Cutoff Plane Research Articles

On the acoustic wedge absorber design in underwater and its interior pressure computation in a chamber

This study presents a design of wedged shape absorber used in underwater in range of high frequency. The analysis of a set of periodical wedges, where each wedge is oriented 90 deg with other wedges. The set of periodical wedges is analyzed using finite element methods as a 3-D virtual impedance tube. The incident wave is on the normal direction of the tube. This 3-D model is able to simplify to a simple 2-D model and a two-point transfer function method is employed to compute reflection coefficient. The ation of frequencies higher than the cut-off plane wave frequency is addressed of that higher duct acoustic modes are excited by the wedge. These higher modes are recognized as stationary non-propagating waves, not contributing reflected waves away from the wedge. An impedance value associated with the reflection coefficient is identified based on plane wave condition. The impedance value is applied to surfaces of a closed space to computed interior pressures.

Energy-based universal failure criterion and strength-Poisson's ratio relationship for isotropic materials

The prediction of material failures has been one of the most important topics in engineering design since the onset of human civilization. To date, a plethora of failure criteria have been developed, particularly for homogeneous isotropic materials. However, many of them have limited usage for specific groups of materials, are obscure in their origin, or different from the actual phenomena at the microscopic and macroscopic scales. Therefore, based on the most fundamental concept of energy, this study aims to establish a universal failure criterion for homogeneous full-density isotropic materials. The developed failure criterion requires three independent load-bearing capabilities of the material, that is, tensile (T), compressive (C), and shear (S) strengths, as criterion calibrators for applicability to a wide range of materials, including those with extremely ductile to exceedingly brittle behaviors. Energy and polynomial invariants expansion approaches were used to formulate the universal failure criterion, and both yielded a perfect dual relationship. The criterion in the energy form revealed a new physical insight into the zero-energy bound or fracture criterion, which corresponds to an intrinsic cut-off plane in a failure envelope. Comparisons between the experimental data across a broad spectrum of material types and the proposed failure criterion were in excellent agreement in both the stress and energy spaces. The strength-Poisson's ratio relationship was also derived for the first time, demonstrating that only two strength properties are independent and that three important bounding conditions for isotropic materials exist: (1) S/C = 0 when T/C = 0; (2) when T/C = 1 and S/C = 1/3, Poisson's ratio v = 0.5; and (3) v = −1 when T/S and C/S approach zero.

Performance Features of Tooth Gearing in Gear Hydraulic Machines

Abstract The paper presented determines that the rotation velocities of gears and radii connecting the axes of rotation of the gears with the point of their teeth gearing are not equal with each other. It is explained by the relative slip of involute gear profiles during their rolling. This phenomenon will become a prerequisite for further development of creation of mathematical models in the context of theory of gear hydraulic machines. The models can explain a number of specific phenomena in the operation of gear hydraulic machines, such as pressure and input pulsations, dynamics of hydraulic oil in the cut-off plane, combined torque pulsations in gear hydraulic motors and others.

Delay time and persistent oscillations for a shifted quantum shutter

We derive an exact analytical solution to the time-dependent Schrödinger equation based on a resonant state expansion, to explore the time-evolution of cutoff plane waves scattered by finite range potentials, within a shifted quantum shutter model. The latter allows to control both, the position of the shutter and an hypothetical detector, which are initially separated by a distance ΔX. The dynamical advance-time (negative delay-time), ΔT, is explored for the particular case of a delta potential well, by measuring the difference of the first maxima of the time-diffraction pattern of the probability density, corresponding to the free and delta potential cases. We show that in general, ΔT exhibits a monotonic behaviour as a function of ΔX, and derive a simple formula for the timescale by using the symmetry and rescaling properties of the dynamical solution. We demonstrate that below a critical value of the shutter-detector separation, ΔX c , the monotonic behaviour of ΔT is hindered due to an oscillatory phenomena of the probability density, known as persistent oscillations, that drastically distorts the maxima used in the measurement process. These persistent oscillations are periodic Rabi-type oscillations that arise from an interplay between the incidence energy of the initial quantum wave and the bound state of the system, and their frequency play an important role in the dynamics of the delay time.

