Infinite Mode Research Articles

Real normal operators and Williamson’s normal form

A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite dimensional situation is also proved using elementary techniques. The second result is used to establish the main theorem of this article, which is a generalization of Williamson's normal form for bounded positive operators on infinite dimensional separable Hilbert spaces. This has applications in the study of infinite mode Gaussian states.

Infinite mode quantum Gaussian states

Quantum Gaussian states on Boson Fock spaces are quantum versions of Gaussian distributions. In this paper, we explore infinite mode quantum Gaussian states. We extend many of the results of Parthasarathy in [ 14 , 16 ] to the infinite mode case, which includes various characterizations, convexity and symmetry properties.

Experimental study of heat transfer performance of compact wavy channel with nanofluids as the coolant medium: Real time non-intrusive measurements

Heat transfer performance of nanofluids in the context of corrugated compact channels has been experimentally investigated through real-time, non-intrusive diagnostic technique. The corrugated channel (dimensions: 50 mm (length) × 10 mm (width) × 4 mm (depth); hydraulic diameter of 5.7 mm) comprises of two horizontal wavy plates aligned in an in-phase configuration. Amplitude and period of the wavy plates have been kept constant. Experiments have been performed with varying concentrations of Al2O3/water-based nanofluids for Re = 350–1000. For reference, experiments have also been conducted using water as the base fluid and a plane channel with the same hydraulic diameter as that of the corrugated channel. Convective field has been mapped using a Mach-Zehnder interferometer. Results have been qualitatively as well as quantitatively interpreted to characterize the heat transfer performance of nanofluids as the coolant medium. Interferograms recorded under infinite fringe setting mode captured the phenomena of flow detachment and re-attachment at the wavy sections of the corrugated channel and their dependence on nanofluids concentration. Thermal boundary layer profiles at such sections are seen to be locally perturbed due to flow detachment and its subsequent attachment to the principal wall of the channel. Quantitative data retrieved through the wedge fringe setting interferograms revealed a clear enhancement in heat transfer coefficient for the combination of nanofluids and corrugated channel in comparison with that achieved through water in the plane and/or corrugated channel. For any given Re and channel configuration, the heat transfer coefficient is seen to increase with increasing concentration of dilute nanofluids. For the wavy channel, an enhancement of ≈37% in heat transfer rates with 0.02% volume concentration of nanofluids is achieved at Re = 350 in comparison to the plane channel at the similar levels of nanoparticles volume concentration.

Design of infinite sliding mode state observer with application to CO2 absorption system of space station

The CO2 absorption system plays the important roles in controlling the partial pressure of CO2 and providing the condensed CO2 for Sabatier reduction device. This paper deals with the design of the state observer of the CO2 absorption system in the environment control and life support system of the space station. The main design difficulty is that the dynamic model of the CO2 absorption system is described by the partial differential equation, which causes to the traditional state observer based on ordinary differential equation is no longer applicable. In order to solve this problem, an infinite dimensional slide mode observer algorithm is proposed. This algorithm firstly uses a new projection approximation method to transform the partial differential equation to ordinary differential equation, and then estimates the system state by using sliding mode observer with better robustness to the model approximation error and external disturbance. Compared with the traditional algorithm, the proposed method not only applies to the more general case, e.g. the case of non-orthogonal basis, but also effectively reduces the influence of approximation error and disturbances. Next, the detail realization procedure is illustrated by using a simulation example. The simulation results show that the new algorithm can effectively estimate the state of the CO2 absorption system and further guarantee robust to the model error and external disturbances.

Dual-frequency geometric phase metasurface for dual-mode vortex beam generator

Vortex beams are believed to be an effective way to extend communication capacity for its infinite mode in theory, but the available efforts suffer from the issues of single operating frequency and fixed operation mode, as well as certain radiation direction. In this paper, we propose a new way to design a dual-frequency geometric phase metasurface to solve these issues. The metasurface consists of two perfect half plates, realized by an I-shaped bar and split ring resonator, respectively, which can control the reflection phases at two distinct frequencies independently by rotating each structure. As a proof of concept, a dual-mode vortex beam generator with different reflection angles are simulated and measured. There is a good agreement between the simulation and experimental results, which approves the feasibility of generating dual-mode vortex beams with controlled radiation directions at two distinct frequencies. Our findings can motivate the realization of high-performance metadevices with multifunctionalities or operating at other frequency domains.

