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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr = 0.7 and in liquid mercury at Pr = 0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Finally, despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Thus, our results have interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Welch Method and Bootstrapping Applied to Subcritical Gamma Noise

We measured the prompt neutron decay constant 𝛼 of the CROCUS zero-power reactor at the Swiss Federal Institute of Technology Lausanne using cross-power spectral density (CPSD) analysis of gamma-gamma correlations from two trans-stilbene organic scintillators positioned near the reactor core. We measured critical and subcritical states, with water levels ranging from 960 mm (critical) to 800 mm (𝜌=−1.4 $ subcritical). Our analysis used the Welch method, dividing signal segments for fast Fourier transform (FFT) frequency analysis and applying bootstrapping uncertainty quantification that uses Welch-defined segments. Results demonstrated a clear increase in the measured 𝛼 as reactor reactivity decreased, distinguishing critical from subcritical conditions. At the 960-mm critical level, 𝛼 was estimated at 155.9 ± 0.7 s −1 , and for the 800-mm subcritical level, 𝛼 increased significantly to 367.3 ± 6.9 s –1 . A linear regression of subcritical states yielded a critical estimate of 154.0 ± 3.1 s –1 , aligning with the static 𝛼 estimate at critical. The bootstrapping method produced normally distributed 𝛼 estimates, confirming data consistency. The gamma CPSD 𝛼 estimates clearly distinguish reactor states and improve monitoring of zero-power reactors. The future deployment of modular and microreactors as potential candidates for noise analysis is demonstrated in CROCUS, particularly zero-power mock-ups of new designs. The improvement of noise analysis in the subcritical domain from this work will support experimental data for reactor deployment and procedure.

CROCUS↗
DOE OSTI2016

Spatiotemporal modeling of node temperatures in supercomputers

Los Alamos National Laboratory (LANL) is home to many large supercomputing clusters. These clusters require an enormous amount of power (~500-2000 kW each), and most of this energy is converted into heat. Thus, cooling the components of the supercomputer becomes a critical and expensive endeavor. Recently a project was initiated to investigate the effect that changes to the cooling system in a machine room had on three large machines that were housed there. Coupled with this goal was the aim to develop a general good-practice for characterizing the effect of cooling changes and monitoring machine node temperatures in this and other machine rooms. This paper focuses on the statistical approach used to quantify the effect that several cooling changes to the room had on the temperatures of the individual nodes of the computers. The largest cluster in the room has 1,600 nodes that run a variety of jobs during general use. Since extremes temperatures are important, a Normal distribution plus generalized Pareto distribution for the upper tail is used to model the marginal distribution, along with a Gaussian process copula to account for spatio-temporal dependence. A Gaussian Markov random field (GMRF) model is used to model the spatial effects on the node temperatures as the cooling changes take place. This model is then used to assess the condition of the node temperatures after each change to the room. The analysis approach was used to uncover the cause of a problematic episode of overheating nodes on one of the supercomputing clusters. Lastly, this same approach can easily be applied to monitor and investigate cooling systems at other data centers, as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Stellar velocity dispersion and anisotropy of the Milky Way inner halo

We measure the three components of velocity dispersion, σ{sub R}, σ{sub θ}, σ{sub ϕ}, for stars within 6 < R < 30 kpc of the Milky Way using a new radial velocity sample from the MMT telescope. We combine our measurements with previously published data so that we can more finely sample the stellar halo. We use a maximum likelihood statistical method for estimating mean velocities, dispersions, and covariances assuming only that velocities are normally distributed. The alignment of the velocity ellipsoid is consistent with a spherically symmetric gravitational potential. From the spherical Jeans equation, the mass of the Milky Way is M(R⩽12 kpc)=1.3×10{sup 11} M{sub ⊙} with an uncertainty of 40%. We also find a region of discontinuity, 15 ≲ R ≲ 25 kpc, where the estimated velocity dispersions and anisotropies diverge from their anticipated values, confirming the break observed by others. We argue that this break in anisotropy is physically explained by coherent stellar velocity structure in the halo, such as the Sgr stream. To significantly improve our understanding of halo kinematics will require combining radial velocities with future Gaia proper motions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Detecting anomalies in CMB maps: a new method

