Elliptic Solutions of ABS Lattice Equations

Elliptic N-soliton-type solutions, i.e. solutions emerging from the application of N consecutive B\"acklund transformations to an elliptic seed solution, are constructed for all equations in the ABS list of quadrilateral lattice equations, except for the case of the Q4 equation which is treated elsewhere. The main construction, which is based on an elliptic Cauchy matrix, is performed for the equation Q3, and by coalescence on certain auxiliary parameters, the corresponding solutions of the remaining equations in the list are obtained. Furthermore, the underlying linear structure of the equations is exhibited, leading, in particular, to a novel Lax representation of the Q3 equation.Comment: 42 pages, 3 diagram

Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function

Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity has paved the way for the analysis of jamming as an "inverted critical point" in which the direct correlation function $c(r)$ diverges. We establish quantitative relationships between various singularities in $c(r)$ and the total correlation function $h(r)$ that provide a concrete means of identifying features that must be expressed in $c(r)$ if one hopes to reproduce details in the pair correlation function accurately. We also analyze systems of three-dimensional monodisperse hard-spheres of diameter $D$ as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) and Torquato-Jiao (TJ) packing algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling $c(r) \propto -1/r$ as $r \rightarrow 0$ and show that this, along with the developing delta function at $c(D)$, is a consequence of the growing long-rangedness in $c(r)$. Near the freezing density, we identify qualitative differences in the structure factor $S(k)$ as well as $c(r)$ between TJ- and LS-generated configurations and link them to differences in the protocols' packing dynamics. Configurations from both algorithms have structure factors that approach zero in the low-wavenumber limit as jamming is approached and are shown to exhibit a corresponding power-law decay in $c(r)$ for large $r$ as a consequence. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a means of monitoring for an incipient rigid network

Multiplicative renormalizability and quark propagator

The renormalized Dyson-Schwinger equation for the quark propagator is studied, in Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability, and reproduces the correct leading order perturbative behavior, non-trivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced, with infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.Comment: 17 pages; minor corrections, comparison to lattice results added; accepted for publication in Phys. Rev.

Dynamical symmetry breaking, confinement with flat-bottom potential

In this article, we calculate the dressed quark propagator with the flat bottom potential in the framework of the rain-bow Schwinger-Dyson equation. Then based on the nonperturbative dressed quark propagator, we calculate the $\pi$ decay constant and the quark condensate. The $\pi$ decay constant is an important parameter in describing the interplay between dynamical symmetry breaking and confinement, while the quark condensate is an order parameter for dynamical chiral symmetry breaking. To implement confinement, we prove that the dressed quark propagator has no poles on the real timelike $p^2$ axial, the absence of Kallen-Lehmann spectral representation obviously precludes the existence of free quarks.Comment: 10 pages,3 figure

Interleukin‐12p70-dependent interferon‐γ production is crucial for resistance in African trypanosomiasis

African trypanosomiasis encompasses diseases caused by pathogenic trypanosomes, infecting both humans and animals. In the present article, we dissected the possible role of members of the interleukin ( IL)-12 family during infection with Trypanosoma brucei brucei and Trypanosoma evansi in mice. IL-12p35(-/-) , IL-12p40(-/-) , and IL-12p35(-/-)/p40(-/-) mice were susceptible to both pathogens, as was demonstrated by the increased mortality among these mice, compared with wild-type C57BL/6 mice. The different IL-12p70(-/-) mouse strains showed similar mortality kinetics, suggesting that IL-12p70 - but not the IL-12p80 homodimer or IL-23 plays a crucial role in survival. Although there were similar plasma levels of immunoglobulin (Ig) M and IgG2a in IL-12-deficient mice and wild-type mice, interferon (IFN) - g production, especially during early infection, was severely impaired in all IL-12p70(-/-) mouse strains, demonstrating an IL-12p70 - dependent mechanism for IFN-gamma production. Because IFN-gamma receptor-deficient mice (IFN-gamma R-/(-)) were also highly susceptible to both Trypanosoma species, IL-12p70 - dependent IFN-gamma production seems to be the important mechanism involved in resistance against both pathogens

A constructive approach to the soliton solutions of integrable quadrilateral lattice equations

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund transformation, and the method of solving a Riccati map by exploiting two kn own particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler's lattice equation (or Q4).Comment: 22 page

Infrared Behaviour of Propagators and Vertices

We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by P(k^2):= 1/[1+Pi(k^2)], where Pi(k^2) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest P(k^2=0)=0 and Max[P(k^2)]~10 neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of P(k^2) via numerical simulations.Comment: 10 pages, 2 figure

Electromagnetic Pion Form Factor and Neutral Pion Decay Width

The electromagnetic pion form factor, $F_\pi(q^2)$, is calculated for spacelike-$q^2$ in impulse approximation using a confining quark propagator, $S$, and a dressed quark-photon vertex, $\Gamma_\mu$, obtained from realistic, nonperturbative Dyson-Schwinger equation studies. Good agreement with the available data is obtained for $F_\pi(q^2)$ and other pion observables, including the decay $\pi^0 \rightarrow \gamma\,\gamma$. This calculation suggests that soft, nonperturbative contributions dominate $F_\pi(q^2)$ at presently accessible~$q^2$.Comment: 25 pages, LaTeX, elsart.sty, 5 figures, To appear in Nucl. Phys.

Taijiquan the 'Taiji World' way: Towards a cosmopolitan vision of ecology.

In this article, we present a case study analysis of data gathered on the practice of the art of Taijiquan (Tai Chi Chuan) in one UK context. Our interest in looking at this physical culture was in exploring if/how physical cultures of shared embodied experience and practice may help “sow the seeds of environmental awareness”. In so doing, we illustrate certain affinities between this interpretation of the art and Beck’s idea of a “cosmopolitan vision of ecology”. We present an analysis of documentary and interview data of one English Taijiquan organisation and how it currently promotes the idea of interconnectedness, wellbeing and an alternative meta-narrative for living through the practice of Taijiquan. We conclude that, while further research is needed, there is evidence that a cosmopolitan vision for ecology is emerging in physical cultures such as Taijiquan