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This paper considers the boundary stabilisation problem of an underactuated system of coupled time-fractional partial differential equations (PDEs) with different space-dependent diffusivity by sta...

Introduction. The influence of two ways of organizing scalar product on the convergence rate of the solution in the energy method of boundary states is considered. The method is based on the spaces of internal and boundary states which are conjugated through isomorphism. Both spaces are orthonormalized using one scalar product or another. The desired state is expanded in the Fourier series according to the elements of the orthonormalized basis; and the coefficients of this linear combination are determined. The two methods differ in the assignment of scalar products and the calculation of the Fourier coefficients.Materials and Methods. In relation to the method of boundary states, a new theory of organizing a scalar product in the spaces of internal and boundary states is proposed. Computational algorithms are constructed for its practical implementation. In the traditional (first) approach, the internal energy of elastic deformation is used as an orthogonalizer in the space of internal states. Here, the Fourier coefficients are the work of given forces on the basis vectors of displacement of the boundary points. In the studied (second) approach, scalar products are integrals of the cross products of the basis force vectors at the boundary. Accordingly, the Fourier coefficients are calculated as integrals of the product of the given forces at the body boundary by the basic force vectors.Results. A numerical study of the first primal axisymmetric problem of the elasticity theory for a transversely isotropic cylinder in the absence and presence of mass forces is conducted. In the absence of mass forces, an analysis of the elas-tic fields obtained for the same number of used basic elements has shown that the second method has the greatest accuracy of the results. Under solving the problem with the presence of mass forces, the second method did not show effi-ciency in terms of the uniqueness of the solution; however, it is quite suitable for constructing a multitude of elastic fields used to solve more complex problems.Discussion and Conclusions. The results obtained can be used to solve boundary-value problems of mechanics of not only an anisotropic body, but also an isotropic one. When solving more complex problems, such as contact and mixed ones, the issue of the rate of convergence requires a separate study.

Данная статья посвящена развитию метода граничных состояний на класс задач механики твердого деформируемого тела, включающих сингулярности физического характера. Сформировано множество специальных решений, соответствующих сосредоточенным силовым воздействиям на поверхности гладкого трехмерного тела. Каждое специальное решение включено в базисы пространств внутренних и граничных состояний. В качестве примеров эффективности использования специальных решений методом граничных состояний построены напряжённо-деформированные состояния тел шарообразной формы под воздействием сосредоточенных сил. This article is devoted to the development of the method of boundary states into a class of problems of mechanics of a solid deformable body, including singularities of a physical nature. Many special solutions have been formed corresponding to concentrated force actions on the surface of a smooth three-dimensional body. Each special solution is included in the bases of spaces of internal and boundary states. As examples of the effectiveness of using special solutions using the boundary state method, stress-strain states of spherical bodies are constructed under the influence of concentrated forces.

We discuss two methods that, through a combination of cyclically gluing copies of a given $n$-party boundary state in AdS/CFT and a canonical purification, creates a bulk geometry that contains a boundary homologous minimal surface with area equal to 2 or 4 times the $n$-party entanglement wedge cross-section, depending on the parity of the party number and choice of method. The areas of the minimal surfaces are each dual to entanglement entropies that we define to be candidates for the $n$-party reflected entropy. In the context of AdS$_3$/CFT$_2$, we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions., 20 pages, 7 figures; added references, one figure, and expanded discussion on black holes and the boundary state

We introduce a simple Ginzburg-Landau model to describe coupled orders, such as antiferromagnetism and superconductivity in high-Tc cuprate superconductors, using which we can study the spatial modulation of the doping rate. We study junctions between non-doped and highly doped materials of cuprates. Possibility of a novel superconducting boundary state is suggested, which appears at temperatures higher than the maximum transition temperature of the bulk material at optimal doping. Experimental possibilities to realize this state is also discussed.

The authors show that a gapped boundary state of (3+1)-dimensional topological superconductor in a specific class with time reversal symmetry must carry nontrivially quantized chiral central charge.

