Two-dimensional Probability Density Research Articles

THE USE OF MODEL DISTRIBUTIONS IN THE ANALYSIS OF QUEUING SYSTEMS WITH CORRELATED ARRIVALS

The article considers the task of determining the waiting time for a request in a queue in a general-type single-channel queueing system when time intervals between incoming requests are correlated. For solving the task, it is proposed to carry out decorrelation of specified time intervals using the discrete cosine transform. Generally, to analyze arbitrary distributions included in the expression for a decorrelated sequence, one can suggest an approach based on the approximation of unknown densities by a model distribution. The calculation of cumulants and moments of random variables is very simple compared to the analytical methods. Based on the found final set of cumulants, a model probability density can always be reproduced with a certain error. Generally, to calculate the average waiting time of a request in a queue, it is necessary to determine the correlation properties and one-dimensional probability density of time intervals between incoming requests, synthesize a two-dimensional probability density of a sequence of given intervals that has a measured correlation function, and, further, calculate joint moments and cumulants for correlated values, on which their model density is built.

Characterizing a supernova’s standing accretion shock instability with neutrinos and gravitational waves

We perform a novel multimessenger analysis for the identification and parameter estimation of the standing accretion shock instability (SASI) in a core-collapse supernova with neutrino and gravitational-wave (GW) signals. In the neutrino channel, this method performs a likelihood ratio test for the presence of SASI in the frequency domain. For gravitational-wave signals we process an event with a modified constrained likelihood method. Using simulated supernova signals, the properties of the Hyper-Kamiokande neutrino detector, and O3 LIGO interferometric data, we produce the two-dimensional probability density function (PDF) of the SASI activity indicator and calculate the probability of detection PD as well as the false identification probability PFI. We discuss the probability to establish the presence of the SASI as a function of the source distance in each observational channel, as well as jointly. Compared to a single-messenger approach, the joint analysis results in a PD (at PFI=0.1) of SASI activities that is larger by up to ≈40% for a distance to the supernova of 5 kpc. We also discuss how accurately the frequency and duration of the SASI activity can be estimated in each channel separately. Our methodology is suitable for implementation in a realistic data analysis and a multimessenger setting.8 MoreReceived 24 November 2022Accepted 24 February 2023DOI:https://doi.org/10.1103/PhysRevD.107.083017© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasExtrasolar neutrino astronomyGravitational wavesNovae & supernovaeTechniquesGravitational wave detectionGravitational wave detectorsNeutrino detectorsGravitation, Cosmology & Astrophysics

FEATURES OF THE IMPLEMENTATION OF THE SPEAKER IDENTIFICATION SOFTWARE SYSTEM

The proposed architecture of the identification software system in the form of class and sequence diagrams. The main criteria for assessing the accuracy of speaker identification were studied and possible sources of loss of speaker identification accuracy were identified, which can be used when building a speaker identification system. A software system based on the proposed architecture and previously developed identification algorithms and methods was created.
 The following conclusions can be drawn on the basis of the performed research: approaches to the construction of existing announcer identification systems are considered; the main criteria for assessing the accuracy of announcer identification were investigated and the main sources of loss of accuracy during announcer identification were identified; the structural construction of the announcer identification system is considered, taking into account the identified sources of loss of accuracy during announcer identification; the proposed architecture of the speaker identification system in the UML language in the form of class and sequence diagrams; a software system was built that implements the functions of speech signal identification according to the methods and algorithm proposed in previous works.
 The software system uses a ranking method based on three different criteria. These include: calculation of the proximity of two-dimensional probability density function curves for the frequency of the main tone and the location in the spectrum of three frequency ranges that are extracted from the speech recorded in the speech signal; calculation of the proximity of the probability density function curves for each of these features separately; calculation of the degree of closeness of the absolute maxima of the formant spectra extracted from the speech recorded in the speech signal.

Missense Mutations Modify the Conformational Ensemble of the α-Synuclein Monomer Which Exhibits a Two-Phase Characteristic.

