A Sharp Lieb-Thirring Inequality for Functional Difference Operators

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators is a resonance state.

Self-Alignment/Navigation Performance Analysis in the Accelerometer Resonance State Generated by Dither Motion of Ring Laser Gyroscope in Laser Inertial Navigation System

In this paper, we theoretically analyzed the self-alignment/navigation performance in the accelerometer resonance state generated by dither motion of ring laser gyroscope in LINS and verified it through simulation. As a result of analysis, it is confirmed that the amplitude of the accelerometer measurement amplified in the accelerometer resonance state is decreased in the process of sampling per the navigation calculation period and that frequency is changed by the aliasing effect too. It was also analysed that the attitude error in self-alignment is determined by the amplitude/frequency of the accelerometer measurement, the gain of the self-alignment loop, and the velocity and position error in the navigation is determined by the amplitude/frequency/phase error of the accelerometer measurement. This analysis and simulation results show that the self-alignment and navigation performance is not be degraded only when the amplification factor of the accelerometer measurement in the accelerometer resonance state is 3 or less

The explanation of some exotic states in the $$cs{\bar{c}}{\bar{s}}$$ tetraquark system

Inspired by the recent observation of $$\chi _{c0}(3930)$$ χ c 0 ( 3930 ) , X(4685) and X(4630) by the LHCb Collaboration and some exotic resonances such as X(4350), X(4500), etc. by several experiment collaborations, the $$cs{\bar{c}}{\bar{s}}$$ c s c ¯ s ¯ tetraquark systems with $$J^{PC}=0^{++}$$ J PC = 0 + + , $$1^{++}$$ 1 + + , $$1^{+-}$$ 1 + - and $$2^{++}$$ 2 + + are systematically investigated in the framework of the quark delocalization color screening model(QDCSM). Two structures, the meson–meson and diquark–antidiquark structures, as well as the channel-coupling of all channels of these two configurations are considered in this work. The numerical results indicate that the molecular bound state $$D^{-}_{s}D_{s}^{+}$$ D s - D s + with $$J^{PC}=00^{++}$$ J PC = 00 + + can be supposed to explain the $$\chi _{c0}(3930)$$ χ c 0 ( 3930 ) . Besides, by using the stabilization method, several resonant states are obtained. Among these states, X(4350), X(4500) and X(4700) can be explained as the compact tetraquark states with $$J^{PC}=00^{++}$$ J PC = 00 + + , and the X(4274) is possible to be a candidate of the compact tetraquark state with $$J^{PC}=1^{++}$$ J PC = 1 + + . Apart from that, the $$J^{PC}=0^{++}$$ J PC = 0 + + resonance state with energy range 4028–4033 MeV, the two $$J^{PC}=2^{++}$$ J PC = 2 + + resonance states with energy range of 4394–4448 MeV and 4526–4536 MeV are possible to be new exotic states, which are indeed worthy of attention. More experimental tests are expected to check the existence of all these possible resonance states.

Non-contact Crack Detection in Metals Using a Cutoff-Cavity Probe

This paper presents a non-contact method for the detection of surface cracks in metal materials through a forced-resonance microwave method (FRMM) using a cutoff cavity-backed narrow slot as a crack detection probe without using a vector network analyzer (VNA) at microwave frequencies. The FRMM uses the deviations in the ammeter or voltmeter readings of the forcefully obtained resonance of a cutoff-cavity probe for a metal material with or without cracks. The cutoff cavity-backed narrow slot on metal with no cracks produces a series resonance (maximum current) or a parallel resonance through an external control element located on a post inside the cutoff cavity. Cracks were detected by a change in this forced-resonance state (maximum current) when the cutoff-cavity probe was scanned over a crack. The characteristic crack signal was derived from the resonance current deviation on the ammeter located on a post inside the cavity probe. Galerkin’s method of moments was used to obtain a forced-resonance state from which the crack signal of the FRMM was calculated. The experimental measurements for non-contact (remote or lift-off) crack detection are also presented.

A Defect Detection Method for the Surface of Metal Materials Based on an Adaptive Ultrasound Pulse Excitation Device and Infrared Thermal Imaging Technology

Ultrasonic excitation has been widely used in the detection of microcracks on metal surfaces, but there are problems such as poor excitation effect of ultrasonic pulse, long time to reach the best excitation, and difficult to find microcracks. In this paper, an adaptive ultrasonic pulse excitation device and infrared thermal imaging technology have been combined, as well as their control method, to solve the problem. The adaptive ultrasonic pulse excitation device adds intelligent modules to realize automatic adjustment of detection parameters, which can quickly obtain reliable excitation; the multidegree-of-freedom base realizes the three-dimensional direction change of the ultrasonic gun to adapt to different excitation occasions. When the appropriate ultrasonic excitation makes microcracks in the resonance state, the microcracks can be frictionated, which produce heat rise with the temperature. Then, the microcrack defect can be detected by the infrared thermal instrument through the different surface temperatures with imaging recognition method. Our detection experiments of the titanium alloy plates and the aluminum alloy profiles of marine engineering show that the method can get reliable detection parameters in a short time and measure the crack length effectively. It can be used in many aspects such as crack detection in mechanical structures or complex equipment operating conditions and industrial production processes.