We define the "kink transform" as a one-sided boost of bulk initial data about the Ryu-Takayanagi surface of a boundary cut. For a flat cut, we conjecture that the resulting Wheeler-DeWitt patch is the bulk dual to the boundary state obtained by Connes cocycle (CC) flow across the cut. The bulk patch is glued to a precursor slice related to the original boundary slice by a one-sided boost. This evades ultraviolet divergences and distinguishes our construction from one-sided modular flow. We verify that the kink transform is consistent with known properties of operator expectation values and subregion entropies under CC flow. CC flow generates a stress tensor shock at the cut, controlled by a shape derivative of the entropy; the kink transform reproduces this shock holographically by creating a bulk Weyl tensor shock. We also go beyond known properties of CC flow by deriving novel shock components from the kink transform., Comment: 43 pages, 7 figures

We formulate and close the boundary state bootstrap for factorizing K-matrices in AdS/CFT. We found that there are no boundary degrees of freedom in the boundary bound states, merely the boundary parameters are shifted. We use this family of boundary bound states to describe the D3-D5 system for higher dimensional matrix product states and provide their asymptotic overlap formulas. In doing so we generalize the nesting for overlaps of matrix product states and Bethe states., 17 pages, some explanations and references added

We show that limit shapes for the stochastic 6-vertex model on a cylinder with the uniform boundary state on one end are solutions to the Burger type equation. Solutions to these equations are studied for step initial conditions. When the circumference of the cylinder goes to infinity the solution corresponding to critical initial densities coincides with the one found by Borodin, Corwin and Gorin.

Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminates topological entanglement entropy. We show that if the state at the boundary of a subregion is a stabilizer state, then it has a non-zero spurious contribution to the region if and only if, the state is in a non-trivial one-dimensional $G_1\times G_2$ symmetry-protected-topological (SPT) phase. However, we provide a candidate of a boundary state that has a non-zero spurious contribution but does not belong to any such SPT phase., 5+7 pages, 4 figures v2:published in PRResearch: Rapid Communication. Title is modified. Minor errors are fixed

In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. A large family of such inequalities have been proven under the assumption that the bulk geometry is static, using a method involving contraction maps. By using kinematic space techniques, we show that in two boundary (three bulk) dimensions, all entropy inequalities that can be proven in the static case by contraction maps must also hold in holographic states with time dependence., 37 pages, 10 figures

In this paper, we first use the original complexity equals action (CA) conjecture to discuss the complexity growth rate in both perturbative Einsteinian cubic gravity and nonperturbative Einstein-Weyl gravity. We find that the CA complexity growth rates in these cases are divergent. To avoid this divergence, we modify the original conjecture, in which we assume that the complexity of the boundary state equals the boundary actions contributed by the null segments as well as the joints of the Wheeler-DeWitt patch. Then, the late-time growth rate of this modified holographic complexity is given by entropy S times temperature T of the black holes, which is in agreement with the circuit analysis. Finally, to test its rationality, we also investigate the switchback effect by evaluating it in a Vaidya geometry and analyze the results in circuit models.

We show that topological phases of the Dirac system in arbitral even dimensional space are simulated by $LC$ electric circuits with operational amplifiers. The lattice Hamiltonian for the hypercubic lattice in $2n$ dimensional space is characterized by the $n$-th Chern number. The boundary state is described by the Weyl theory in $2n-1$ dimensional space. They are well observed by measuring the admittance spectrum. They are different from the disentangled $n$-th Chern insulators previously reported, where the $n$-th Chern number is a product of the first Chern numbers. The results are extended to non-Hermitian systems with complex Dirac masses. The non-Hermitian $n$-th Chern number remains to be quantized for the complex Dirac mass.

