Spectrally arbitrary ray patterns

AbstractAn n×n ray pattern A is said to be spectrally arbitrary if for every monic nth degree polynomial f(x) with coefficients from C, there is a matrix in the pattern class of A such that its characteristic polynomial is f(x). In this article the authors extend the nilpotent-Jacobi method for sign patterns to ray patterns, establishing a means to show that an irreducible ray pattern and all its superpatterns are spectrally arbitrary. They use this method to establish that a particular family of n×n irreducible ray patterns with exactly 3n nonzeros is spectrally arbitrary. They then show that every n×n irreducible, spectrally arbitrary ray pattern has at least 3n-1 nonzeros

Fibroblasts derived from long-lived insulin receptor substrate 1 null mice are not resistant to multiple forms of stress

Reduced signalling through the insulin/insulin-like growth factor-1 signalling (IIS) pathway is a highly conserved lifespan determinant in model organisms. The precise mechanism underlying the effects of the IIS on lifespan and health is currently unclear, although cellular stress resistance may be important. We have previously demonstrated that mice globally lacking insulin receptor substrate 1 (Irs1−/−) are long-lived and enjoy a greater period of their life free from age-related pathology compared with wild-type (WT) controls. In this study, we show that primary dermal fibroblasts and primary myoblasts derived from Irs1−/− mice are no more resistant to a range of oxidant and nonoxidant chemical stressors than cells derived from WT mice

Building Booster Separation Aerodynamic Databases for Artemis II

NASAs Artemis II mission will mark the return of humans to near-lunar space for the first time since Apollo. Shortly after launch on the Space Launch System (SLS), a critical phase of ascent occurs when 16 small rockets fire to push the boosters away from the core. Minimizing the risk of failure during separation requires the construction of multiple 13-dimensional databases, including perturbations in position, flight conditions, and engine thrust. The SLS Computational Fluid Dynamics team used NASAs FUN3D flow solver on the Pleiades and Electra supercomputers to run 5,780 simulations at nominal conditions and over 8,000 simulations with a core stage engine failure to generate the databases needed to verify the booster separation system for Artemis II

Noncirculant Toeplitz matrices all of whose powers are Toeplitz

summary:Let $a$, $b$ and $c$ be fixed complex numbers. Let $M_n(a,b,c)$ be the $n\times n$ Toeplitz matrix all of whose entries above the diagonal are $a$, all of whose entries below the diagonal are $b$, and all of whose entries on the diagonal are $c$. For $1\leq k\leq n$, each $k\times k$ principal minor of $M_n(a,b,c)$ has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of $M_n(a,b,c)$. We also show that all complex polynomials in $M_n(a,b,c)$ are Toeplitz matrices. In particular, the inverse of $M_n(a,b,c)$ is a Toeplitz matrix when it exists

Use of Evanescent Plane Waves for Low-Frequency Energy Transmission Across Material Interfaces

The transmission of sound across high-impedance difference interfaces, such as an air-water interface, is of significant interest for a number of applications. Sonic booms, for instance, may affect marine life, if incident on the ocean surface, or impact the integrity of existing structures, if incident on the ground surface. Reflection and refraction at the material interface, and the critical angle criteria, generally limit energy transmission into higher-impedance materials. However, in contrast with classical propagating waves, spatially decaying incident waves may transmit energy beyond the critical angle. The inclusion of a decaying component in the incident trace wavenumber yields a nonzero propagating component of the transmitted surface normal wavenumber, so energy propagates below the interface for all oblique incident angles. With the goal of investigating energy transmission using incident evanescent waves, a model for transmission across fluid-fluid and fluid-solid interfaces has been developed. Numerical results are shown for the air-water interface and for common air-solid interfaces. The effects of the incident wave parameters and interface material properties are also considered. For the air-solid interfaces, conditions can be found such that no reflected wave is generated, due to impedance matching among the incident and transmitted waves, which yields significant transmission increases over classical incident waves

The minimum upper bound on the first ambiguous power of an irreducible, nonpowerful ray or sign pattern

AbstractLet A be an n×n irreducible ray or sign pattern matrix. If A is a sign pattern, it is shown that either A is powerful or else Ak has an ambiguous entry for some k⩽n2-2n+2, and further, sign patterns based on the Wielandt graph show that this bound is the best possible. If A is a ray pattern, partial results for the same bound are given

The Construction of Acoustic Waveforms from Plane Wave Components to Enhance Energy Transmission into Solid Media

