Real Amplitude Research Articles

Hierarchical multiple-image encryption based on the cascaded interference structure and vector stochastic decomposition algorithm

A new kind of hierarchical multiple-image encryption method based on the cascaded interference structure and vector stochastic decomposition algorithm is proposed. In this method, by using the nonequal modulus decomposition and vector stochastic decomposition algorithm, the Kth-level secret image modulated by a random phase distribution is analytically encoded into a Kth-level phase-only mask (POM) key and the (K−1)th-level complex amplitude field whose real amplitude is the (K−1)th-level secret image. Then, served as the input condition, the generated complex amplitude field is further encoded into a (K−1)th-level POM key and the (K−2)th-level complex amplitude, and so on, until the 1st-level complex amplitude field is decomposed into two POMs: one is the 1st-level key, and the other is the ciphertext. When decryption occurs, only when the high-level users simultaneously obtain all the phase keys, the correct sequential orders of phase keys, and the correct geometrical parameters, all the secret images are retrieved successfully. Both theoretical analysis and numerical simulations verify the feasibility of this method.

Does Hofstetter's equation predict the real amplitude of accommodation in children?

PurposeThe aim was to determine the distribution and associated factors of accommodative amplitude (AA) in six‐ to 12‐year‐old children and compare the results with those calculated using Hofstetter's formula.MethodsIn a cross‐sectional study in 2015, random sampling was done from urban and rural populations of Shahroud, northern Iran. Participating schoolchildren were examined for manifest, cycloplegic and subjective refraction, as well as uncorrected vision and visual acuity. The AA was measured with Donders’ push‐up method using a ruler. The near point of convergence (NPC) was also measured.ResultsOf the 6,624 selected children, 5,620 participated in the study and after applying the exclusion criteria, the final analyses were done on data from 5,444 schoolchildren. The mean age of the final sample was 9.24 ± 1.71 years (from six to 12 years) and 53.6 per cent (n = 2,919) were boys. Mean measured AA was 14.44 D (95 per cent confidence interval [CI]: 14.33–14.55). In all age groups, the mean measured AA was less than the predicted mean value calculated with the Hofstetter's equation. Mean measured AA was 14.44 D (95 per cent CI: 14.28–14.59) and 14.45 D (95 per cent CI: 14.29–14.6) in boys and girls, respectively (p = 0.926). AA significantly declined with age (coefficient: −0.18, 95 per cent CI: −0.23 to −0.12, p < 0.001). Mean AA in emmetropic, myopic and hyperopic children was 14.31 D, 17.30 D and 14.87 D, respectively. Older age (coefficient = −0.18), living in rural areas (coefficient = −0.48) and NPC (coefficient = 0.47) inversely related with AA and higher AA was associated with a shift of the spherical equivalent refraction toward myopia (coefficient = −0.41).ConclusionThe differences among groups with different types of refractive error and high AA in children with myopia are important findings of this study. The results of the present study suggest that Hofstetter's formula provides inaccurate AA estimates in children and thus, the interpretation of this index requires further population‐based studies in different racial and ethnic groups.

A New Approach to the Fatigue Life Prediction for Notched Components Under Multiaxial Cyclic Loading

A new fatigue life prediction approach for notched components is proposed under multiaxial cycle loading. Firstly, the pseudo equivalent strain-real equivalent stress relationship is determined by utilizing the Neuber’s rule and the material stress-strain relation under proportional loading. Secondly, the pseudo elastic strain histories at the notch need to be solved for the investigated notched components under multiaxial cyclic loading. Thirdly, for the pseudo elastic strain histories, it is proposed that the Shang–Wang multiaxial fatigue damage parameter can be used to substitute the equivalent strain under proportional loading to take account of the additional hardening due to the non-proportionality of external loadings. Meanwhile, the real equivalent stress amplitude at the notch can be solved. Fourthly, based on the real equivalent stress amplitude at the notch integrated with the Neuber’s rule, the real equivalent strain amplitude can be determined. Finally, the real equivalent strain amplitude is utilized to predict the fatigue crack initiation lifetime of notched components. The proposed method is verified by the experimental data of SAE 1045 notched shaft specimens under proportional and non-proportional cyclic loading. The results showed the prediction errors are mostly within a factor of 2.