The effects of the crack location on the whirl motion of a breathing cracked rotor with rotational damping

Abstract The stability analysis based on the root locus method is proposed to study the whirl motion of a breathing cracked rotor in different crack locations. By the multiple scales method, the eigen-value problem of the infinite order complex mode solutions of the breathing cracked rotor system is discussed. The Campbell diagrams, decay rate plots and roots locus plots of the finite approach from 1st order to 41th order complex mode solutions are compared to find that the 5th order finite approach of the complex mode solutions is the most efficient approximation order, which is verified by the ensuing numerical simulation of the transient response of the breathing cracked rotor system. The effects of the crack position on the stability of the whirl motion of the breathing cracked rotor are analyzed by the decay rate plot of the fifth order approach. The result shows that the crack position affects the super critical resonance region from the 2nd order to the 5th order complex mode, and has no effects on the 1st order complex mode of the whirl motion, and the vibration stability of the subcritical and critical resonance region are less affected. The super critical instability of the system in the crack position at 2 l / L = 0.75 is most affected by rotational damping. These results provide practical references for fault diagnosis, condition monitoring and dynamic balance control technology of heavy loading rotating machinery.

Infinite-mode double-grating interferometer for investigating thermal-lens-acting fluid dynamics

In this paper, we introduce the use of an infinite-mode double-grating interferometer in investigating the fluid dynamics induced by a thermal lens when an intense laser beam—which we call the pump beam—passes through a liquid sample containing strongly absorbing nanoparticles. As the pump beam passes through the sample in normal conditions, since absorption occurs over the beam’s trace, temperature increases and density decreases. The density and temperature changes in the sample can be translated to a phase shift in the passing of a plane probe beam through the sample. By causing two parts of the probe beam to interfere, one part passing from the thermal lens area and the other from another area of the sample spatially separate from the first, it is possible to determine the phase shift value. When the propagation directions of the interfering beams are parallel, infinite-mode double-grating interference fringes are formed. In the infinite mode, the formation and evolution of interference fringes directly reflects any change of density or temperature in the sample. The thermal convection is detected visually and quantitatively determined by chasing the first infinite-mode interference fringe produced. In this work, the measurement of the thermal convection velocity is reported in detail. The measured value is comparable with values obtained with other methods under the same conditions. The proposed method is reliable and very simple; further, the convection process can be visualized in real-time.

Mean field dynamics of some open quantum systems.

We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of [Formula: see text]. The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit [Formula: see text], of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.

Knowledge of the infinite immediate mode of extension in Spinoza

Davant la consuetudinaria consideracio que, d’acord amb Spinoza, el coneixement segons la rao ho es de les coses, que son modes finits d’un dels dos atributs divins coneguts per la ment humana, el Pensament i l’Extensio, entenem provar en aquest treball, sobre la literalitat del tractament de la questio per part del filosof en el Llibre Segon de l’Ethica (E 2), que les nocions comunes o les propietats comunes de les coses (objecte, en efecte, del segon genere de coneixement) son en puritat el mode infinit immediat de l’Extensio, que Spinoza defineix clarament en la carta 64 (Ep64) com el moviment i el repos. Es conclou que, a diferencia de com ocorre amb la scientia intuitiva, el coneixement de segon genere no ho es de singulars (tampoc d’universals o transcendentals, ja que per a Spinoza aquests no existeixen en un sentit ontic), sino del mode infinit de l’Extensio que se segueix, en termes absoluts, de la naturalesa divina.

Second-order perturbation theory: The problem of infinite mode coupling

Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.

Unbiased contaminant removal for 3D galaxy power spectrum measurements

We assess and develop techniques to remove contaminants when calculating the 3D galaxy power spectrum. We separate the process into three separate stages: (i) removing the contaminant signal, (ii) estimating the uncontaminated cosmological power spectrum, (iii) debiasing the resulting estimates. For (i), we show that removing the best-fit contaminant mode subtraction), and setting the contaminated components of the covariance to be infinite (mode deprojection) are mathematically equivalent. For (ii), performing a Quadratic Maximum Likelihood (QML) estimate after mode deprojection gives an optimal unbiased solution, although it requires the manipulation of large $N_{\rm mode}^2$ matrices ($N_{\rm mode}$ being the total number of modes)}, which is unfeasible for recent 3D galaxy surveys. Measuring a binned average of the modes for (ii) as proposed by \citet*[FKP]{Feldman} is faster and simpler, but is sub-optimal and gives rise to a biased solution. We present a method to debias the resulting FKP measurements that does not require any large matrix calculations. We argue that the sub-optimality of the FKP estimator compared with the QML estimator, caused by contaminants is less severe than that commonly ignored due to the survey window.