α-Synuclein is an intrinsically disordered protein occurring in different conformations and prone to aggregate in β-sheet structures, which are the hallmark of the Parkinson disease. Missense mutations are associated with familial forms of this neuropathy. How these single amino-acid substitutions modify the conformations of wild-type α-synuclein is unclear. Here, using coarse-grained molecular dynamics simulations, we sampled the conformational space of the wild type and mutants (A30P, A53P, and E46K) of α-synuclein monomers for an effective time scale of 29.7 ms. To characterize the structures, we developed an algorithm, CUTABI (CUrvature and Torsion based of Alpha-helix and Beta-sheet Identification), to identify residues in the α-helix and β-sheet from Cα -coordinates. CUTABI was built from the results of the analysis of 14,652 selected protein structures using the Dictionary of Secondary Structure of Proteins (DSSP) algorithm. DSSP results are reproduced with 93% of success for 10 times lower computational cost. A two-dimensional probability density map of α-synuclein as a function of the number of residues in the α-helix and β-sheet is computed for wild-type and mutated proteins from molecular dynamics trajectories. The density of conformational states reveals a two-phase characteristic with a homogeneous phase (state B, β-sheets) and a heterogeneous phase (state HB, mixture of α-helices and β-sheets). The B state represents 40% of the conformations for the wild-type, A30P, and E46K and only 25% for A53T. The density of conformational states of the B state for A53T and A30P mutants differs from the wild-type one. In addition, the mutant A53T has a larger propensity to form helices than the others. These findings indicate that the equilibrium between the different conformations of the α-synuclein monomer is modified by the missense mutations in a subtle way. The α-helix and β-sheet contents are promising order parameters for intrinsically disordered proteins, whereas other structural properties such as average gyration radius, R g , or probability distribution of R g cannot discriminate significantly the conformational ensembles of the wild type and mutants. When separated in states B and HB, the distributions of R g are more significantly different, indicating that global structural parameters alone are insufficient to characterize the conformational ensembles of the α-synuclein monomer.

Algorithm for assessing changes in the functional state of muscles of the maxillofacial area of athletes using individual relaxation occlusal splints or mouth guards

The paper proposes an algorithm for assessing changes in the functional state of bilaterally located muscles. The proposed algorithm is based on the analysis of two-dimensional distribution function and two-dimensional probability density of the amplitude of electromyograms of the muscles under study. The paper proposes criteria for assessing the symmetry and asymmetry of muscle activity, presents the results of the study of changes in the functional state of the temporalis muscles and the masseter muscles for a group of athletes. During sports competitions and preparing to them, athletes are exposed to high physical and emotional stress which leads to a premature decrease in the functional activity of the muscles causing changes in the biomechanics of movements. The reasons that lead to a decrease in the functional activity of the muscles are as follows: occlusal disharmony; changes in bite and / or interalveolar distance, hypertonicity of the muscles of the maxillofacial region. Ultimately, these reasons lead to a deterioration in sports performance. The group of the athletes under study involved 10 males aged 23 to 24 years, who are engaged in combat sports at a professional level. Each athlete underwent a clinical examination, palpation and isometric tests of the muscles of the maxillofacial region (MR) and temporomandibular joints (TMJ), auscultation of the TMJ, control of occlusion (using copy paper and T-scan apparatus), cone-beam computed tomography (CBCT) of the dentoalveolar system (DAS) and electromyography (EMG) of the muscles of the maxillofacial region. At this stage of the research, each athlete received individual relaxation occlusal splints or mouthguards of two types: 2.0 mm thick soft one and 3.0 mm thick semi-rigid one. It was recommended to the athletes that they should wear the splints for 1–2 months in the following manner: to wear 2.0 mm thick soft splint on an ongoing basis, excluding food intakes and the training process, whereas 3.0 mm thick semi-rigid splints should be used during the training process and other types of physical activity, as well as at competitions.

On the Digital Simulation of the Random Process Following the Two-Dimensional Nakagami Distribution

Random processes following the Nakagami probability distribution occur in the multipath radio communication channels and describe the received signal fluctuations (i.e. – fading) in various conditions and frequency ranges. In this paper, a digital algorithm and a device based on it are considered for simulating such processes with the specified two-dimensional probability density. Particularly, a procedure for building the Markov model of such processes and an algorithm for generating samples of a random or pseudorandom process following the specified two-dimensional Nakagami distribution are introduced. The opportunities for both the hardware and the software implementation of the algorithm are also considered. The statistical characteristics of the simulated random process are studied and the simulation accuracy is estimated. For the hardware implementation of the simulator, the field-programmable gate arrays are suggested.

Whole-Brain Imaging of Subvoxel T1-Diffusion Correlation Spectra in Human Subjects.