The reliability of microseismic moment-tensor solutions: Surface versus borehole monitoring

Source mechanisms of microseismic events, resolved as moment-tensor solutions, usually are obtained using either surface monitoring arrays, which appear to obtain mechanisms with high shear components, or borehole arrays, which tend to constrain more variable mechanisms with higher tensile components; however, the corresponding reliability of the solutions remains unclear. Synthetic tests are therefore conducted to compare the reliability of moment-tensor solutions from surface and two- and three-well borehole arrays based purely on geometry. Moment-tensor inversion is carried out for synthetically generated amplitudes with added random noise, and the bias and variance in the solutions are calculated. For the surface array, all inversions are able to constrain reliable results (with negligible bias and low variance), whereas borehole geometries with two wells produce reliable results only when including P- and S-wave amplitudes recorded on three components in the inversion (as is usual). Surface array inversion results show less bias and variance in the results compared with borehole results, and the three-borehole geometry shows significantly lower biases and estimation variances than the two-borehole geometry, most likely due to a greater sampling of the focal sphere. These results may explain in part why downhole moment-tensor inversion studies tend to resolve more variable mechanisms than surface arrays. Nonetheless, as well as geometry, other influences (e.g., signal-to-noise ratio) will influence the reliability of the solutions in real settings and different amplitude strengths of pure shear or tensile mechanisms combined with different path lengths, and thus energy dissipation for borehole or surface acquisitions also may play a role. Nonetheless, tests such as those in this study are useful to help design appropriate monitoring geometries and/or understand possible sources of bias and uncertainty in moment-tensor interpretations.

Estimates of oscillatory integrals with stationary phase and singular amplitude: Applications to propagation features for dispersive equations

AbstractIn this paper, we study time‐asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of phases which may have a stationary point of real order and amplitudes allowed to have an integrable singular point. The resulting estimates provide optimal decay rates which show explicitly the influence of these two particular points. Then we apply these abstract results to solution formulas of a class of dispersive equations on the line defined by Fourier multipliers. Under the hypothesis that the Fourier transform of the initial data has a compact support or an integrable singular point, we derive uniform estimates of the solutions in space‐time cones, describing their motions when the time tends to infinity. The method permits also to show that symbols having a restricted growth at infinity may influence the dispersion of the solutions: we prove the existence of a cone, depending only on the symbol, in which the solution is time‐asymptotically localized. This corresponds to an asymptotic version of the notion of causality for initial data without compact support.

Dimensional crossover of the charge density wave transition in thin exfoliated VSe2

Isolating single unit-cell thin layers from the bulk matrix of layered compounds offers tremendous opportunities to design novel functional electronic materials. However, a comprehensive thickness dependence study is paramount to harness the electronic properties of such atomic foils and their stacking into synthetic heterostructures. Here we show that a dimensional crossover and quantum confinement with reducing thickness result in a striking non-monotonic evolution of the charge density wave transition temperature in VSe2. Our conclusion is drawn from a direct derivation of the local order parameter and transition temperature from the real space charge modulation amplitude imaged by scanning tunnelling microscopy. This study lifts the disagreement of previous independent transport measurements. We find that thickness can be a non-trivial tuning parameter and demonstrate the importance of considering a finite thickness range to accurately characterize its influence.

Lensless complex amplitude image retrieval through a visually opaque scattering medium.

We propose and experimentally demonstrate lensless complex amplitude image retrieval through a visually opaque scattering medium from spatially fluctuating fields using intensity measurement and a phase-retrieval algorithm. The complex amplitude information of the hidden object is encoded in the form of a real and nonnegative amplitude function represented as an interference pattern. A single charge coupled device (CCD) image of the scattered light collected through a visually opaque optical diffuser contains enough information to digitally regenerate the interference pattern. Furthermore, a lensless configuration is implemented which eliminates any possible aberration effects associated with optical components, and this further has promising applications where the use of imaging optics is not feasible. Experimental results for the recovery of complex fields corresponding to optical vortices of two different topological charges are presented.