The transmission of acoustic energy into solid materials is of interest in a wide range of applications, including ultrasonic imaging and nondestructive testing. However, the large impedance mismatch at the solid interface generally limits the transmission of incident acoustic energy. With the goal of improving the fraction of the energy transmitted into solid materials, the use of various bounded spatial profiles, including commonly-employed forms, such as Gaussian distributions, as well as newly-constructed profiles, has been investigated. The spatial profile is specified as the pressure amplitude distribution of the incident wave. Bounded acoustic beams are represented here as sums of harmonic plane waves, and results obtained for the optimal parameters of incident plane wave components are used to inform the construction of bounded wave profiles. The effect of the form of the spatial profile is investigated, with the total energy carried by the incident wave held constant as the profile is varied, and the relationship with the plane wave components which superimpose to form the bounded wave is discussed. Direct comparisons are made for the efficiency of the energy transmission of different profiles. The results reveal that, by tuning the form of the profile, substantial improvements in the total energy transmission can be achieved as compared to Gaussian and square waveforms

On The Use Of Evanescent Plane Waves For Low-Frequency Energy Transmission Across Material Interfaces

The transmission of airborne sound into high-impedance media is of interest in several applications. For example, sonic booms in the atmosphere may impact marine life when incident on the ocean surface, or affect the integrity of existing structures when incident on the ground. Transmission across high impedance-difference interfaces is generally limited by reflection and refraction at the surface, and by the critical angle criterion. However, spatially decaying incident waves, i.e., inhomogeneous or evanescent plane waves, may transmit energy above the critical angle, unlike homogeneous plane waves. The introduction of a decaying component to the incident trace wavenumber creates a nonzero propagating component of the transmitted normal wavenumber, so energy can be transmitted across the interface. A model of evanescent plane waves and their transmission across fluid-fluid and fluid-solid interfaces is developed here. Results are presented for both air-water and air-solid interfaces. The effects of the incident wave parameters (including the frequency, decay rate, and incidence angle) and the interfacial properties are investigated. Conditions for which there is no reflection at the air-solid interface, due to impedance matching between the incident and transmitted waves, are also considered and are found to yield substantial transmission increases over homogeneous incident waves

Low-Frequency Energy Transmission across Material Interfaces using Incident Evanescent Waves

Transmission of airborne sound into higher-impedance materials is of interest in a range of applications. Sonic booms, for example, may adversely affect marine life, if incident on the ocean surface, or may produce underground pressure waves potentially capable of impacting the integrity of existing structures, if incident on the ground surface. Energy transmission into higher-impedance materials is generally limited by significant reflection and refraction at the material interface, and by the critical angle criteria. However, unlike classical waves, spatially-decaying, or evanescent, incident waves can transmit energy at angles beyond the critical angle. When a decaying component is introduced into the incident trace wavenumber, the interaction at the interface produces a nonzero propagating component of the transmitted surface normal wavenumber, so energy is transmitted across the interface for all oblique incident angles. With the aim of investigating energy transmission using incident evanescent waves, a model for pressure and intensity transmission across the fluid-fluid and fluid-solid interfaces has been developed. Numerical results are given for common interfaces that include the air-water interface and typical air-solid interfaces, where the effects of the incident wave parameters and interface material properties are considered as well. For the air-solid interfaces, conditions can be tuned such that no reflected wave is generated at the interface, owing to impedance matching between the incident and transmitted waves, which yields considerable transmission increases over classical incident waves

Stress and Energy Transmission by Inhomogeneous Plane Waves into Dissipative Media

The characteristics of sound transmission into real, or dissipative, media differ from those of transmission into lossless media. In particular, when a plane wave in a fluid is incident upon a real, dissipative elastic material, the transmitted waves are in general inhomogeneous, even when the incident wave is itself homogeneous and incident at a sub-critical angle; and more significantly, energy transmission occurs even above the critical angle. In addition, for any real incidence angle, the parameters of an incident inhomogeneous wave may be tuned so that there is no reflection from the surface of a viscoelastic solid. That phenomenon may be exploited in applications requiring energy transmission into solids. In this work, the transmission of incident inhomogeneous, as well as homogeneous, acoustic waves into solid materials is characterized; a hysteretic damping model is assumed. Numerical results are presented for the transmitted stress and energy distributions for typical solid materials, including polymer-based solids. The conditions for total transmission, i.e., no reflection at the interface, are explored, where the propagation angle, degree of inhomogeneity, and frequency of the incident wave are varied for a given material. These investigations show substantial transmission gains in the vicinity of the zero of the reflection coefficient, compared to homogeneous incident waves