T1 relaxation and water mobility generate eloquent MRI tissue contrasts with great diagnostic value in many neuroradiological applications. However, conventional methods do not adequately quantify the microscopic heterogeneity of these important biophysical properties within a voxel, and therefore have limited biological specificity. We describe a new correlation spectroscopic (CS) MRI method for measuring how T1 and mean diffusivity (MD) co-vary in microscopic tissue environments. We develop a clinical pulse sequence that combines inversion recovery (IR) with single-shot isotropic diffusion encoding (IDE) to efficiently acquire whole-brain MRIs with a wide range of joint T1-MD weightings. Unlike conventional diffusion encoding, the IDE preparation ensures that all subvoxel water pools are weighted by their MDs regardless of the sizes, shapes, and orientations of their corresponding microscopic diffusion tensors. Accordingly, IR-IDE measurements are well-suited for model-free, quantitative spectroscopic analysis of microscopic water pools. Using numerical simulations, phantom experiments, and data from healthy volunteers we demonstrate how IR-IDE MRIs can be processed to reconstruct maps of two-dimensional joint probability density functions, i.e., correlation spectra, of subvoxel T1-MD values. In vivo T1-MD spectra show distinct cerebrospinal fluid and parenchymal tissue components specific to white matter, cortical gray matter, basal ganglia, and myelinated fiber pathways, suggesting the potential for improved biological specificity. The one-dimensional marginal distributions derived from the T1-MD correlation spectra agree well with results from other relaxation spectroscopic and quantitative MRI studies, validating the T1-MD contrast encoding and the spectral reconstruction. Mapping subvoxel T1-diffusion correlations in patient populations may provide a more nuanced, comprehensive, sensitive, and specific neuroradiological assessment of the non-specific changes seen on fluid-attenuated inversion recovery (FLAIR) and diffusion-weighted MRIs (DWIs) in cancer, ischemic stroke, or brain injury.

Low-Frequency Seismic Noise Properties in the Japanese Islands.

The records of seismic noise in Japan for the period of 1997–2020, which includes the Tohoku seismic catastrophe on 11 March 2011, are considered. The following properties of noise are analyzed: The wavelet-based Donoho–Johnston index, the singularity spectrum support width, and the entropy of the wavelet coefficients. The question of whether precursors of strong earthquakes can be formulated on their basis is investigated. Attention is paid to the time interval after the Tohoku mega-earthquake to the trends in the mean properties of low-frequency seismic noise, which reflect the constant simplification of the statistical structure of seismic vibrations. Estimates of two-dimensional probability densities of extreme values are presented, which highlight the places in which extreme values of seismic noise properties are most often realized. The estimates of the probability densities of extreme values coincide with each other and have a maximum in the region: , . The main conclusions of the conducted studies are that the preparation of a strong earthquake is accompanied by a simplification of the structure of seismic noise. It is shown that bursts of coherence between the time series of the day length and the noise properties within annual time window precede bursts of released seismic energy. The value of the lag in the release of seismic energy relative to bursts of coherence is about 1.5 years, which can be used to declare a time interval of high seismic hazard after reaching the peak of coherence.

Modified Algorithm for Rapid Choice of Spread Coefficients for Kernel Estimates of Multidimensional Probability Densities

An original method for rapid choice of the spread coefficients of the kernel functions in nonparametric estimates of multidimensional Rosenblatt–Parzen type probability densities is justified. The proposed method makes it possible to substantially increase the computational efficiency of the procedure for optimizing kernel estimates of the probability density for statistical data from a large sample volume compared to the traditional method. The proposed approach is based on analyzing a formula for the optimum parameter of the spread coefficients of a multidimensional kernel estimate for the probability density. Relationships are found between the nonlinear functional of the probability density and its derivatives up to second order, including of the antikurtosis coefficients of random variables. The spread coefficients for each random variable are represented as the product of an undetermined parameter and their mean square deviation. The effect of the error in recovering the established functional dependences on the approximation properties of the kernel estimate of the probability density is determined. These results are implemented in the form of a method for synthesis and analysis of a fast algorithm for choosing the spread coefficients of the kernel estimate of a two-dimensional probability density of independent random variables. The proposed method is implemented using data on the quantitative characteristics of a family of log-normal distribution laws.