Ever since WMAP announced its first results, different analyses have shown that there is weak evidence for several large-scale anomalies in the CMB data. While the evidence for each anomaly appears to be weak, the fact that there are multiple seemingly unrelated anomalies makes it difficult to account for them via a single statistical fluke. So, one is led to considering a combination of these anomalies. But, if we ''hand-pick'' the anomalies (test statistics) to consider, we are making an a posteriori choice. In this article, we propose two statistics that do not suffer from this problem. The statistics are linear and quadratic combinations of the a{sub ℓ m}'s with random co-efficients, and they test the null hypothesis that the a{sub ℓ m}'s are independent, normally-distributed, zero-mean random variables with an m-independent variance. The motivation for considering multiple modes is this: because most physical models that lead to large-scale anomalies result in coupling multiple ℓ and m modes, the ''coherence'' of this coupling should get enhanced if a combination of different modes is considered. In this sense, the statistics are thus much more generic than those that have been hitherto considered in literature. Using fiducial data, we demonstrate that the method works and discuss how it can be used with actual CMB data to make quite general statements about the incompatibility of the data with the null hypothesis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Solving puzzles of GW150914 by primordial black holes

The black hole binary properties inferred from the LIGO gravitational wave signal GW150914 posed several serious problems. The high masses and low effective spin of black hole binary can be explained if they are primordial (PBH) rather than the products of the stellar binary evolution. Such PBH properties are postulated ad hoc but not derived from fundamental theory. We show that the necessary features of PBHs naturally follow from the slightly modified Affleck-Dine (AD) mechanism of baryogenesis. The log-normal distribution of PBHs, predicted within the AD paradigm, is adjusted to provide an abundant population of low-spin stellar mass black holes. The same distribution gives a sufficient number of quickly growing seeds of supermassive black holes observed at high redshifts and may comprise an appreciable fraction of Dark Matter which does not contradict any existing observational limits. Testable predictions of this scenario are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Stochastic particle production in a de Sitter background

Here, we explore non-adiabatic particle production in a de Sitter universe for a scalar spectator field, by allowing the effective mass m 2 (t) of this field and the cosmic time interval between non-adiabatic events to vary stochastically. Two main scenarios are considered depending on the (non-stochastic) mass M of the spectator field: the conformal case with M 2 =2H 2 , and the case of a massless field. We make use of the transfer matrix formalism to parametrize the evolution of the system in terms of the "occupation number", and two phases associated with the transfer matrix; these are used to construct the evolution of the spectator field. Assuming short-time interactions approximated by Dirac-delta functions, we numerically track the change of these parameters and the field in all regimes: sub- and super-horizon with weak and strong scattering. In all cases a log-normally distributed field amplitude is observed, and the logarithm of the field amplitude approximately satisfies the properties of a Wiener process outside the horizon. We derive a Fokker-Planck equation for the evolution of the transfer matrix parameters, which allows us to calculate analytically non-trivial distributions and moments in the weak-scattering limit.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

INERTIAL RANGE TURBULENCE OF FAST AND SLOW SOLAR WIND AT 0.72 AU AND SOLAR MINIMUM

We investigate Venus Express observations of magnetic field fluctuations performed systematically in the solar wind at 0.72 Astronomical Units (AU), between 2007 and 2009, during the deep minimum of solar cycle 24. The power spectral densities (PSDs) of the magnetic field components have been computed for time intervals that satisfy the data integrity criteria and have been grouped according to the type of wind, fast and slow, defined for speeds larger and smaller, respectively, than 450 km s{sup −1}. The PSDs show higher levels of power for the fast wind than for the slow. The spectral slopes estimated for all PSDs in the frequency range 0.005–0.1 Hz exhibit a normal distribution. The average value of the trace of the spectral matrix is −1.60 for fast solar wind and −1.65 for slow wind. Compared to the corresponding average slopes at 1 AU, the PSDs are shallower at 0.72 AU for slow wind conditions suggesting a steepening of the solar wind spectra between Venus and Earth. No significant time variation trend is observed for the spectral behavior of both the slow and fast wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

GWAS supported by computer vision identifies large numbers of candidate regulators of in planta regeneration in Populus trichocarpa

