Island for gravitationally prepared state and pseudo entanglement wedge

We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra-ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

Cylinder liner wear as a function of selected physicochemical indicators of engine oil

The paper presents a new method of forecasting the durability of piston-rings-cylinder (PRC) liner assembly of the internal combustion engine on the basis of observed changes of physical and chemical properties of engine oil. Methods used so far for the durability evaluation of the PRC group required collecting information about the moments when the assembly reached its boundary state or used kinetic models of wear designed using accelerated research of real objects. In the proposed method, for the evaluation of durability of engine cylinders information gathered form engine oil is used. Course of changes of the proposed index of change intensity of kinematic viscosity at the temperature of 100°C – Cv100 allows for evaluation of the durability of PRC assembly of an IC engine. Obtained value was positively verified using forecasting method related to the technical criteria based on the assessment of the wear intensity.

Математическая модель многоочагового усталостного повреждения заклепочных соединений

Multiple Site Damage (MSD) is one of the significant damaging factors that limit the airworthiness of aging fleet aircrafts. In case of MSD multiple fatigue cracks initiates and propagates at the rivet holes. Those cracks are relatively short in length, but with a sufficiently large number of them and an unfavorable arrangement along the rivet joint, they can join together and form a crack of a dangerous length. To prevent this type of damage it is necessary to have adequate methods for predicting the boundary state of riveted joints during MSD. A useful approach is a numerical experiment based on Monte-Carlo simulation of the MSD main random factors – the formation of initial cracks and their growth. This paper presents a probabilistic model for predicting the initial stage of MSD – destruction of at least one bridge between the adjacent holes. A level I model is considered, which describes the process of fatigue failure of specimens without rivets but with multiple holes, which are typical for riveted joints. The initiation of fatigue cracks and their growth are modeled taking into account the laws of damage development obtained experimentally on specimens with multiple cracks. So, to simulate the random initiation of cracks in time the Weibull distribution is used. The parameters of this distribution depend on the applied stress. The growth of cracks is described by the Paris' equation, taking into account the experimentally confirmed correlation between the coefficients of this equation. The model assumes that each initiated crack propagates according to a random value of the Paris' equation exponent. The distribution of such a random value corresponds to a logarithmically normal law with experimentally obtained parameters. The criterion for the possible join of opposite cracks growing from adjacent holes is the uniting of plastic deformation zones at the tips of such cracks. The results of modeling are presented in the form of multiple site damage realization field of points in the coordinates of the number of cycles before the initiation of cracks vs. the number of cycles before the destruction of the bridge between holes.

The Solution of Boundary Value Problems of Various Types with Consideration of Volume Forces for Anisotropic Bodies of Revolution

In this work, we studied the axisymmetric elastic equilibrium of transversely isotropic bodies of revolution, which are simultaneously under the influence of surface and volume forces. The construction of the stress-strain state is carried out by means of the boundary state method. The method is based on the concepts of internal and boundary states conjugated by an isomorphism. The bases of state spaces are formed, orthonormalized, and the desired state is expanded in a series of elements of the orthonormal basis. The Fourier coefficients, which are quadratures, are calculated. In this work, we propose a method for forming bases of spaces of internal and boundary states, assigning a scalar product and forming a system of equations that allows one to determine the elastic state of anisotropic bodies. The peculiarity of the solution is that the obtained stresses simultaneously satisfy the conditions both on the boundary of the body and inside the region (volume forces), and they are not a simple superposition of elastic fields. Methods are presented for solving the first and second main problems of mechanics, the contact problem without friction and the main mixed problem of the elasticity theory for transversely isotropic finite solids of revolution that are simultaneously under the influence of volume forces. The given forces are distributed axisymmetrically with respect to the geometric axis of rotation. The solution of the first main problem for a non-canonical body of revolution is given, an analysis of accuracy is carried out and a graphic illustration of the result is given

Decentralized MPC-Based Trajectory Generation for Multiple Quadrotors in Cluttered Environments

Challenges in motion planning for multiple quadrotors in complex environments lie in overall flight efficiency and the avoidance of obstacles, deadlock, and collisions among themselves. In this paper, we present a gradient-free trajectory generation method for multiple quadrotors in dynamic obstacle-dense environments with the consideration of time consumption. A model predictive control (MPC)-based approach for each quadrotor is proposed to achieve distributed and asynchronous cooperative motion planning. First, the motion primitives of each quadrotor are formulated as the boundary state constrained primitives (BSCPs) which are constructed with jerk limited trajectory (JLT) generation method, a boundary value problem (BVP) solver, to obtain time-optimal trajectories. They are then approximated with a neural network (NN), pre-trained using this solver to reduce the computational burden. The NN is used for fast evaluation with the guidance of a navigation function during optimization to guarantee flight safety without deadlock. Finally, the reference trajectories are generated using the same BVP solver. Our simulation and experimental results demonstrate the superior performance of the proposed method.

Spectrum of end of the world branes in holographic BCFTs

We study overlaps between two regularized boundary states in conformal field theories. Regularized boundary states are dual to end of the world branes in an AdS black hole via the AdS/BCFT. Thus they can be regarded as microstates of a single sided black hole. Owing to the open-closed duality, such an overlap between two different regularized boundary states is exponentially suppressed as $$ \left\langle \left.{\psi}_a\right|{\psi}_b\right\rangle \sim {e}^{-O\left({h}_{ab}^{\left(\min \right)}\right)} $$ ψ a ψ b ∼ e − O h ab min , where $$ {h}_{ab}^{\left(\min \right)} $$ h ab min is the lowest energy of open strings which connect two different boundaries a and b. Our gravity dual analysis leads to $$ {h}_{ab}^{\left(\min \right)} $$ h ab min = c/24 for a pure AdS3 gravity. This shows that a holographic boundary state is a random vector among all left-right symmetric states, whose number is given by a square root of the number of all black hole microstates. We also perform a similar computation in higher dimensions, and find that $$ {h}_{ab}^{\left(\min \right)} $$ h ab min depends on the tensions of the branes. In our analysis of holographic boundary states, the off diagonal elements of the inner products can be computed directly from on-shell gravity actions, as opposed to earlier calculations of inner products of microstates in two dimensional gravity.

Boundary state bootstrap and asymptotic overlaps in AdS/dCFT

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.

Boundary RG flows for fermions and the mod 2 anomaly

Boundary conditions for Majorana fermions in d=1+1d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N2N Majorana fermions that preserve a U(1)^NU(1)N symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge gg. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by g^2_{IR} / g^2_{UV} = \mathrm{dim} \, \mathcal{O}gIR2/gUV2=dim𝒪, the dimension of the perturbing boundary operator. Any relevant operator necessarily has \mathrm{dim} \, \mathcal{O} < 1dim𝒪<1, ensuring that the central charge decreases in accord with the gg-theorem.

Natural vibration characteristics determination of elastic beam with attachments based on a transfer matrix method

The transfer matrix method for multibody system takes into account the accuracy of the equations of motion and the efficiency of the algorithm. Especially if a system is composed of flexible and rigid components, transfer matrix method for multibody system reduces the dynamics problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundary are made up of rotation angles, displacements, shear forces, and bending moments, which are normally half known and half unknown. The proposed transfer matrix method for multibody system of multibody system dynamics to determine the vibration characteristics is easy to formulate, systematic to apply, and simple to code. The purpose of this study is to introduce a modeling and simulation idea of beam with attachments based on transfer matrix method for multibody system. Numerical results for several examples of beam with attachments are presented to demonstrate the validity of this method.