Storm surges in the Gulf of Finland of the Baltic Sea

The characteristics of storm surges in different regions of the Gulf of Finland in the second half of the XX and the beginning of the XXI centuries were investigated on the basis of tide gauge measurements of sea level, instrumental observations of the wind and data from the reanalysis of meteorological fields. A criterion for identifying storm surges, taking into account spatial changes in their intensity, is proposed. The results indicate that depending on the year and the location of the station, the number of storm surges varies in the Gulf of Finland in a wide range: from 0 - 1 to 16 - 52 cases per year. The average duration of storm surges varies from 6.7 to 9.0 hours, and the maximum reaches 26 to 96 hours. Shown that in recent decades, in most regions, there has been a tendency towards a decrease in the number of storm surges, their dispersion and sea level maximum. The distributions of the probabilities of wind and atmospheric pressure during storm surges are given. Estimates of two-dimensional probability densities indicate that during storm surges, winds blowing from the west and southwest with speeds of 4-13 m / s are most likely. At the northern coast and at the top of the bay, the most probable values of atmospheric pressure during storm surges are 995 hPa. On the southern coast of the Gulf of Finland, atmospheric pressure values of 1005 - 1015 hPa are most likely. The results obtained indicate that the atmospheric pressure over the Gulf of Finland during storm surges is not very low. This is due to the fact that the trajectories of the centers of cyclones causing storm surges pass north of the Gulf of Finland. Analysis of meteorological information also showed the presence of significant negative trends in interannual variations in the dispersion of the horizontal atmospheric pressure gradient, average values and maximums of wind speed. It is concluded that the revealed changes in the characteristics of storm surges are associated with a decrease in the intensity of cyclogenesis in the atmosphere over the Baltic Sea in recent decades.

Mathematical Model of Object Classifier based on Bayesian Approach

The paper claims that the primary importance in solving the classification problem is to find the conditions for dividing the General complexity into classes, determine the quality of such a bundle, and verify the classifier model. We consider a mathematical model of a non-randomized classifier of features obtained without a teacher, when the number of classes is not set a priori, but only its upper bound is set. The mathematical model is presented in the form of a statement of a minimax conditional extreme task, and it is a problem of searching for the matrix of belonging of objects to a class, and representative (reference) elements within each class. The development of the feature classifier is based on the synthesis of two-dimensional probability density in the coordinate space: classes-objects. Using generalized functions, the probabilistic problem of finding the minimum Bayesian risk is reduced to a deterministic problem on a set of non-randomized classifiers. At the same time, the use of specially introduced constraints fixes non-randomized decision rules and plunges the integer problem of nonlinear programming into a General continuous nonlinear problem. For correct synthesis of the classifier, the dispersion curve of the isotropic sample is necessary. It is necessary to use the total intra-class and inter-class variance to characterize the quality of classification. The classification problem can be interpreted as a particular problem of the theory of catastrophes. Under the conditions of limited initial data, a minimax functional was found that reflects the quality of classification for a quadratic loss function. The developed mathematical model is classified as an integer nonlinear programming problem. The model is given using polynomial constraints to the form of a General problem of nonlinear continuous programming. The necessary conditions for the bundle into classes are found. These conditions can be used as sufficient when testing the hypothesis about the existence of classes.

Quantifying interfacial parameters of upward and downward annular flow condensation from high-speed visualization

Condensation of R-134a in upward and downward annular flow was experimentally studied in a 5-mm ID transparent test section using a LED-based image processing technique. In addition to the flow orientation, the frequency of the film structures was quantified in terms of the following parameters: total mass flow rate, condensation heat transfer rates (outlet vapor quality) and test section inclination with respect to the horizontal. The image processing technique combined Fourier analysis and the Kernel density estimation technique to calculate the two-dimensional (amplitude–frequency) probability density function of the film flow structure as a function of the independent parameters. Although the tube inclination and the condensation rate showed some influence on the frequency of the interfacial waves, the most significant effect was due to the flow orientation, which resulted in abrupt frequency changes apparently linked to flow regime transitions dictated by shear and gravity forces.

