CyberSec Research

Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range of frequencies results in continuous eigencurves that are of relevance in practical applications of ultrasonic measurement systems. Recent research has shown that eigencurves of parameter-dependent eigenvalue problems can alternatively be computed as solutions of a system of ordinary differential equations, which are obtained by postulating an exponentially decaying residual of a modal solution. This general concept for solving parameter-dependent matrix equations is, in this context, known as Zeroing Neural Networks or Zhang Neural Networks (ZNN). We exploit this idea to develop an efficient method for computing the dispersion curves of plate structures coupled to unbounded solid or fluid media. In these scenarios, the alternative formulation is particularly useful since the boundary conditions give rise to nonlinear terms that severely hinder the application of traditional solvers.

The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more striking in the case of a free particle. By manipulating the parameter and integrating out, the statistical average of the multiplicative Lagrangian and Hamiltonian naturally arises. Astonishingly, from this statistical viewpoint, the relativistic Lagrangian and Hamiltonian emerge with remarkable elegance. On the action level, this formalism unveils a deeper connection: the spacetime of Einstein's theory reveals itself from a statistical perspective through the action associated with the multiplicative Lagrangian. This suggests that the multiplicative Lagrangian/Hamiltonian framework offers a profound and beautiful foundation, one that reveals the underlying unity between classical and relativistic descriptions in a way that transcends traditional formulations. In essence, the multiplicative approach introduces a richer and more intricate structure to our understanding of physics, bridging the gap between different theoretical realms through a statistical perspective.

While Liouville's theorem is first order in time for the phase-space distribution itself, the relativistic mass-shell constraint $p^\mu p_\mu = m^2$ is naively second order in energy. We argue it is reasonable to unify both energy branches within a single Hamiltonian by factorising $(p^2 - m^2)$ in analogy with Dirac's approach in relativistic quantum mechanics. We show the resulting matrix-based Liouville equation remains first order and naturally yields a $4\times4$ matrix-valued probability density function in phase space as a classical analogue of a relativistic spin-half Wigner function.

This paper analyzes the stress distribution in a two-dimensional elastic disk under diametric loading, with a focus on enhancing the understanding of concrete and rock materials' mechanical behavior. The study revisits the Brazilian test and addresses its high shear stress issue near loading points by exploring the ring test, which introduces a central hole in the disk. Using dynamic elasticity theory, we derive stress distributions over time and extend the analysis to static conditions. This approach distinguishes between longitudinal and transverse wave effects, providing a detailed stress field analysis. By drawing parallels with curved beam theories, we demonstrate the applicability of dynamic elasticity theory to complex stress problems, offering improved insights into the stress behavior in elastic disks.

This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper presents both an analytical solution and a numerical approximation to the Falling Astronaut Problem and compares the educational merit of the two approaches. The analytical solution is exact; however, the derivation requires techniques that are more advanced than what is typically seen in an introductory undergraduate physics course. In contrast, the numerical approximation presents a novel application of concepts with which a first-semester undergraduate is likely to be familiar. The paper stresses the pedagogical implications of this problem, specifically the opportunity for introductory undergraduate students to learn the utility of differential equations, numerical approximations, and data spreadsheets. On a more fundamental level, the paper argues that the Falling Astronaut Problem presents an instructional opportunity for physics students to acquire a nuanced and informative lens through which to conceptualize cause and effect in the universe.

We propose a structural variational resolution of the Abraham-Lorentz-Dirac (ALD) pathologies. By deriving the Variational Kinematic Constraint (VKC) and the Variational Dynamics Constraint (VDC) from the particle's proper-time perspective, we show that self-induced variations are forbidden and dynamics arise solely from first-order proper-time variations of external fields. Consequently, self-force terms are excluded at the variational level, eliminating runaway solutions and non-causal behavior without regularization. Our framework further provides a first-principles derivation of minimal coupling and reveals gauge invariance as a necessary consequence of proper-time-based variational structure.

It is well-known that band gaps, in the frequency domain, can be achieved by using periodic metamaterials. However it has been challenging to design materials with broad band gaps or that have multiple overlapping band gaps. For periodic materials this difficulty arises because many different length scales would have to be repeated periodically within the same structure to have multiple overlapping band gaps. Here we present an alternative: to design band gaps with disordered materials. We show how to tailor band gaps by choosing any combination of Helmholtz resonators that are positioned randomly within a host acoustic medium. One key result is that we are able to reach simple formulae for the effective material properties, which work over a broad frequency range, and can therefore be used to rapidly design tailored metamaterials. We show that these formulae are robust by comparing them with high-fidelity Monte Carlo simulations over randomly positioned resonant scatterers.

Realizing metasurfaces for anomalous scattering is fundamental to designing reflector arrays, reconfigurable intelligent surfaces, and metasurface antennas. However, the basic cost of steering scattering into non-specular directions is not fully understood. This paper derives tight physical bounds on anomalous scattering using antenna array systems equipped with non-local matching networks. The matching networks are explicitly synthesized based on the solutions of the optimization problems that define these bounds. Furthermore, we analyze fundamental limits for metasurface antennas implemented with metallic and dielectric materials exhibiting minimal loss within a finite design region. The results reveal a typical 6dB reduction in bistatic radar cross section (RCS) in anomalous directions compared to the forward direction. Numerical examples complement the theory and illustrate the inherent cost of achieving anomalous scattering relative to forward or specular scattering for canonical configurations.

We use a Legendre polynomial expansion to find the electrostatic potential of a uniformly charged disk. We then use the potential to find the electric field of the disk.

