The Hopf Skyrmion in QCD with Adjoint Quarks

We consider a modification of QCD in which conventional fundamental quarks are replaced by Weyl fermions in the adjoint representation of the color SU(N). In the case of two flavors the low-energy chiral Lagrangian is that of the Skyrme-Faddeev model. The latter supports topologically stable solitons with mass scaling as N^2. Topological stability is due to the existence of a nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify, at the level of the fundamental theory, adjoint QCD, an underlying reason responsible for the stability of the corresponding hadrons. We argue that all "normal" mesons and baryons, with mass O(N^0), are characterized by (-1)^Q (-1)^F =1, where Q is a conserved charge corresponding to the unbroken U(1) surviving in the process of the chiral symmetry breaking (SU(2) \to U(1) for two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the case at hand). We argue that there exist exotic hadrons with mass O(N^2) and (-1)^Q (-1)^F = -1. They are in one-to-one correspondence with the Hopf Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in F, namely F \to F - {\cal H} where {\cal H} is the Hopf invariant. To detect this phenomenon we have to extend the Skyrme-Faddeev model by introducing fermions.Comment: 18 pages, 3 figures; v.2: a reference and a comment added; v.3: two comments added, figures improve

The New Fat Higgs: Slimmer and More Attractive

In this paper we increase the MSSM tree level higgs mass bound to a value that is naturally larger than the LEP-II search constraint by adding to the superpotential a $\lambda S H_{u}H_{d}$ term, as in the NMSSM, and UV completing with new strong dynamics {\it before} $\lambda$ becomes non-perturbative. Unlike other models of this type the higgs fields remain elementary, alleviating the supersymmetric fine-tuning problem while maintaining unification in a natural way.Comment: 14 pages and 2 figures. Added references and updated argument about constraints from reheating temperatur

Efficiency at maximum power of thermally coupled heat engines

We study the efficiency at maximum power of two coupled heat engines, using thermoelectric generators (TEGs) as engines. Assuming that the heat and electric charge fluxes in the TEGs are strongly coupled, we simulate numerically the dependence of the behavior of the global system on the electrical load resistance of each generator in order to obtain the working condition that permits maximization of the output power. It turns out that this condition is not unique. We derive a simple analytic expression giving the relation between the electrical load resistance of each generator permitting output power maximization. We then focuse on the efficiency at maximum power (EMP) of the whole system to demonstrate that the Curzon-Ahlborn efficiency may not always be recovered: the EMP varies with the specific working conditions of each generator but remains in the range predicted by irreversible thermodynamics theory. We finally discuss our results in light of non-ideal Carnot engine behavior.Comment: 11 pages, 7 figure

Explicitly solvable cases of one-dimensional quantum chaos

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit and exact

Vortex -- Kink Interaction and Capillary Waves in a Vector Superfluid

Interaction of a vortex in a circularly polarized superfluid component of a 2d complex vector field with the phase boundary between superfluid phases with opposite signs of polarization leads to a resonant excitation of a ``capillary'' wave on the boundary. This leads to energy losses by the vortex--image pair that has to cause its eventual annihilation.Comment: LaTeX 7 pages, no figure

Quantum Transport in Molecular Rings and Chains

We study charge transport driven by deformations in molecular rings and chains. Level crossings and the associated Longuet-Higgins phase play a central role in this theory. In molecular rings a vanishing cycle of shears pinching a gap closure leads, generically, to diverging charge transport around the ring. We call such behavior homeopathic. In an infinite chain such a cycle leads to integral charge transport which is independent of the strength of deformation. In the Jahn-Teller model of a planar molecular ring there is a distinguished cycle in the space of uniform shears which keeps the molecule in its manifold of ground states and pinches level crossing. The charge transport in this cycle gives information on the derivative of the hopping amplitudes.Comment: Final version. 26 pages, 8 fig