Fuzing license plate recognition data and vehicle trajectory data for lane-based queue length estimation at signalized intersections

Queue length is one of the most important performance measures for signalized intersections. With recent advancements in connected vehicles and intelligent mobility technologies, utilizing vehicle trajectory data to estimate queue length has received considerable attentions. However, most of the existing methods are based on some assumptions, such as known arrival patterns and/or high penetration rates. Besides, existing models would probably be unstable or invalid under sparse trajectory environment. Hence, license plate recognition (LPR) data is introduced in this study to fuze with the vehicle trajectory data, and then, a lane-based queue length estimation method is proposed. First, by matching the LPR data with probe vehicle data, the two-dimensional probability density distribution of discharge headway and stop-line crossing time of various kinds of vehicles, i.e., queued and nonqueued vehicle for undersaturated condition and twice-queued and once-queued vehicle for oversaturated condition, can be calibrated. Then, the Bayesian theory is adopted to derive the lane-based queue length for undersaturated condition as well as the initial queue for oversaturated condition with the largest possibility, respectively. Where probe vehicle trajectories, if existed, will provide the boundaries for the estimated queue lengths. Finally, the performance of the proposed method is evaluated using both simulation and empirical data. Simulation results show that the proposed method could produce accurate estimates of queue lengths for both undersaturated and oversaturated conditions and can achieve reliable estimates even under low penetration rate (3%). Empirical results show that the proposed method outperforms an existing method using probe vehicle trajectories only.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Field of coherence of GPS-measured earth tremors

A new method for investigating the coherence field of the noise component of high-frequency GPS time series is proposed. The method is applied to the main territory of the USA, which is characterized by a dense network of GPS stations. The data are presented in steps of 5 min from February 28, 2013, until June 29, 2019, on the Nevada Geodetic Laboratory Web site. The proposed method estimates the spatial distribution of the mean values of multiple coherence, calculated within nodes of a regular grid, between GPS coordinates of a given number of nearest operable stations and the periods at which the maximum values of coherence are reached. The two-dimensional probability density of the positions of places where the coherence maximum is most often realized is estimated. These estimates can be obtained for the entire history of observations and also in a sliding time window of a given length, which makes it possible to trace the dynamics of changes in time in the coherence field of the earth’s tremor. The entropy of the two-dimensional probability density of places of concentration of maximum values of coherence allows us to distinguish seasonal changes in the structure of the coherence field of GPS noise. To study the temporal dynamics, we use the auxiliary time series of changes in the maximum multiple coherence at 50 reference points located throughout the study area. The study of the coherence properties of this auxiliary 50-dimensional time series (“secondary coherence”) in a 180-day sliding time window highlighted a series of synchronization bursts of earth’s surface tremors.

Opto-electronic properties of twisted bilayer graphene quantum dots

The electronic and interband optical properties of vertically coupled stacked graphene quantum dots are investigated using the tight-binding method. Both zigzag and armchair edge configurations are taken into account. In particular, the effect of the geometrical shape (triangular or circle-like) and, most prominently, of the angle of twisting between layers is mainly addressed. The optical response is analyzed from the calculated imaginary part of the dielectric function. It is found that the interband absorption threshold is highly dependent on the dot size and geometry: For armchair triangular bilayer graphene dots the optical gap exhibits a moderate increase for smaller angles of twisting, and the structure behaves as an intermediate to a wide gap semiconductor; whereas zigzag triangular bilayer graphene dots are small gap systems in which the twisting causes the appearance of zero-gap states associated with the variation of HOMO and LUMO states resulting from the breaking of zero-energy degeneracy. In the latter case, it is shown that the low-energy transitions between those states are responsible for the main optical response of the structures which indicates possible applications in the THz optoelectronics. Circular dots are chosen in commensurable configurations and also show stronger low-energy absorption thresholds. A particular feature appearing in this case is the presence of Bravais-Moiré patterns in the two-dimensional probability density distributions for large enough dot radii.

Exploring Bayesian parameter estimation for chiral effective field theory using nucleon–nucleon phase shifts

We recently developed a Bayesian framework for parameter estimation in general effective field theories. Here we present selected results from using that framework to estimate parameters with a nucleon–nucleon (NN) potential derived using chiral effective field theory (χEFT): the semi-local NN potential of Epelbaum, Krebs, and Meißner (EKM). There are many NN scattering data, up to high energies, and with rather small errors. Imposing a penalty for unnatural low-energy constants (LECs) therefore has a small effect on the fits, unless only a small fraction of the NN data is used in the fit. In contrast, we have found that including an estimate of higher orders in χEFT plays an important role in robust parameter estimation. We present two case studies where our Bayesian machinery illuminates physics issues. The first involves the EKM potential at fourth order in the χEFT expansion: the two-dimensional posterior probability density function (pdf) for the fourth-order s-wave LECs obtained from the Nijmegen PWA93 phase shifts indicates these parameters in the NN potential are degenerate. We trace this feature of the pdf to the presence of an operator in the fourth-order NN potential that vanishes on-shell. The second case study examines the stability of LEC extractions as more data at higher energies are included in the fit. We show that as long as χEFT truncation errors are properly accounted for in the parameter estimation, the LEC values extracted using our Bayesian approach are not sensitive to the maximum energy chosen for the fit. Uncorrelated and fully correlated models for the truncation errors are compared, pointing the way to the use of Gaussian processes to more generally model the correlation structure.

