Abstract:
We analyze inelastic 2 to 2 scattering amplitudes for gauge bosons and Nambu-Goldstone bosons in deconstructed Higgsless models. Using the (KK) Equivalence Theorem in 4D (5D), we derive a set of general sum rules among the boson masses and multi-boson couplings that are valid for arbitrary deconstructed models. Taking the continuum limit, our results naturally include the 5D Higgsless model sum rules for arbitrary 5D geometry and boundary conditions; they also reduce to the elastic sum rules when applied to the special case of elastic scattering. For the case of linear deconstructed Higgsless models, we demonstrate that the sum rules can also be derived from a set of general deconstruction identities and completeness relations. We apply these sum rules to the deconstructed 3-site Higgsless model and its extensions; we show that in 5D ignoring all higher KK modes (n>1) is inconsistent once the inelastic channels become important. Finally, we discuss how our results generalize beyond the case of linear Higgsless models.

Abstract:
By large-distance asymptotics, in conventional scattering theory, at the cost of losing the information of the distance between target and observer, one arrives at an explicit expression for scattering wave functions represented by a scattering phase shift. In the present paper, together with a preceding paper (T. Liu,W.-D. Li, and W.-S. Dai, JHEP06(2014)087), we establish a rigorous scattering theory without imposing large-distance asymptotics. We show that even without large-distance asymptotics, one can also obtain an explicit scattering wave function represented also by a scattering phase shift, in which, of course, the information of the distance is preserved. Nevertheless, the scattering amplitude obtained in the preceding paper depends not only on the scattering angle but also on the distance between target and observer. In this paper, by constructing a scattering boundary condition without large-distance asymptotics, we introduce a scattering amplitude, like that in conventional scattering theory, depending only on the scattering angle and being independent of the distance. Such a scattering amplitude, when taking large-distance asymptotics, will recover the scattering amplitude in conventional scattering theory. The present paper, with the preceding paper, provides a complete scattering theory without large-distance asymptotics.

Abstract:
We study the LHC signatures of new gauge bosons in the minimal deconstruction Higgsless model (MHLM). We analyze the $W'$ signals of $pp\to W' \to WZ$ and $pp\to W'jj \to WZjj$ processes at the LHC, including the complete signal and background calculation in the gauge invariant model and have demonstrated the LHC potential to cover the whole parameter space of the MHLM model.

Abstract:
Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance concentrations at the opposite membrane surfaces. The Green's function of the diffusion equation is found for the derived boundary condition and the exact solution of the equation is given.

Abstract:
We discuss a model in which the boundary condition decides the four dimensional cosmological constant. It is reviewed in a primitive way that boundary conditions are required by the action principle.

Abstract:
In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness $\delta$ is so small that some non-negligible slip may occur at the fluid-solid interface. This paper assesses the impact of the slip by revisiting the classical problem of steady acoustic streaming over a flat boundary with the Navier boundary condition $u|_{y=0} = L_\mathrm{s} \partial_y u|_{y=0}$, where $u$ is the velocity tangent to the boundary $y=0$, and the parameter $L_\mathrm{s}$ is the slip length. The limit outside the boundary layer provide an effective slip velocity. A general expression is obtained for the streaming velocity outside the boundary layer as a function of the dimensionless parameter $L_\mathrm{s}/\delta$. Particularising to travelling and standing waves shows that the boundary slip respectively increases and decreases the streaming velocity.

Abstract:
The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.

Abstract:
The Nahm pole boundary condition for certain gauge theory equations in four and five dimensions is defined by requiring that a solution should have a specified singularity along the boundary. In the present paper, we show that this boundary condition is elliptic and has regularity properties analogous to more standard elliptic boundary conditions. We also establish a uniqueness theorem for the solution of the relevant equations on a half-space with Nahm pole boundary conditions. These results are expected to have a generalization involving knots, with applications to the Jones polynomial and Khovanov homology.

Abstract:
In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin. In this setting we find the renormalization group flow of U(2) family of boundary conditions exactly. We show that the well-known scale-independent subfamily of boundary conditions are realized as fixed points. We also discuss the duality between two distinct boundary conditions from the renormalization group point of view. Generalizations to conformal mechanics and quantum graph are also discussed.