Analysis of Nonlinear Cyclically Symmetric Isolation Sistem of a Cargo in a Container under Plane Harmonic Vibrations

The problem of calculating the system of a cylindrical shaped load transverse damping installed in a coaxial container is considered. This system has several annular belts of insulation with a cyclically symmetric arrangement of shock absorbers along the circumferential direction. A simple dynamic model of one insulation belt formed by polyurethane tunnel-type shock absorbers is investigated. Such shock absorbers have a high energy absorption coefficient and can operate at very high drafts comparable to their height, which is important when the space between the cargo and the container wall is limited. Within the proposed model framework, a harmonic nonlinear analysis of cargo plane oscillations under kinematic excitation coming from the container is considered. A method for reducing a nonlinear cyclically symmetric system with discrete elastic elements, which allows limiting the analysis to the calculation of a vibration isolation system with one degree of freedom, is proposed. Using the harmonic linearization procedure, the amplitude-frequency characteristics of oscillations and plots of vibration isolation coefficients of cargo at different values of excitation amplitude have been obtained. The results are verified by comparing the analytical solution with the results of numerical integration for a non-reduced nonlinear system with two degrees of freedom. The obtained solution allows choosing the vibration isolation belt parameters, in particular the number of shock absorbers and their stiffness, depending on the conditions of kinematic excitation and permissible overload

Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.

Quantum simulation of PT-arbitrary-phase-symmetric systems

Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT-symmetric systems and its featured properties start to be investigated. In this work, we develop the PT- and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT-φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT-symmetry, unifying the PT and anti-PT symmetries and having properties intermediate between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH-system of two-dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.

Four-band non-Abelian topological insulator and its experimental realization

Very recently, increasing attention has been focused on non-Abelian topological charges, e.g., the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple entangled bulk bandgaps and support nontrivial edge states that manifest the non-Abelian topological features. Furthermore, a system with an even or odd number of bands will exhibit a significant difference in non-Abelian topological classification. To date, there has been scant research investigating even-band non-Abelian topological insulators. Here, we both theoretically explore and experimentally realize a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference in the four-dimensional (4D) rotation sense on the stereographically projected Clifford tori. We show the evolution of the bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way towards other even-band systems.

Experimental demonstration of coherence flow in PT- and anti-PT-symmetric systems

Non-Hermitian parity-time ($${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T ) and anti-parity-time ($${{{{{{{\mathcal{APT}}}}}}}}$$ APT )-symmetric systems exhibit novel quantum properties and have attracted increasing interest. Although many counterintuitive phenomena in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems were previously studied, coherence flow has been rarely investigated. Here, we experimentally demonstrate single-qubit coherence flow in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems using an optical setup. In the symmetry unbroken regime, we observe different periodic oscillations of coherence. Particularly, we observe two complete coherence backflows in one period in the $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T -symmetric system, while only one backflow in the $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric system. Moreover, in the symmetry broken regime, we observe the phenomenon of stable value of coherence flow. We derive the analytic proofs of these phenomena and show that most experimental data agree with theoretical results within one standard deviation. This work opens avenues for future study on the dynamics of coherence in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems.

Negative imaginariness and positive realness analysis of state-space symmetric systems with interval uncertainty

In this article, the state-space symmetric systems with symmetrical interval uncertainty that have positive real and negative imaginary properties are studied. First, a necessary and sufficient test in view of a state matrix is derived for a state-space symmetric system to be negative imaginary, which allows having poles at the origin. Second, bounds on symmetrical interval uncertainty that guarantee the positive realness and negative imaginariness of state-space symmetric systems are provided. Finally, the main results are illustrated by a resistor–capacitor network and a numerical design example.

Orientation dependent transverse relaxation in human brain white matter: The magic angle effect on a cylindrical helix

Purpose: To overcome limitations of prior orientation-dependent R2 and R2* formalisms in white matter (WM) with a novel framework based on magic angle effect. Methods: A cylindrical helix model was developed embracing both anisotropic rotational and translational diffusions of ordered water in WM, with the former characterized by an axially symmetric system. Both R2 and R2* were divided into isotropic (R2i) and anisotropic parts, R2a*f(ε-ε0,α), with α denoting a funnel opening angle and ε0 an orientation (ε) offset relative to DTI-derived primary diffusivity direction. The proposed framework (Fit A) was compared with prior model without ε0 (Fit B) and applied to published R2 and R2* in WM of underdeveloped, healthy, and diseased conditions. Goodness of fit was characterized by root-mean-square error (RMSE). F-test and Pearson correlation coefficient (PCC) were used with statistical significance set to P ≤ .05. Results: Fit A significantly outperformed Fit B as demonstrated by reduced RMSEs in myelin water (i.e., 0.349 vs. 0.724). The fitted ε0 was in good agreement with the calculated ε0 from DTI directional diffusivities. Significant positive (R2i) and negative (α and R2a) correlations were found with aging (demyelination) in adults while ε0 showed a weak positive correction (PCC=0.11, P= .28). Compared to those from healthy adult WM, the fits of R2i, R2a, and α from neonates were considerably reduced but ε0 increased, consistent with limited myelination. Conclusion: The developed framework can better characterize anisotropic transverse relaxation in WM, shedding new light on myelin microstructural alterations at the molecular level.