Non-intrusive dynamic measurements of nanofluid-based heat transfer phenomena under thermally developing flow regime in the context of compact channels

Laser interferometry-based forced convective heat transfer experiments in the context of compact channels using nanofluids are reported. Experiments have been carried out under thermally-developing flow conditions for a range of Reynolds numbers. De-ionized water and alumina/water-based dilute nanofluids have been employed as the coolant medium. The nanofluid-based experiments employ three volumetric concentrations of 0.01%, 0.03% and 0.05%. Projection data of the convective fields have been recorded using a Mach–Zehnder interferometer. Phenomena such as thermal boundary layer profiles and thickness of thermal boundary layer have been interpreted based on the infinite fringe setting mode of the interferometer, while the quantitative information in the form of whole-field temperature distributions and heat transfer coefficients have been retrieved from the wedge fringe setting. Effects of increasing Reynolds numbers and volumetric concentrations of nanofluids on thermal boundary layer profiles and the resultant heat transfer rates have been investigated. Results of the experiments carried out at low Reynolds number (Re<513) reveal that the thermal boundary layer profiles are nearly insensitive to the changes in the concentrations of dilute nanofluids, while a significant enhancement in the heat transfer coefficient is seen as the concentrations of nanofluid is increased. On other hand, at higher Reynolds numbers, increasing concentrations of dilute nanofluids leads to a considerable increase in the thickness of thermal boundary layer that is accompanied with a mild deterioration in the heat transfer rates. Based on the primary findings of the experiments, that are purely non-intrusive in nature, various plausible mechanisms that govern the heat transfer characteristics of dilute nanofluids have been discussed.

The Effect of Green Marketing on Customer Satisfaction and Loyalty and Willingness to Positive Oral Advertising WOM (Case Study of the Cooperative Societies in Urmia)

This study tries to analyze the effect of green marketing on satisfaction and loyalty and willingness to positive oral advertising of clients. The study is applied in terms of aim and descriptive-research field study in terms of data collection and research consisted of all customers of cooperative organization of Urmia. Due to unlimited number of population, the sample size calculations were used in infinite mode of society. The number of samples was calculated by Cochran formula as 384. Simple random sampling method and data collection tool using a researcher developed questionnaire to take advantage of a standardized questionnaire based on the Likert scale were used. Descriptive and inferential statistical methods and Structural Equation Modeling and Smart P.L.S software version 2 have been used in order to test the hypotheses of this research. The results suggest that green marketing is effective on customer satisfaction and loyalty and willingness to positive oral Advertising.

Looking for Spinoza's Missing Mediate Infinite Mode of Thought

Looking for <scp>S</scp>pinoza's Missing Mediate Infinite Mode of Thought

Interferometric study of nanofluid-based heat transfer phenomena in compact channels

The present work is concerned with the interferometric measurements of dilute nanofluid-based heat transfer enhancement in compact rectangular channels. The heat transfer experiments have been conducted in forced convection regime for a range of Reynolds number. Simultaneously developing flow regimes have been considered. Al2O3-based dilute nanofluids with volume concentrations of 0.01% and 0.05% have been employed with deionized water as the base fluid. A Mach–Zehnder interferometer has been used to record the line-of-sight images of the convective fields inside the channel. Interferometry experiments have been performed in infinite as well as wedge fringe-setting mode of the interferometer. The images recorded in infinite fringe setting mode have been qualitatively interpreted to understand the effect of increasing volume concentration of nanofluids on phenomena like disruption of thermal boundary layer, temperature gradients etc. The interferograms corresponding to the wedge fringe-setting mode have been quantitatively analyzed to retrieve the whole field temperature distribution inside the compact channel, local variation of heat transfer coefficient for the range of volume concentration of nanofluids and Reynolds numbers studied in the present work. Results have been presented in the form of interferometric images, the contours of two-dimensional temperature distribution, local variation of thermal boundary layer thicknesses and heat transfer coefficients along the length of the channel and percentage enhancement in heat transfer rates due to increasing volume concentration of nanofluids for each Reynolds number. The experimental study clearly reveals a reduction in the thickness of the thermal boundary layer with increasing volume concentration of nanofluids and hence the increasing strength of the thermal gradients. An overall enhancement of heat transfer coefficient by a factor of about 1.7–2 in the case of nanofluid is observed in comparison with that obtained with the base fluid.

