, Yndurain derives a {\it robust lower bound} for this radius, which disagrees with earlier determinations. We show that such a bound does not exist: the "derivation" relies on an incorrect claim. Moreover, we discuss the physics of the form factors associated with the operators \ubar u, \dbar d and \sbar s and show that their structure in the vicinity of the K \Kbar threshold is quite different. Finally, we draw attention to the fact that the new data on the slope of the scalar K_l3 form factor confirm a recent, remarkably sharp theoretical prediction.Comment: 13 pages, 2 figures. v2: minor changes - version to appear on Phys. Lett. B. v3: Published version. Values of the measured K-pi radii correcte

Can one see the number of colors in eta, eta-prime --> pi^+ pi^- gamma?

We investigate the decays eta, eta-prime --> pi^+ pi^- gamma up to next-to-leading order in the framework of the combined 1/N_c and chiral expansions. Counter terms of unnatural parity at next-to-leading order with unknown couplings are important to acommodate the results both to the experimental decay width and the photon spectrum. The presence of these coefficients does not allow for a determination of the number of colors from these decays.Comment: 8 pages, 2 figure

Classical limit for semi-relativistic Hartree systems

We consider the three-dimensional semi-relativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove, using Wigner transformation techniques, that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interaction, with an additional size constraint in the attractive case.Comment: 10 page