In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport via counterpropagating boundary states can be tailored in ways that overcome the constraints imposed by Hermiticity. Non-Hermitian boundary state engineering specifically enables the enhancement of boundary transport relative to bulk motion, helical transport with a preferred direction, and chiral transport in the same direction on opposite boundaries. We explain the experimental relevance of our findings for the example of photonic waveguide lattices., 5 pages, 6 figures + supplemental; as published

In this article, we investigate zero-modes for a dynamical (rotating-moving) D$p$-brane, coupled to the electromagnetic and tachyonic background fields. This work is done by the boundary state methods, in three cases of bosonic and fermionic boundary states and superstring partition function. By analyzing the obtained zero-modes in either of the cases, interesting results will be obtained. Our findings demonstrate the importance of the zero-mode and its effects on the background fields and the defined internal properties of the described system., Comment: 15 pages, 1 table

For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode $k$ qudits into $N-k$ qudits, with $k\leq \left \lfloor{N/2} \right \rfloor$, where the local dimension $d$ is prime. We use these methods to analyse the concatenation of such quantum codes and link this procedure to entanglement swapping. Using our techniques, we investigate the spread of quantum information on a tensor network code formerly used as a toy model for the AdS/CFT correspondence. In this network, we show how corrections arise to the Ryu-Takayanagi formula in the case of entangled input state, and that the bound on the entanglement entropy of the boundary state is saturated for absolutely maximally entangled input states., Comment: 11 pages, 7 figures

The development of plastic deformation in flexible pavements has been a topic of research for several decades. Different models are available to predict this type of distress. However, the conditions defined by high loads with different stress paths than those traditionally considered during the development of performance models may cause their application to analyze non-standard vehicles to be limiting. This work presents a predictive model of permanent deformation that reduces the limitations usually encountered during the analysis of superheavy vehicles' effect on flexible pavements. The model includes mechanistic-empirical pavement analysis concepts and combines them with shakedown theory principles to identify the deformation states and associated deformation rate. The model was developed from cyclic triaxial tests and offered an analytical tool to define the boundary state of the granular materials and estimate the expected range of deformation during the passage of a superheavy vehicle over the pavement.

The process of opinion formation rarely boils down to accepting or rejecting the social consensus of others, despite the considerable research (since Sch, 1956 [5] ) that has been focused on such situations. In this paper, we propose a mathematical model of threshold-type delay differential equations describing the relationship between two subpopulations with opposite opinions and the opinion spread dynamics. We study the quantitative as well as qualitative properties of our model, and we present results on positivity and boundedness, local stability of equilibria and global stability of the boundary state under certain conditions. Further analysis of the model show that the system exhibits either a forward transcritical or a backward bifurcation. Furthermore, numerical simulations and sensitivity analysis are performed to study the impact of the relevant parameters of the model on the achievement of the consensus.

It is conjectured that the average energy provides an upper bound on the rate at which the complexity of a holographic boundary state grows. In this paper, we perturb a holographic CFT by a relevant operator with a time-dependent coupling, and study the complexity of the time-dependent state using the \textit{complexity equals action} and the \textit{complexity equals volume} conjectures. We find that the rate of complexification according to both of these conjectures has UV divergences, whereas the instantaneous energy is UV finite. This implies that neither the \textit{complexity equals action} nor \textit{complexity equals volume} conjecture is consistent with the conjectured bound on the rate of complexification.

Using the boundary state formalism we investigate the effect of tachyon condensation process on a rotating and moving D$p$-brane with various background fields in the bosonic string theory. The rotation and motion are inside the brane volume. We demonstrate that some specific rotations and/or motions can preserve the brane from instability and collapse., 11 pages, Latex, No figure

У статті висвітлено сутність та роль прикордонних станів у проектуванні дизайн-систем. Увага дизайнерів переноситься з остаточного результату на процес формування нової структури шляхом цілеспрямованого проектування ситуацій деструктивного або конструктивного характеру. Прикордонний стан – це неперервний процес побудови нової емерджентної властивості відкритої дизайн-системи (на візуальному та концептуальному рівнях). Формами прояву прикордонних станів виступають структурно-функціональні та синтетичні перетворення. Їх прихована потенція розкриває різні аспекти цілісної системи у контексті природного і соціального середовища. Виявлено, що прикордонні стани в дизайні є експериментальною основою для створення тапрогнозування нових інтегрованих дизайн-систем і напрямків проектування.