Physics of the interior of a spherical, charged black hole with a scalar field

We analyse the physics of nonlinear gravitational processes inside a spherical charged black hole perturbed by a self-gravitating massless scalar field. For this purpose we created an appropriate numerical code. Throughout the paper, in addition to investigation of the properties of the mathematical singularities where some curvature scalars are equal to infinity, we analyse the properties of the physical singularities where the Kretschmann curvature scalar is equal to the planckian value. Using a homogeneous approximation we analyse the properties of the spacetime near a spacelike singularity in spacetimes influenced by different matter contents namely a scalar field, pressureless dust and matter with ultrarelativistic isotropic pressure. We also carry out full nonlinear analyses of the scalar field and geometry of spacetime inside black holes by means of an appropriate numerical code with adaptive mesh refinement capabilities. We use this code to investigate the nonlinear effects of gravitational focusing, mass inflation, matter squeeze, and these effects dependence on the initial boundary conditions. It is demonstrated that the position of the physical singularity inside a black hole is quite different from the positions of the mathematical singularities. In the case of the existence of a strong outgoing flux of the scalar field inside a black hole it is possible to have the existence of two null singularities and one central $r=0$ singularity simultaneously

Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and other areas. A Schnol type theorem is proven that allows one to detect that a point belongs to the spectrum when a generalized eigenfunction with an subexponential growth integral estimate is available. A theorem on spectral gap opening for ``decorated'' quantum graphs is established (its analog is known for the combinatorial case). It is also shown that if a periodic combinatorial or quantum graph has a point spectrum, it is generated by compactly supported eigenfunctions (``scars'').Comment: 4 eps figures, LATEX file, 21 pages Revised form: a cut-and-paste blooper fixe

Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are Hamilton-Jacobi equations with convex ($L^1$ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $\bar H$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed $s_T$. An important problem in turbulent combustion theory is to study properties of $s_T$, in particular how $s_T$ depends on the flow amplitude $A$. In this paper, we will study the behavior of $\bar H=\bar H(A,d)$ as $A\to +\infty$ at any fixed diffusion constant $d > 0$. For the cellular flow, we show that $$\bar H(A,d)\leq O(\sqrt {\mathrm {log}A}) \quad \text{for all $d>0$}.$$ Compared with the inviscid G-equation ($d=0$), the diffusion dramatically slows down the front propagation. For the shear flow, the limit \nit $\lim_{A\to +\infty}{\bar H(A,d)\over A} = \lambda (d) >0$ where $\lambda (d)$ is strictly decreasing in $d$, and has zero derivative at $d=0$. The linear growth law is also valid for $s_T$ of the curvature dependent G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square root of log growt

Method of individual forecasting of sow reproductive performance on the basis of a non-linear canonical model of a random sequence

Improvement of sow reproductive performance is a key factor determining the efficiency of the pig production cycle and profitability of pork production. This article presents the solution of an important scientific and practical problem of individual forecasting of sow reproduction . The population used for the present study is from a pig farm managed by the Limited Liability Company (LLC) ‘Tavriys’kisvyni’ located in Skadovsky district (Kherson region, Ukraine). The experimental materials used for this study consisted of 100 inds. of productive parent sows of the Large White breed.The litter size traits – the total number of piglets born (TNB), number of piglets born alive (NBA) and number of weaned piglets (NW) – were monitored in the first eight parities over an eleven year period (2007–2017). The method of the forecasting of sow litter size is developed based on the non-linear canonical model of the random sequence of a litter size change. The proposed method allows us to take maximum account of stochastic peculiarities of sow reproductive performance and does not impose any restrictions on the random sequence of a litter size change (linearity, stationarity, Markov property, monotony, etc.). The block diagram of the algorithm presented in this work reflects the peculiarities of calculation of the parameters of a predictive model. The expression for the calculation of an extrapolation error allows us to estimate the necessary volume of a priori and a posteriori information for achieving the required quality of solving the forecasting problem. The results of the numerical experiment confirmed the high accuracy of the proposed method of forecasting of sow reproduction. The method offered by us almost doubles the accuracy of forecasting of sow litter size compared to the use of the Wiener and Kalman methods. Thus, average forecast error decreases across the range of features TNB (1.71), NBA (1.68) and NW (1.25 piglets). Apparently, this may reflect a higher level of manifestation of the genetically determined level of individual sow fertility at the moment of piglet weaning. The higher adequacy of the developed mathematical model with regard to NW can be also due to the fact that the relations between sow litter size in different farrowings primarily have a non-linear character, which is taken into maximum account in our offered model. Given non-linearity, on the other hand, turns out to be a significant factor determining a lower estimation of the repeatability value for NW compared to the estimations for TNB and NBA. The use of the developed method will help to improve the efficiency of pig farming