Horizontal-vertical Spectral Ratio Method in Microtremor to Estimate Engineering Bedrock Thickness at Sedati Mud Volcano

Based on field study, Sedati Mud Volcano located in a line with Gunung Anyar Mud Volcano and occurred by increased pressure in the compression area and rapid loss of gas. The combination of both fast-growing constructions of infrastructures and the presence of the mud volcanoes brings new challenges in Sidoarjo city. The purpose of this scientific research is to determine the sedimentary thickness around Sedati mud volcano. Only a few data show real amplitude spectrum, which represent high contrast impedance. At some point, there are several peaks indicating the presence of contrast impedance between layers. Based on 20 processed data, Sedati Mud Volcano has a 30 – 70m engineering bedrock thickness and natural frequency between 0.5 until 14.4 Hz. The enhancement of natural frequency tends to occur along decrement of layer thickness in the upper basement layer. The result shows the natural frequency parameter and its amplification is slightly variated around Sedati Mud Volcano, as caused by sedimentary lateral depth variation and/or the presence of variation on existing rock. Further analysis indicates a fault inside the area of mud volcano as possible reason behind the occurring mudflow.

Real topological string amplitudes

We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude {mathcal{G}}_{chi } , at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to mathcal{N}=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g′ = −χ + 1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude {mathrm{mathcal{F}}}_g .

Impact of inelastic processes on the chaotic dynamics of a Bose-Einstein condensate trapped into a moving optical lattice

We investigate the dynamics of a Bose-Einstein condensate with attractive two-body and repulsive three-body interactions between atoms trapped into a moving optical lattice and subjected to some inelastic processes (a linear atomic feeding and two dissipative terms related to dipolar relaxation and three-body recombination). We are interested in finding out how the nonconservative terms mentioned above act on the dynamical behaviour of the condensate, and how they can be used in the control of possible chaotic dynamics. Seeking the wave function of condensate on the form of Bloch waves, we notice that the real amplitude of the condensate is governed by an integro-differential equation. As theoretical tool of prediction of homoclinic and heteroclinic chaos, we use the Melnikov method, which provides two Melnikov functions related to homoclinic and heteroclinic bifurcations. Applying the Melnikov criterion, some regions of instability are plotted in the parameter space and reveal complex dynamics (solitonic stable solutions, weak and strong instabilities leading to collapse, growth-collapse cycles and finally to chaotic oscillations). It comes from some parameter space that coupling the optical intensity and parameters related to atomic feeding and atomic losses (dissipations) as control parameters can help to reduce or annihilate chaotic behaviours of the condensate. Moreover, the theoretical study reveals that there is a certain ratio between the atomic feeding parameter and the parameters related to the dissipation for the occurrence of chaotic oscillations in the dynamics of condensate. The theoretical predictions are verified by numerical simulations (Poincare sections), and there is a certain reliability of our analytical treatment.

Higgs bosons at high pT

We present a calculation of $H+j$ at NLO including the effect of a finite top-mass. Where possible we include the complete dependence on $m_t$. This includes the leading order amplitude, the infrared poles of the two-loop amplitude and the real radiation amplitude. The remaining finite piece of the virtual correction is considered in an asymptotic expansion in $m_t$, which is accurate to $m_t^{-4}$. By successively including more $m_t$-exact pieces, the dependence on the asymptotic series diminishes and we find convergent behavior for $p_T^H>m_t$ for the first time. Our results justify rescaling by the $m_t$-exact LO cross section to model top-mass effects in EFT results up to $p_T$ of 250 to 300 GeV. We show that the error made by using the LO rescaling becomes comparable to the NNLO scale uncertainty for such large energies. We implement our results into the Monte Carlo code MCFM.

