We extend previous work on dynamical AdS/QCD models by introducing an extra ingredient under the form of a background magnetic field, this to gain insight into the influence such field can have on crucial QCD observables. Therefore, we construct a closed form analytic solution to an Einstein-Maxwell-dilaton system with a magnetic field. We specifically focus on the deconfinement transition, reporting inverse magnetic catalysis, and on the string tension, reporting a weaker/stronger confinement along/perpendicular to the magnetic field. The latter, being of importance to potential modelling of heavy quarkonia, is in qualitative agreement with lattice findings.

In this paper we present a complete and exact spectral analysis of the $(1+1)$-dimensional model that Jackiw and Rebbi considered to show that the half-integral fermion numbers are possible due to the presence of an isolated self charge conjugate zero mode. The model possesses the charge and particle conjugation symmetries. These symmetries mandate the reflection symmetry of the spectrum about the line $E=0$. We obtain the bound state energies and wave functions of the fermion in this model using two different methods, analytically and exactly, for every arbitrary choice of the parameters of the kink, i.e. its value at spatial infinity ($\theta_0$) and its scale of variations ($\mu$). Then, we plot the bound state energies of the fermion as a function of $\theta_0$. This graph enables us to consider a process of building up the kink from the trivial vacuum. We can then determine the origin and evolution of the bound state energy levels during this process. We see that the model has a dynamical mass generation process at the first quantized level and the zero-energy fermionic mode responsible for the fractional fermion number, is always present during the construction of the kink and its origin is very peculiar, indeed. We also observe that, as expected, none of the energy levels crosses each other. Moreover, we obtain analytically the continuum scattering wave functions of the fermion and then calculate the phase shifts of these wave functions. Using the information contained in the graphs of the phase shifts and the bound states, we show that our phase shifts are consistent with the weak and strong forms of the Levinson theorem. Finally, using the weak form of the Levinson theorem, we confirm that the number of the zero-energy fermionic modes is exactly one.

We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS$_{3}$ group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.

The melting of a heavy quark-antiquark bound state depends on the screening phenomena associated with the binding energy, as well as scattering phenomena associated with the imaginary part of the potential. We study the imaginary part of the static potential of heavy quarkonia moving in the strongly coupled plasma. The imaginary potential dependence on the velocity of the traveling bound states is calculated. Non-zero velocity leads to increase of the absolute value of the imaginary potential. The enhancement is stronger when the quarkonia move orthogonal to the quark-gluon plasma maximizing the flux between the pair. Moreover, we estimate the thermal width of the moving bound state and find it enhanced compared to the static one. Our results imply that the moving quarkonia dissociate easier than the static ones in agreement with the expectations.

In the presence of finite chemical potential $\mu$, we holographically compute the entanglement of purification in a $2+1$- and $3+1$-dimensional field theory and also in a $3+1$-dimensional field theory with a critical point. We observe that compared to $2+1$- and $3+1$-dimensional field theories, the behavior of entanglement of purification near critical point is different and it is not a monotonic function of $\frac{\mu}{T}$ where $T$ is the temperature of the field theory. Therefore, the entanglement of purification distinguishes the critical point in the field theory. We also discuss the dependence of the holographic entanglement of purification on the various parameters of the theories. Moreover, the critical exponent is calculated.

Considering the importance of correctly understanding the dynamics of microstructure materials for their applications in related technologies, by eliminating the shortcomings and some overlooked physical concepts in the existing asymmetric elastic theories, we have presented an asymmetric elastodynamic model based on a U(1) gauge theory with quantum electrodynamics (QED) structure. Accordingly, we have shown that there is a correspondence between an elastic theory, which can explain the behavior of elastic waves within an asymmetric elastic medium, and QED. More specific, we have indicated that the corresponding elastic wave equations are somehow analogous to QED ones. In this regard, by adding vibrational degrees of freedom and introducing a gauge property of the waves of displacement for the waves of rotation, we have generalized and modified the related Cosserat theory (CT) for an elastic environment. Thus on macro scales, the elastic waves can possess the QED treatment. This analogy provides a new paradigm of fermions and bosons. Also, from experimental point of view, we have shown that the behavior of elastic waves in a granular medium is equivalent to behavior of light in dispersive media, which can be explained using QED. Hence, contrary to the Cosserat and discrete models, this amended CT has qualitatively been indicated to be consistent with the corresponding empirical observations.

The routing algorithms for parallel computers, on-chip networks, multi-core processors, and multiprocessors system-on-chip (MP-SoCs) exhibit router failures must be able to handle interconnect router failures that render a symmetrical mesh non-symmetrically. When developing a routing methodology, the time complexity of calculation should be minimal, and thus complicated routing strategies to introduce profitable paths may not be appropriate. Several reports have been released in the literature on using the concept of fault rings to provide detour paths to messages blocked by faults and to route messages around the fault regions. In order to analyze the performance of such algorithms, it is required to investigate the characteristics of fault rings. In this paper, we introduce a novel performance index of network reliability presenting the probability of message facing fault rings, and evaluating the performance-related reliability of adaptive routing schemes in n-D mesh-based interconnection networks with a variety of common cause fault patterns. Sufficient simulation results of Monte-Carlo method are conducted to demonstrate the correctness of the proposed analytical model.

In this paper we calculate the Casimir energy for a massive fermionic field confined between two points in one spatial dimension, with the MIT Bag Model boundary condition. We compute the Casimir energy directly by summing over the allowed modes. The method that we use is based on the Boyer's method, and there will be no need to resort to any analytic continuation techniques. We explicitly show the graph of the Casimir energy as a function of the distance between the points and the mass of the fermionic field. We also present a rigorous derivation of the MIT Bag Model boundary condition.