Plant regeneration is an important dimension of plant propagation and a key step in the production of transgenic plants. However, regeneration capacity varies widely among genotypes and species, the molecular basis of which is largely unknown. Association mapping methods such as genome-wide association studies (GWAS) have long demonstrated abilities to help uncover the genetic basis of trait variation in plants; however, the performance of these methods depends on the accuracy and scale of phenotyping. To enable a large-scale GWAS of in planta callus and shoot regeneration in the model tree Populus, we developed a phenomics workflow involving semantic segmentation to quantify regenerating plant tissues over time. We found that the resulting statistics were of highly non-normal distributions, and thus employed transformations or permutations to avoid violating assumptions of linear models used in GWAS. We report over 200 statistically supported quantitative trait loci (QTLs), with genes encompassing or near to top QTLs including regulators of cell adhesion, stress signaling, and hormone signaling pathways, as well as other diverse functions. Our results encourage models of hormonal signaling during plant regeneration to consider keystone roles of stress-related signaling (e.g. involving jasmonates and salicylic acid), in addition to the auxin and cytokinin pathways commonly considered. The putative regulatory genes and biological processes we identified provide new insights into the biological complexity of plant regeneration, and may serve as new reagents for improving regeneration and transformation of recalcitrant genotypes and species.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Uncertainty quantification of mass models using ensemble Bayesian model averaging

Developments in the description of the masses of atomic nuclei have led to various nuclear mass models that provide predictions for masses across the whole chart of nuclides. These mass models play an important role in understanding the synthesis of heavy elements in the rapid neutron capture ( r ) process. However, it is still a challenging task to estimate the size of uncertainty associated with the predictions of each mass model. In this work, a method called ensemble Bayesian model averaging (EBMA) is introduced to quantify the uncertainty of one-neutron separation energies (S 1 n ) which are directly relevant in the calculations of r -process observables. Here, this Bayesian method provides a natural way to perform model averaging, selection, and uncertainty quantification, by combining the mass models as a mixture of normal distributions whose parameters are optimized against the experimental data, employing the Markov chain Monte Carlo method using the no-u-turn sampler. The EBMA model optimized with all the experimental S 1 n from the AME2003 nuclides are shown to provide reliable uncertainty estimates when tested with the new data in the AME2020.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Lattice quantum chromodynamics at large isospin density

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of n-pion correlation functions for n ϵ {1, … , N} using a single N × N matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 charged pions using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass m π = 170 MeV and spacetime volumes of (4.4 3 × 8.8) fm 4 and (5.8 3 × 11.6) fm 4 . We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well-approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential μ I ~ 1.5m π , signaling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound, c s , in the medium is seen to exceed the ideal-gas (conformal) limit ($c^{2}_{s} ≤ 1/3)$ over a wide range of chemical potential before falling towards the asymptotic expectation at μ I ~ 15m π . These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Statistics of baryon correlation functions in lattice QCD

A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in these correlation functions is shown, as long suspected, to result from a sign problem. The log-magnitude and complex phase are found to be approximately described by normal and wrapped normal distributions respectively. Properties of circular statistics are used to understand the emergence of a large time noise region where standard energy measurements are unreliable. Power-law tails in the distribution of baryon correlation functions, associated with stable distributions and “Lévy flights,” are found to play a central role in their time evolution. A new method of analyzing correlation functions is considered for which the signal-to-noise ratio of energy measurements is constant, rather than exponentially degrading, with increasing source-sink separation time. This new method includes an additional systematic uncertainty that can be removed by performing an extrapolation, and the signal-to-noise problem reemerges in the statistics of this extrapolation. It is demonstrated that this new method allows accurate results for the nucleon mass to be extracted from the large-time noise region inaccessible to standard methods. The observations presented here are expected to apply to quantum Monte Carlo calculations more generally. Similar methods to those introduced here may lead to practical improvements in analysis of noisier systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Safe Reinforcement Learning-Based Transient Stability Control for Islanded Microgrids With Topology Reconfiguration

This paper proposes a safe reinforcement learning (RL)-based transient stability emergency control (TSEC) method for islanded microgrids. RL requires extensive interaction with the environment to learn control strategies, hence, a data-driven approach is used as a substitute for time-consuming time-domain simulation calculations. Deep sigma point processes (DSPP), which is a Gaussian process model, is utilized to predict the normal distribution of transient stability of microgrids and to construct a transient stability chance constraint. Reward-constrained policy optimization (RCPO) can simultaneously achieve objective prediction, policy learning, and constraint cost coefficient update across multiple timescales. RCPO interacts with the DSPP-based microgrid environment through a multi-process parallel manner, greatly increasing the training speed. Case studies on a real islanded microgrid demonstrate that the proposed method can efficiently and quickly obtain the optimal emergency control strategy while adhering to all hard constraints.