Time diffraction and Zitterbewegung of two-dimensional massless Dirac excitations

We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cut-off plane wave. We show that the probability density is governed by an interplay between {\it diffraction in time} and {\it Zitterbewegung} phenomena, typical of relativistic quantum shutter systems with nonzero mass. The {\it time-diffraction} appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshinsky in 1952 [Phys. Rev. \textbf{88}, 625] for Schr\"odinger free matter-waves. The {\it Zitterbewegung} manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, $k_y$, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the {\it Zitterbewegung} appears as a series of {\it quantum beats} in the probability density, with a beating frequency $2k_yv_F$, where $v_F$ is the Fermi velocity.

New criteria of radical surgery and long-term outcomes of hilar cholangiocarcinoma management

To develop new criteria of radical surgery for hilar cholangiocarcinoma (HCC). There were 165 HCC patients who underwent surgery in 1986-2016 at the Vishnevsky Institute of Surgery. TNM stage distribution: stage I - 4 (2.4%), II - 45 (27.3%) (29 of them are referred to the 1st period of work), IIIA - 23 (13.9%), IIIB - 41 (24.8%), IVA - 35 (21.2%), IVB - 17 (10.3%). 80 (48%) patients underwent hemihepatectomy, 17 (10%) - advanced hemihepatectomy, 16 (10%) - minor liver resection with common bile duct repair, 52 (32%) - common bile duct repair resection. Kaplan-Meier survival analysis was performed. Cox proportional hazard model was applied to access relationship between survival and prognostic factors. Log-rank test was used to compare both survival curves. R0-resection as followed by 5-year survival rate near 32%. Microvascular invasion was observed in 42.9%, lymphovascular invasion - in 88.2%, positive resection margin - in 59.2%, perineural invasion - in 83.3%, cells in surrounding fatty tissue were revealed in 92.3%. Resection may be considered radical (R0) if all variables are absent, 5-7 negative factors are followed by conditionally radical procedure (R+number of positive factors). Long-term outcomes and significance of new criteria were accessed (p=0.004). New criteria of radical procedure are presented. The last reflects the concept of dependence of 'pure' surgical edge from not only presence or absence of tumor cells in cut-off plane but also from important morphological features of tumor.

Local Field Enhancement Characteristics in a Tapered Metal-Coated Optical Fiber Probe for Nanolithography

In the nanolithography, some exciting developments have been motivated by the tapered metal-coated optical fiber probe irradiated by ultra-fast pulse laser. To explore the related mechanism, the local field is studied using the finite element method in this paper. The simulation results show the reflection at the cut-off plane, edge enhancement effect and surface plasmon resonance become the major factors affecting the near-field. In addition, Based on the near-field distribution and characteristics, the new promising scheme is proposed for near-field nanolithography.

Quantitative colour schlieren development

This work evaluates the potential for producing quantitative data of the density field using a two-dimensional colour schlieren system within the test section of a shock tube. Density gradient components, magnitude and direction, form the basis of the quantitative evaluation. These are encoded onto an imaging plane by means of a colour-coded source mask placed along the optical axis of the schlieren system. Direction is indicated by the relative ratios of the three primary colours: red, green and blue (RGB). Magnitude is indicated by the relative intensities of the RGB values. Sensitivity of the system is adjusted by an iris diaphragm placed in the cutoff plane. The method described is applied to the focusing of a shock wave in a parabolic cavity. The experimental results of the schlieren technique are compared to computational simulations with synthetic two-dimensional colour and magnitude coding applied to the results. The source masks designed and used proved to require a greater intensity light source and thus the design of an LED light source was developed. The CFD solutions were converted into an image format directly comparable to the photographic images obtained. Image processing techniques have been employed to deconstruct photographs to allow for quantitative comparisons with a calibration lens. Density gradient direction has been conclusive; however, density gradient magnitude is not yet accurately determined due to light source constraints.