This paper investigated the phenomenon of non-contact resistance by inserting a non-magnetic metal rod into an induction coil to explore the response changes of an LRC circuit. We focused on analyzing the changes in inductance when non-ferromagnetic materials (such as H59 brass) were inserted into the coil and verified the impact of the copper rod on inductance through theoretical derivation and experimental validation. Based on Maxwell's equations, the magnetic field distribution within the copper rod was thoroughly derived, and the inductance and resistance values were experimentally measured. These results confirm the accuracy of the theoretical model.

We investigate the evolution of dispersive waves governed by linear wave equations, where a finite duration source is applied. The resulting wave may be viewed as the superposition of modes before the source is turned on and after it is turned off. We consider the problem of relating the modes after the source term is turned off to the modes before the source term was turned on. We obtain explicit formulas in both the wavenumber and position representations. A number of special cases are considered. Using the methods presented, we obtain a generalization of the d'Alembert solution which applies to linear wave equations with constant coefficients.

The well-known expressions for the Green's functions for the Helmholtz equation in polar coordinates with Dirichlet and Neumann boundary conditions are transformed. The slowly converging double series describing these Green's functions are reduced by means of successive subtraction of several auxiliary functions to series that converge much more rapidly. A method is given for constructing the auxiliary functions (the first one is identical with the Green's function of the Laplace equation) in the form of single series and in the form of closed expressions. Formulas are presented for summing series of the Fourier-Bessel and Dini type; they are required to implement the two steps of the procedure for accelerating convergence. The effectiveness of the functions constructed is illustrated by the numerical solution of the problem of the dispersion properties of a slotted line with a coaxial circular cylindrical screen.

Recently, a new general wave phenomenon, namely "the anti-localization of non-stationary linear waves", has been introduced and discussed. This is zeroing of the propagating component for a non-stationary wave-field near a defect in infinitely long wave-guides. The phenomenon is known to be observed in both continuum and discrete mechanical systems with a defect, provided that the frequency spectrum for the corresponding homogeneous system possesses a stop-band. In this paper, we show that the anti-localization is also quite common for nonlinear systems. To demonstrate this, we numerically solve several non-stationary problems for an infinite $\beta$-FPUT chain with a defect.

Continuum grid-like frames composed of rigidly jointed beams, wherein bending is the predominant deformation mode, are classic subjects of study in the field of structural mechanics. However, their topological dynamical properties have only recently been revealed. As the structural complexity of the frame increases along with the number of beam members arranged in the two-dimensional plane, the vibration modes also increase significantly in number, with frequency ranges of topological states and bulk states overlapped, leading to hybrid mode shapes. Therefore, concise theoretical results are necessary to guide the identification of topological modes in such planar continuum systems with complex spectra. In this work, within an infinitely long frequency spectrum, we obtain analytical expressions for the frequencies of higher-order topological corner states, edge states, and bulk states in kagome frames and square frames, as well as the criteria of existence of these topological states and patterns of their distribution in the spectrum. Additionally, we present the frequency expressions and the existence criterion for topological edge states in quasi-one-dimensional structures such as bridge-like frames, along with an approach to determine the existence of topological edge states based on bulk topological invariants. These theoretical results fully demonstrate that the grid-like frames, despite being a large class of continuum systems with complex spectra, have topological states (including higher-order topological states) that can be accurately characterized through concise analytical expressions. This work contributes to an excellent platform for the study of topological mechanics, and the accurate and concise theoretical results facilitate direct applications of topological grid-like frame structures in industry and engineering.

The paper deals with the passive control of resonant systems using nonlinear energy sink (NES). The objective is to highlight the benefits of adding nonlinear geometrical damping in addition to the cubic stiffness nonlinearity. The behaviour of the system is investigated theoretically by using the mixed harmonic balance multiple scales method. Based on the obtained slow flow equations, a design procedure that maximizes the dynamic range of the NES is presented. Singularity theory is used to express conditions for the birth of detached resonance cure independently of the forcing frequency. It is shown that the presence of a detached resonance curve is not necessarily detrimental to the performance of the NES. Moreover, the detached resonance curve can be completely suppressed by adding nonlinear damping. The results of the design procedure are then compared to numerical simulations.

In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation Equations. The scheme can be applied to a wide array of slab-like geometries, and for arbitrary material responses. We derive the scheme and investigated how it performs with respect to convergence and accuracy by applying it to the case of light scattering from a simple slab whose nonlinear material response is a sum a very fast electronic vibrational response, and a much slower molecular vibrational response.

Simple and formally exact solutions of nonlinear pendulum are derived for all three classes of motion: swinging, stopping, and spinning. Their unique simplicity should be useful in a theoretical development that requires trackable mathematical framework or in an introductory physics course that aims to discuss nonlinear pendulum. A simple formula for the complete elliptical integral of the first kind is also proposed. It reproduces the exact analytical forms both in the zero and asymptotic limits, while in the midrange maintains average error of 0.06% and maximum error of 0.17%. The accuracy should be sufficient for typical engineering applications.

Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular momentum-conserving Navier--Stokes equations offer a theoretical framework for describing such multiscale fluid dynamics by decomposing total angular momentum into bulk and intrinsic spin components. However, this framework still assumes locally non-solid rotational flows, a condition that remains empirically unverified. This study addresses such unvalidated assumptions intrinsic to the model and extends it within the framework of turbulence hierarchy theory. The theory suggests that under certain conditions, small-scale structures may transfer to larger scales through the rotational viscosity. To verify this, we conducted spectral analyses of freely decaying two-dimensional turbulence initialized with a vortex-concentrated distribution. The results indicate that rotational viscosity exhibits interscale transfer behavior, revealing a new mechanism by which order can propagate from small to large scales in Navier--Stokes turbulence.