The coupled cluster method and entanglement in three fermion systems

The Coupled Cluster (CC) and full CI expansions are studied for three fermions with six and seven modes. Surprisingly the CC expansion is tailor made to characterize the usual stochastic local operations and classical communication (SLOCC) entanglement classes. It means that the notion of a SLOCC transformation shows up quite naturally as a one relating the CC and CI expansions, and going from the CI expansion to the CC one is equivalent to obtaining a form for the state where the structure of the entanglement classes is transparent. In this picture, entanglement is characterized by the parameters of the cluster operators describing transitions from occupied states to singles, doubles, and triples of non-occupied ones. Using the CC parametrization of states in the seven-mode case, we give a simple formula for the unique SLOCC invariant J. Then we consider a perturbation problem featuring a state from the unique SLOCC class characterized by J≠0. For this state with entanglement generated by doubles, we investigate the phenomenon of changing the entanglement type due to the perturbing effect of triples. We show that there are states with real amplitudes such that their entanglement encoded into configurations of clusters of doubles is protected from errors generated by triples. Finally we put forward a proposal to use the parameters of the cluster operator describing transitions to doubles for entanglement characterization. Compared to the usual SLOCC classes, this provides a coarse grained approach to fermionic entanglement.

Detection of Natural Frequencies Using IR Camera

The paper deals with estimation of natural frequencies using IR camera. The object was excited using random noise and infrared camera registered radiation of the object. The measured data was processed by lock-in thermography, when the lock-in frequency was changed in analyzed frequency's region. The output of lock-in process was analyzed. Natural frequencies were detected on the changes of real parts and amplitudes of output infragrams. The significant symptom is detection of patterns in infragrams.

Ultrasound-Based Liver Fat Quantification

Hepatic steatosis is very common and has a broad disease spectrum according to etiology and severity (1). Clinically, the occurrence of non-alcoholic fatty liver disease (NAFLD), the most common type of hepatic steatosis, is strongly correlated with metabolic disease, including type 2 diabetes mellitus and atherosclerotic cardiovascular disease (2). Simple hepatic steatosis can evolve into a more severe stage such as steatohepatitis or cirrhosis. Furthermore, hepatic steatosis is an important risk factor for postoperative complications after major liver resection and living donor liver transplantation (3-7). Hepatic steatosis of ≥ 10% is known to be critical in patients undergoing living donor liver transplantation due to the risks of initial graft dysfunction, poor graft survival and other complications (8-10). The widespread use of liver biopsy, a reference standard for quantification of liver fat, as a screening tool and for monitoring treatment response is limited mainly because of invasiveness. Therefore, noninvasive imaging methods that can quantitatively measure liver fat have been actively investigated. Among them, 1H-magnetic resonance spectroscopy (1H-MRS) has gained ground in the past decade as an alternative noninvasive reference standard for evaluating liver fat content because of its high diagnostic accuracy and reproducibility (1, 2, 11-15). However, MRS is expensive to perform as a screening and monitoring tool for hepatic steatosis. Ultrasound (US) is an imaging modality that is simple and inexpensive to perform and is safe for the patient. To overcome the intrinsic subjectivity associated with the use of US in grading fatty liver, several methods using US image data have been proposed for the quantification of hepatic steatosis (14-20). However, these methods are not widely used in clinical practice, mainly because of their complexity or their use of non-commercial software. Recently, ultrasound-based liver fat quantification tools such as controlled attenuation parameter (CAP) or Acoustic structure quantification (ASQ) have been introduced into clinical practice. CAP measures the degree of ultrasound attenuation due to hepatic fat, which is implemented on Fibroscan. CAP values have been reported to have an excellent diagnostic accuracy for steatosis detection, which an adjusted AUROC of 0.914. However, technical failure rate was reported to be 7.7 % of cases (21). ASQ method is based on statistical analysis of the difference between theoretical and real echo amplitude distribution (22, 23). In a population of living donors for liver transplantation, ASQ provides an excellent quantitative tool for hepatic steatosis, and there is a strong linear correlation (r= - 0.87, P< 0.0001) between focal disturbance ratio measured using ASQ and hepatic fat fraction measured using MR spectroscopy (24).

Adiabatic optimization versus diffusion Monte Carlo methods

Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here, we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k-SAT at k=2,3,4.