High Pressure Phase of LiAlO2: A First Principles Study

The homogeneous structural phase transition between the natural and high-pressure forms of LiAlO2, i.e., γ-LAO and δ-LAO, were investigated by using first principles calculations. For the exchange-correlation functional, the generalized-gradient approximation (GGA) was used in comparison with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. The projector augmented wave (PAW) method was used to allow a relatively low-energy cutoff plane wave expansion outside the core region while maintaining the complicated description of the wave function near the core region. Our calculations showed that both HSE and GGA calculations provided comparable energetic properties. For the electronic properties, the HSE calculations do not suffer from band gaps underestimations but require much more computation demand. The HSE calculations showed that, under hydrostatic pressure, the natural phase γ-LAO is in energetic equilibrium with the high-pressure phase δ-LAO at 2.3 GPa. The calculated equilibrium phase pressures are in a reasonable agreement with the experimental transformation pressure (2 GPa) obtained by an anvil cell technique [J. Solid State Chem. 188, 6 (2008)]. However, the transformation pressure obtained by a shock recovery technique [J. Solid State Chem. 177, 5 (2004)] is much higher (9 GPa). The large difference in the transformation pressure obtained by different experimental techniques could be attributed to the energetic transformation barrier between the two phases. Based on HSE calculations, the enthalpy barrier for the homogeneous transformation between the two phases at the phase equilibrium pressures is 1.8 eV. The band structures and the partial density of states of both γ-LAO and δ-LAO at the ambient pressure are also presented.

Exact analytical description of quantum transients in one-dimensional scattering

An exact analytical solution of the transient behaviour in one-dimensional time-dependent scattering for initial states with a sharp wavefront is derived. This work extends to the full line previous work on the subject for the transmitted and internal interaction regions. We exemplify our findings by considering single and quadruple barrier systems using cutoff plane wave initial states.

Calculating of the Temperature Distribution of Primary Shear Zone in Orthogonal High Speed Cutting Based on the Non-Uniform Volume Moving Heat Source

A method was presented for calculating the temperature distribution of primary shear zone in orthogonal high speed cutting based on the non-uniform volume moving heat source. The temperature distribution of primary shear zone in orthogonal high speed cutting was calculated by the dynamic plastic constitutive relationship and the distribution of strain and strain rate of primary shear zone. The results show that the temperature distribution of primary shear zone is uneven, from the original plane to the cutoff plane, the cutting temperature increases continuously. In the middle of primary shear zone, the change of cutting temperature is larger, at the position near to original plant and cutoff plane, the change of cutting temperature is smaller. The cutting temperature increases with the increase of cutting speed and cutting depth, but decreases with the increase of rake angle. The comparison with existing method shows that the method presented in this paper is not only available, but also simple, convenient and more accord with the fact of orthogonal high speed cutting.

Twin Symmetric E-plane Slab Loaded Waveguide Structure for Point Beam Acceleration

Renewed interest regarding the exploitation of dielectric loaded waveguides in high gradient accelerator structures requires a closed form field formulation as cut-off frequencies and optimisation are problematic for numerical methods. In this paper we will present efficient closed form solution for generic slab loaded waveguide boundary value problems. This solution offers flexibility in a sense that it can be further exploited to derive a Green’s function linking transverse field expressions for planar structures. The developed solution is demonstrated for a twin slab E-plane slab loaded structure coupled to a Point source emitter assembly. The emission characteristics of the point source emitter assembly are optimized to generate a high intensity and focused beam to be fed to this E-plane slab loaded waveguide structure for beam acceleration. The field analysis, mode nomenclature, modal hierarchy, modal bandwidth, cut-off plane, impedance plane and dispersion relations for this accelerating structure is included for sake the of completeness.

High Emittance Electron Beam Source Coupled to Slab Loaded Accelerating Structure

High power line source emitter assembly was coupled to a twin symmetric H-plane slab loaded accelerating structure for beam acceleration. Closed form field analysis of the accelerating structure that includes guideline information regarding modal hierarchy, mode nomenclature, propagation plane, cut-off plane and dispersion relations is presented. Furthermore it was confirmed that by using symmetrically loaded dielectric accelerating structures with one rotated through 90° results in exerting a uniform acceleration impact on a travelling beam passing through the structure.