Physiological Resonance in Empathic Stress: Insights from Nonlinear Dynamics of Heart Rate Variability

Because most humans live and work in populated environments, researchers recently took into account that people may not only experience first-hand stress, but also second-hand stress related to the ability to empathically share another person’s stress response. Recently, researchers have begun to more closely examine the existence of such empathic stress and highlighted the human propensity to physiologically resonate with the stress responses of others. As in case of first-hand stress, empathic stress could be deleterious for health if people experience exacerbated activation of hypothalamic–pituitary–adrenal and autonomic nervous systems. Thus, exploring empathic stress in an observer watching someone else experiencing stress is critical to gain a better understanding of physiological resonance and conduct strategies for health prevention. In the current study, we investigated the influence of empathic stress responses on heart rate variability (HRV) with a specific focus on nonlinear dynamics. Classic and nonlinear markers of HRV time series were computed in both targets and observers during a modified Trier social stress test (TSST). We capitalized on multiscale entropy, a reliable marker of complexity for depicting neurovisceral interactions (brain-to-heart and heart-to-brain) and their role in physiological resonance. State anxiety and affect were evaluated as well. While classic markers of HRV were not impacted by empathic stress, we showed that the complexity marker reflected the existence of empathic stress in observers. More specifically, a linear model highlighted a physiological resonance phenomenon. We conclude on the relevance of entropy in HRV dynamics, as a marker of complexity in neurovisceral interactions reflecting physiological resonance in empathic stress.

A synergistic approach to achieving the high thermoelectric performance of La-doped SnTe using resonance state and partial band convergence

SnTe is an alternate variant of PbTe possessing an analogous valence band(VB) pattern. However, SnTe exhibits low thermoelectric(TE) efficiency due to Sn defects triggering very high carrier concentration (n). Thus,...

Longitudinal vibrations of a cylindrical bar from the action of harmonic forces

The longitudinal vibration of a cylindrical rod has been studied in an elastic medium from the action of axial harmonic forces in a state of compression tension. The consideration took into account the damping of vibration of the rod according to the theory of E.S. Sorokin. Taking into account, internal friction made it possible to approach the real state of the rod as a source of wave radiation. The amplitude-frequency characteristic of the structure is built, taking into account changes in the parameters of the environment and the rod. The possibilities of the emergence of the resonance state of the rod are established. At the same time, cases were considered with and without inelastic properties of the rod material. The analysis of the influence of the properties of the environment and the rod on the amplitude of the displacement of the latter is carried out.

Full-heavy tetraquarks in constituent quark models

The full-heavy tetraquarks $$bb{\bar{b}}{\bar{b}}$$ b b b ¯ b ¯ and $$cc{\bar{c}}{\bar{c}}$$ c c c ¯ c ¯ are systematically investigated within the chiral quark model and the quark delocalization color screening model. Two structures, meson–meson and diquark–antidiquark, are considered. For the full-beauty $$bb{\bar{b}}{\bar{b}}$$ b b b ¯ b ¯ systems, there is no any bound state or resonance state in two structures in the chiral quark model, while the wide resonances with masses around $$19.1-19.4$$ 19.1 - 19.4 GeV and the quantum numbers $$J^{P}=0^{+}$$ J P = 0 + , $$1^{+}$$ 1 + , and $$2^{+}$$ 2 + are possible in the quark delocalization color screening model. For the full-charm $$cc{\bar{c}}{\bar{c}}$$ c c c ¯ c ¯ systems, the results are qualitative consistent in two quark models. No bound state can be found in the meson–meson configuration, while in the diquark–antidiquark configuration there may exist the resonance states, with masses range between 6.2 to 7.4 GeV, and the quantum numbers $$J^{P}=0^{+}$$ J P = 0 + , $$1^{+}$$ 1 + , and $$2^{+}$$ 2 + . And the separation between the diquark and the antidiquark indicates that these states may be the compact resonance states. The reported state X(6900) is possible to be explained as a compact resonance state with $$IJ^{P}=00^{+}$$ I J P = 00 + in present calculation. All these full-charm resonance states are worth searching in the experiments further.