Four-photon nonlinear coherent states

We have introduced the notion of ‘four-photon nonlinear coherent states’ (FPNCSs) as right eigenstates of the fourth power of the generalized annihilation operator . It has been shown that there are four possible sets of such states which all can be expressed as the deformed Schrödinger cat type states derived from the superposition of four nonlinear coherent states (NCSs) which are out of phase. The nonclassical properties of the FPNCSs would be studied for two well-known quantum systems, a Kerr-like medium and a trapped laser-driven ion far from the Lamb-Dicke regime. We have found that the depth or the domain of the nonclassical features of FPNCSs in terms of sub-Poissonian photon statistics, higher order squeezing as well as amplitude-squared squeezing are higher than the corresponding standard states. Specifically, the proposed states in this paper exhibit sub-Poissonian statistics over an extensive range of real amplitudes which is in contrast with the lower level of sub-Poissonian characteristics of four-photon standard coherent states. Also the depth or domain of the nonclassical features of the FPNCSs can be modified by changing the magnitude of the nonlinearity parameters. Analysis of the quasi-probability distributions like Glauber–Sudarshan P-function, Husimi Q-function and Wigner distribution function verifies the nonclassical nature of the presented states. Studying the cavity field evolution in the interaction of a single two-level atom with an even NCS in the framework of f-deformed Jaynes-Cummings model shows that such a system can potentially be considered as a possible source for generating the proposed states.

Continuous waves probing in dynamic acoustoelastic testing

Consolidated granular media display a peculiar nonlinear elastic behavior, which is normally analysed with dynamic ultrasonic testing exploiting the dependence on amplitude of different measurable quantities, such as the resonance frequency shift, the amount of harmonics generation, or the break of the superposition principle. However, dynamic testing allows measuring effects which are averaged over one (or more) cycles of the exciting perturbation. Dynamic acoustoelastic testing has been proposed to overcome this limitation and allow the determination of the real amplitude dependence of the modulus of the material. Here, we propose an implementation of the approach, in which the pulse probing waves are substituted by continuous waves. As a result, instead of measuring a time-of-flight as a function of the pump strain, we study the dependence of the resonance frequency on the strain amplitude, allowing to derive the same conclusions but with an easier to implement procedure.

Study of DNA immobilization on mica surface by atomic force microscopy

Since its discovery, atomic force microscopy (AFM) is widely used to study biological objects and materials, including cells, proteins, and nucleic acids. AFM measurements are carried out in the air as well as in liquid with a very high resolution, even more complex bioprocesses can be monitored in situ under physiological conditions. Successful imaging of DNA molecules on the flat supporting surface typically requires appropriate treatment of mica. The original surface charge of mica is the same as of DNA, i.e. negative. Accordingly, immobilization using bivalent cations (Mg2+, Ni2+, and Co2+), deposition of ethanolamine, and mica surface silanization with alkoxysiloxane derivatives were reported to achieve an optimal concentration and surface arrangement of DNA molecules. Vapours of alkoxysiloxane derivatives led to uniform negatively charged mica surface and it was found that higher ionic radius causes a weaker bond. A better quality and sharper images of DNA molecules were achieved by adjusting the correct real amplitude of the cantilever. This amplitude should correspond with the expected size of the target objects—DNA molecules in the x–y plane of the image. The length of the observed DNA molecules was 1000 bp and the planar width of DNA was 7.8 nm (in reality 3 nm). The AFM spectroscopic mode was particularly useful.

Towards a gauge theory interpretation of the real topological string

We consider the real topological string on certain non-compact toric Calabi-Yau three-folds X, in its physical realization describing an orientifold of type IIA on X with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane BPS states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

Parametric chaos generator operating on a varactor diode with the instability limitation decay mechanism

Equations are derived for a parametric chaos generator containing three oscillatory circuits and a variable-capacitance diode (varactor) and are reduced to equations for slow amplitudes of parametrically interacting modes. With allowance for quadratic nonlinearity, the problem is reduced to a system of three first-order differential equations for Pikovsky–Rabinovich–Trakhtengerts real amplitudes with a Lorenz-type attractor. In a more accurate description of nonlinearity of the varactor, the equations for slow amplitudes are complex-valued, which leads to the loss of robustness of chaotic dynamics, which is typical of the Lorenz attractor. The results of numerical calculations (portraits of attractors and Lyapunov exponents) in models with different approximation levels are compared.