Tunnelling of plane waves through a square barrier

The time evolution of plane waves in the presence of a one-dimensional square quantum barrier is considered. Comparison is made between the cases of an infinite and a cut-off (shutter) initial plane wave. The difference is relevant when the results are applied to the analysis of the tunnelling regime. This work is focused on the analytical calculation of the time-evolved solution and highlights the contribution of the resonant (Gamow) states.

Quantum-shutter approach to tunneling time scales with wave packets

The quantum-shutter approach to tunneling time scales [G. Garc\'{\i}a-Calder\'on and A. Rubio, Phys. Rev. A 55, 3361 (1997)], which uses a cutoff plane wave as the initial condition, is extended to consider certain type of wave packet initial conditions. An analytical expression for the time-evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to the width of the packet when the transmission process occurs in the tunneling regime.

Cut-off frequencies of magnetoplasma slab-loaded waveguides using an iterative finite element method

An iterative finite element method is introduced to calculate the cut-off plane of slab-loaded magnetoplasma waveguides. As the slab filling ratio increases, both the modal cut-off numbers and the singlemode bandwidth reduce. Overmoding is predicted if the bias field is chosen such that the extraordinary wave resonance falls within the waveguide frequency range. Split cut-off numbers are indicative of increased nonreciprocity in the propagation constants. From an investigation of the propagation constants, specific structures and bias conditions are recommended for the development of isolators and differential phase shifters in the frequency range 190–460 GHz.

Exact relativistic time evolution for a step potential barrier

We derive an exact analytic solution to a Klein-Gordon equation for a step potential barrier with cutoff plane wave initial conditions, in order to explore wave evolution in a classical forbidden region. We find that the relativistic solution rapidly evanesces within a depth $2x_p$ inside the potential, where $x_p$ is the penetration length of the stationary solution. Beyond the characteristic distance $2x_p$, a Sommerfeld-type precursor travels along the potential at the speed of light, $c$. However, no spatial propagation of a main wavefront along the structure is observed. We also find a non-causal time evolution of the wavefront peak. The effect is only an apparent violation of Einstein causality.

Dynamical analysis of the buildup process near resonance

The time evolution of the buildup process inside a double-barrier system for off-resonance incidence energies is studied by considering the analytic solution of the time-dependent Schrödinger equation with cutoff plane wave initial conditions. We show that the buildup process exhibits invariances under arbitrary changes on the system parameters, which can be successfully described by a simple and easy-to-use one-level formula. We find that the buildup of the off-resonant probability density is characterized by an oscillatory pattern modulated by the resonant case which governs the duration of the transient regime. This is evidence that off-resonant and resonant tunneling are two correlated processes, whose transient regime is characterized by the same transient time constant of two lifetimes.

Analysis of partial-height ferrite-slab differential phase-shift sections

Rectangular waveguide loaded with transversely magnetized ferrite slabs is a classic arrangement used in the construction of high-power differential phase-shift circulators. The characterization of this structure is extended in this paper by using a combined magnetostatic/microwave finite-element method to evaluate propagation characteristics in terms of material parameters, frequency, and bias field. Magnetic flux density was found to vary by typically 20% across a partial-height ferrite slab. Experimental phase-shift data agreed to within 5% of numerical calculations for a 9.25-GHz device. Supplementary design data are presented for the first higher order mode in the cutoff plane, the effect of material properties on phase shift, and to compare below and above resonance operation.

Dynamical description of the buildup process in resonant tunneling: Evidence of exponential and nonexponential contributions

The buildup process of the probability density inside the quantum well of a double-barrier resonant structure is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with the initial condition of a cutoff plane wave. For one level systems at resonance condition we show that the buildup of the probability density obeys a simple charging up law, $| \Psi (\tau) / \phi | =1-e^{-\tau /\tau_0},$ where $\phi$ is the stationary wave function and the transient time constant $\tau_0$ is exactly two lifetimes. We illustrate that the above formula holds both for symmetrical and asymmetrical potential profiles with typical parameters, and even for incidence at different resonance energies. Theoretical evidence of a crossover to non-exponential buildup is also discussed.