МЕТОД ПІДВИЩЕННЯ ЗАВАДОСТІЙКОСТІ СИСТЕМИ ВИЯВЛЕННЯ, РОСПІЗНАВАННЯ І ЛОКАЛІЗАЦІЇ ЦИФРОВИХ СИГНАЛІВ В ІНФОРМАЦІЙНИХ СИСТЕМАХ

In the process of detection, recognition, and localization of the single means of silent retrieval of information in information systems, the urgent issue is the increase of noise immunity. The article explores the features of using low-pass filters with a quadratic and linear response dependence on the input signal. It is shown that the principle of operation of the filters is that the summation process is performed. In this case, the useful signal is summed coherently, and the interference signal is incoherent, that is, the useful signal increases, and the interference signal decreases. When exposed to inputs, linear and quadratic filters, a rectangular pulse that simulates the signal of modern digital non-voice information, the parameters necessary for use in the future, such as mathematical expectation, correlation coefficient, variance, root mean square, the ratio of signals to interference in temporal and spectral form. We have determined a payoff ratio that shows the efficiency of using low pass filters. The graphs of the envelope voltage at the output of the ideal bandpass filter when exposed to the input of a rectangular pulse - the signal of the means of silent information acquisition, with different duration. The filtration process was simulated at different correlation coefficients, which confirmed the possibility of signal isolation of the means of silent information acquisition by the method of determining the two-dimensional probability density of the interference signal and the background of the general signal. The process of increasing the noise immunity of the system as a whole is considered, it is proved that the increase of noise immunity by 23 % of the system of identification, recognition and localization of the means of silent retrieval of information is achieved by using, in the process of signal processing, narrow-band filters of low frequency.

Scalar dissipation rates in a turbulent partially-premixed dimethyl ether/air jet flame

This paper presents the gradient structure of a turbulent partially premixed dimethyl ether (DME)/air jet flame operating at a jet Reynolds number of 29,300. Temperature and mixture fraction profiles from Raman/Rayleigh/CO-LIF line measurements are used to determine one-dimensional scalar dissipation rates at six axial locations. A major focus of the current work is to assess the effects of experimental artifacts, including spatial resolution, noise, and dimensionality, on the accuracy of the derived scalar dissipation rate. Two-dimensional probability density functions (PDFs) of the mixture fraction gradients are used to determine possible clipping effects due to insufficient spatial resolution. This resolution limit is compared to values determined from one-dimensional dissipation spectra and scaling laws. Spatial resolution also is investigated using laminar flame calculations in conjunction with optical-blur filters representing the experimental setup. The impact of noise is treated by error propagation methods. Monte Carlo simulations and experimental data from laminar flames are used to verify and validate the models used to predict noise propagation for the measurements of the absolute gradients, squared gradients, and scalar dissipation rates. Gradient and scalar dissipation rate detection limits and contribution from apparent dissipation (due to noise effects) are presented as functions of measurement signal-to-noise ratios. A noised lognormal function is introduced to investigate the impact of noise on derived PDFs and corresponding statistical moments of the measured scalar gradients and the scalar dissipation rate within the turbulent flame. Results from the turbulent flame measurements are presented in the form of scatter plots and conditional statistics to examine turbulence-chemistry interaction and develop a database for model assessment. Specifically, the results are compared to laminar flame calculations over a broad range of strain rates with multi-component and unity Lewis number transport assumptions. This comparison is used to assess the relevance of differential diffusion effects on scalar dissipation rates in the turbulent flame.

Comparison of the Efficiency of Methods of Digitizing the Range of Values of Dependent Random Variables During Synthesis of a Nonparametric Assessment of Two-Dimensional Probability Density

Optimal and heuristic methods of digitizing the range of values of a two-dimensional random variable are compared. Conditions of the scope of these methods are defined in re-establishing the normal law of distribution of two dependent random variables. Results of computational tests are examined.