14 SOLAR ENERGY↗
DOE OSTI2024

An experimentally validated electro-thermal EV battery pack model incorporating cycle-life aging and cell-to-cell variations

Lithium-ion batteries are used in a wide variety of applications. To meet the power and energy demands of these applications battery packs are composed of hundreds to thousands of cells. The electrical and thermal interactions between cells introduce additional complexity in the pack dynamics. To capture these effects, a battery pack model composed of 192 cells based on a first-generation (2012) Nissan Leaf battery pack is developed in MATLAB/Simulink/Simscape. Here, with this model, we simulate the electrical dynamics (using a first-order equivalent-circuit model), the thermal dynamics (using a first-order lumped-parameter thermal model), and the aging dynamics (using a semi-empirical severity factor-based model) of every cell in the pack and we also create a pack thermal model that explicitly captures the heat exchange between the modules, and the cells contained within, during operation. The models are calibrated and validated, both at the cell and pack level, with experimental data. Two different case studies of this pack model are investigated. In the first case study, an initial, normally-distributed, cell-to-cell capacity variation is introduced and its effect on the pack voltage and module temperatures is studied. In the second case study, we deliberately insert cells with lower than nominal capacity into the pack and we investigate how this type of initial cell-to-cell capacity variation affects the pack’s ability to deliver energy over time. Finally, we also study how parallel-connected cells can reduce the effects of cell-to-cell variations at the expense of increased aging of the pack overall.

25 ENERGY STORAGE↗
DOE OSTI2018

High-Frequency Greenhouse Gas Flux Measurement System Detects Winter Storm Surge Effects on Salt Marsh

The physical controlling factors on coastal plant communities are among the most dynamic of known ecosystems, but climate change alters coastal surface and subsurface hydrologic regimes, which makes rapid measurement of greenhouse gas fluxes critical. Greenhouse gas exchange rates in these terrestrial–aquatic ecosystems are highly variable worldwide with climate, soil type, plant community, and weather. Therefore, increasing data collection and availability should be a priority. Here, we demonstrate and validate physical and analytical modifications to automated soil–flux chamber measurement methods for unattended use in tidally driven wetlands, allowing the high–frequency capture of storm surge and day/night dynamics. Winter CO 2 flux from Sarcocornia perennis marsh to the atmosphere was significantly greater during the day (2.8 mg m –2 h –1 ) than the night (2.2 mg m –2 h –1 ) (p < 0.001), while CH 4 was significantly greater during the night (0.16 μg m –2 h –1 ) than the day (–0.13 μg m –2 h –1 ) (p = 0.04). The magnitude of CO 2 flux during the day and the frequency of CH 4 flux were reduced during a surge (p < 0.001). Surge did not significantly affect N 2 O flux, which without non–detects was normally distributed around –24.2 ng m –2 h –1 . Analysis of sustained–flux global potentials for increased storm surge frequency scenarios, 2020 to 2100, suggested that the marsh in winter remains an atmospheric CO 2 sink. The modeled results showed an increased flux of CO 2 to the atmosphere, while in soil, the uptake of CH 4 increased and N 2 O uptake decreased. We present analytical routines to correctly capture gas flux curves in dynamic overland flooding conditions and to flag data that are below detection limits or from unobserved chamber–malfunction situations. Storm surge is an important phenomenon globally, but event–driven, episodic factors can be poorly estimated by infrequent sampling. Here, deployment of this system in coastal marshes worldwide would permit its inclusion in flux calculations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Statistics for Testing Under Adverse Conditions

Here we develop a statistical basis for limited adverse testing. This type of testing simultaneously evaluates system performances against minimum requirements and minimizes costs, particularly for large scale engineering projects. Because testing is often expensive and narrow in scope, the data obtained is relatively limited—precisely the opposite of the recent “large data” movement but no less compelling. Although a remarkably common approach for industrial and large-scale government projects, a statistical basis for adverse testing remains poorly explored. Here we prove mathematically, under specific conditions, that setting each independent variable to an adverse condition leads to a similar level of adversity in the dependent variable. For example, setting all normally distributed independent variables to at least their 95th percentile values leads to a result at the 95th percentile. The analysis considers sample size estimates to clarify the value of replicates in this type of testing, determines how many of the independent variables must be set to adverse condition values, and highlights the essential assumptions, so that engineers, statisticians, and subject matter experts know when this statistical framework may be applied successfully.