Reflection phase of electromagnetic bandgap structure measurement based on parallel‐plate waveguide system

A carefully designed parallel-plate waveguide measurement system is constructed to measure the reflection phase of a compact electromagnetic bandgap (EBG) structure. A quasi-plane wave is created in the parallel-plate waveguide chamber, which is the basic condition of phase measurement. Two EBG samples with different parameters are measured in this system. The data of the two samples agree well with those of infinite array EBG mode simulations, which proves that this measurement method has good accuracy and reliability. This system reduces the cost of EBG reflection phase measurement and the samples used in the experiment have a much smaller size.

Infinite mode analysis of a general model with external harmonic excitation

This study proposes a general solution procedure for infinite mode analysis. The equation of motion is written in a general form using spatial differential operators, which are suitable for perturbation techniques. The multiple time scales method is applied directly to solve the proposed equation of motion. General investigations of some resonance cases are provided, such as parametric, sum type, difference type, and a combination of sum and difference type resonances. The proposed general solution procedure is applied to one- and two-dimensional problems. The results demonstrate that this general solution procedure obtains good solutions in the dynamic analysis of beams, plates, and other structures.

Interferometry based whole-field heat transfer measurements of an impinging turbulent synthetic jet

The present work is concerned with exploring the potential of refractive index-based imaging techniques for investigating the heat transfer characteristics of impinging turbulent synthetic jets. The line-of-sight images of the convective field have been recorded using a Mach Zehnder interferometer. Heat transfer experiments have been conducted in infinite fringe setting mode of the interferometer with air as the working fluid. The effect of the excitation frequency of the synthetic jet on the resultant temperature distribution and local heat transfer characteristics has been studied. The fringe patterns recorded in the form of interferograms have first been qualitatively discussed and thereafter, quantitatively analyzed to determine the two-dimensional temperature field. Local heat transfer coefficients along the width of the heated copper block have been determined from the temperature field distribution thus obtained from the interferograms. The results have been presented in the form of interferometric images recorded as a function of frequency of the synthetic jet, corresponding two-dimensional temperature distributions and local variation of heat transfer coefficients. Interferometric measurements predicted maxima of the heat transfer coefficient at the resonance frequency of the synthetic jet and at a jet-to-plate surface spacing (z/d) of 3. These observations correlate well with the thermocouple-based measurements of temperature and heat transfer coefficient performed simultaneously during the experiments. The interferometry-based study, as reported in the present work for the first time in the context of synthetic jets, highlights the importance of refractive index-based imaging techniques as a potential tool for understanding the local heat transfer characteristics of synthetic jets.

Thermoelastic properties evolution and damping phenomena of Cameroonian calcined bauxite stabilized with calcium dialuminate refractory cement

Two castable refractory concretes were made respectively from samples of high alumina calcined bauxite and calcium dialuminate (CaO·2Al2O3) refractory cement. Each castable refractory concrete was made up of 8% wt refractory cement and w/c=0.40 and then stabilized at 105°C for 48h. The refractory concretes were characterized by determination of Young׳s modulus according to infinite mode, dilatometric behavior, apparent density and apparent porosity. Measurement of Resonance Frequency and Damping Analysis (RFDA) to determine the Young׳s modulus and damping phenomena up to 1620°C were done as well. Young׳s modulus of castable refractory concrete which was initially 28.3GPa and apparent porosity of 38.2% at 105°C led respectively to 90.4GPa and 24.2% after treatment at 1500°C. The study of Young׳s modulus versus temperature showed significant decrease around 300°C (dehydration of cement) followed by an increase between 800 and 1620°C (sintering of concrete). Important damping phenomena were noticeable respectively around 880 and 1280°C which resulted in certain imperfections in castable refractory concrete, expressed as crystallization of calcium aluminate (CA) and calcium dialuminate (CA2). Young׳s modulus of 9GPa at 1620°C showed that elaborated refractory concrete could be suitable for the construction of kiln in steel or ceramic industries.

Identifying Spinoza’s Immediate Infinite Mode of Extension

The immediate infinite mode of extension is one of the more mysterious elements of Spinoza’s ontology. Despite its importance to Spinoza’s metaphysical system, Spinoza tells us very little about this mode. In the effort to make some progress on this question, I examine three prominent hypotheses about this mode’s identity: the Force Interpretation, the Nomic Interpretation, and the Kinetic Interpretation. I argue, first, that both the Force Interpretation and the Nomic Interpretation are subject to a number of serious objections. Second, I argue that in spite of scholars’ claims to the contrary, the Kinetic Interpretation is a live option.