42 ENGINEERING↗
DOE OSTI2014

Comparison of two methods for minimizing the effect of delayed charge on the dose delivered with a synchrotron based discrete spot scanning proton beam

Purpose: Delayed charge is a small amount of charge that is delivered to the patient after the planned irradiation is halted, which may degrade the quality of the treatment by delivering unwarranted dose to the patient. This study compares two methods for minimizing the effect of delayed charge on the dose delivered with a synchrotron based discrete spot scanning proton beam. Methods: The delivery of several treatment plans was simulated by applying a normally distributed value of delayed charge, with a mean of 0.001(SD 0.00025) MU, to each spot. Two correction methods were used to account for the delayed charge. Method one (CM1), which is in active clinical use, accounts for the delayed charge by adjusting the MU of the current spot based on the cumulative MU. Method two (CM2) in addition reduces the planned MU by a predicted value. Every fraction of a treatment was simulated using each method and then recomputed in the treatment planning system. The dose difference between the original plan and the sum of the simulated fractions was evaluated. Both methods were tested in a water phantom with a single beam and simple target geometry. Two separate phantom tests were performed. In one test the dose per fraction was varied from 0.5 to 2 Gy using 25 fractions per plan. In the other test the number fractions were varied from 1 to 25, using 2 Gy per fraction. Three patient plans were used to determine the effect of delayed charge on the delivered dose under realistic clinical conditions. The order of spot delivery using CM1 was investigated by randomly selecting the starting spot for each layer, and by alternating per layer the starting spot from first to last. Only discrete spot scanning was considered in this study. Results: Using the phantom setup and varying the dose per fraction, the maximum dose difference for each plan of 25 fractions was 0.37–0.39 Gy and 0.03–0.05 Gy for CM1 and CM2, respectively. While varying the total number of fractions, the maximum dose difference increased at a rate of 0.015 Gy and 0.0018 Gy per fraction for CM1 and CM2, respectively. For CM1, the largest dose difference was found at the location of the first spot in each energy layer, whereas for CM2 the difference in dose was small and showed no dependence on location. For CM1, all of the fields in the patient plans had an area where their excess dose overlapped. No such correlation was found when using CM2. Randomly selecting the starting spot reduces the maximum dose difference from 0.708 to 0.15 Gy. Alternating between first and last spot reduces the maximum dose difference from 0.708 to 0.37 Gy. In the patient plans the excess dose scaled linearly at 0.014 Gy per field per fraction for CM1 and standard delivery order. Conclusions: The predictive model CM2 is superior to a cumulative irradiation model CM1 for minimizing the effects of delayed charge, particularly when considering maximal dose discrepancies and the potential for unplanned hot-spots. This study shows that the dose discrepancy potentially scales at 0.014 Gy per field per fraction for CM1.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-C-18A-04: 3D Markerless Registration of Lung Based On Coherent Point Drift: Application in Image Guided Radiotherapy

Purpose: This study evaluated a new probabilistic non-rigid registration method called coherent point drift for real time 3D markerless registration of the lung motion during radiotherapy. Method: 4DCT image datasets Dir-lab (www.dir-lab.com) have been used for creating 3D boundary element model of the lungs. For the first step, the 3D surface of the lungs in respiration phases T0 and T50 were segmented and divided into a finite number of linear triangular elements. Each triangle is a two dimensional object which has three vertices (each vertex has three degree of freedom). One of the main features of the lungs motion is velocity coherence so the vertices that creating the mesh of the lungs should also have features and degree of freedom of lung structure. This means that the vertices close to each other tend to move coherently. In the next step, we implemented a probabilistic non-rigid registration method called coherent point drift to calculate nonlinear displacement of vertices between different expiratory phases. Results: The method has been applied to images of 10-patients in Dir-lab dataset. The normal distribution of vertices to the origin for each expiratory stage were calculated. The results shows that the maximum error of registration between different expiratory phases is less than 0.4 mm (0.38 SI, 0.33 mm AP, 0.29 mm RL direction). This method is a reliable method for calculating the vector of displacement, and the degrees of freedom (DOFs) of lung structure in radiotherapy. Conclusions: We evaluated a new 3D registration method for distribution set of vertices inside lungs mesh. In this technique, lungs motion considering velocity coherence are inserted as a penalty in regularization function. The results indicate that high registration accuracy is achievable with CPD. This method is helpful for calculating of displacement vector and analyzing possible physiological and anatomical changes during treatment.

60 APPLIED LIFE SCIENCES↗