Cylindrical Region Research Articles

3D fluid model analysis on the generation of negative hydrogen ions for negative ion source of NBI

A radio-frequency (RF) inductively coupled negative hydrogen ion source (NHIS) has been adopted in the China Fusion Engineering Test Reactor (CFETR) to generate negative hydrogen ions. By incorporating the level-lumping method into a three-dimensional fluid model, the volume production and transportation of H− in the NHIS, which consists of a cylindrical driver region and a rectangular expansion chamber, are investigated self-consistently at a large input power (40 kW) and different pressures (0.3–2.0 Pa). The results indicate that with the increase of pressure, the H− density at the bottom of the expansion region first increases and then decreases. In addition, the effect of the magnetic filter is examined. It is noteworthy that a significant increase in the H− density is observed when the magnetic filter is introduced. As the permanent magnets move towards the driver region, the H− density decreases monotonically and the asymmetry is enhanced. This study contributes to the understanding of H− distribution under various conditions and facilitates the optimization of volume production of negative hydrogen ions in the NHIS.

Optimal design of thin-layered composites for type IV vessels: Finite element analysis enhanced by ANN

For a type IV hydrogen storage vessel, the complexity of the mechanical system is a result of the increased number of thin-layered composites and geometrical details at dome parts, which significantly prolongs the computation time for traditional numerical analysis and optimal design. In this work, a framework couples machine learning (ML) and finite element (FE) analysis is proposed for a 70 MPa type IV vessel. Providing an approach that allows the winding parameters optimization process to include the corresponded feasible dome geometry. High-fidelity FE models are established and different failure modes are included. The artificial neural network (ANN) is developed and coupled with the FE models, where the irregularity of directional material distribution on both cylindrical and dome regions is adequately considered during the optimization process. Winding parameters extended by practical production modifications such as transition areas and layer ending adjustments are introduced to the modified input layer of ANN, to ensure the integrality of the complex geometrical details. The computational cost is greatly reduced with satisfying accuracy compared to FE analysis, where the optimized lay-up scheme could be obtained with a prediction error of less than 2% on the damage state function. The associated simulation results show an obvious improvement in mechanical response under designed burst pressure. Particularly, the prototypical vessels are further produced to carry out comparative experiments, which indicate that the burst pressure of the type IV vessel has been improved from 145 MPa to 157.74 MPa. This is also consistent with the numerical prediction of burst pressure using Hashin failure criteria and progressive damage analysis.

Fat mitigation strategies to improve image quality of radial 4D flow MRI in obese subjects.

This study addresses the challenges in obtaining abdominal 4D flow MRI of obese patients. We aimed to evaluate spectral saturation and inner volume excitation as methods to mitigating artifacts originating from adipose signals, with the goal of enhancing image quality and improving quantification. Radial 4D flow MRI acquisitions with fat mitigation (inner volume excitation [IVE] and intermittent fat saturation [FS]) were compared to a standard slab selective excitation (SSE) in a test-retest study of 15 obese participants. IVE selectively excited a cylindrical region of interest, avoiding contamination from peripheral adipose tissue, while FS globally suppressed fat based on spectral selection. Acquisitions were evaluated qualitatively based on expert ratings and quantitatively based on conservation of mass, test-retest repeatability, and a divergence free quality metric. Errors were evaluated statistically using the absolute and relative errors, regression, and Bland-Altman analysis. IVE demonstrated superior performance quantitatively in the conservation of mass analysis in the portal vein, with higher correlation and lower bias in regression analysis. IVE also produced flow fields with the lowest divergence error and was rated best in overall image quality, delineating small vessels, and producing the least streaking artifacts. Evaluation results did not differ significantly between FS and SSE. Test-retest reproducibility was similarly high for all sequences, with data suggesting biological variations dominate the technical variability. IVE improved hemodynamic assessment of radial 4D flow MRI in the abdomen of obese participants while FS did not lead to significant improvements in image quality or flow metrics.

The Quasi-Boundary Regularization Method for Recovering the Initial Value in a Nonlinear Time–Space Fractional Diffusion Equation

In this paper, we consider the inverse problem for identifying the initial value problem of the time–space fractional nonlinear diffusion equation. The uniqueness of the solution is proved by taking the fixed point theorem of Banach compression, and the ill-posedness of the problem is analyzed through the exact solution. The quasi-boundary regularization method is chosen to solve the ill-posed problem, and the error estimate between the regularization solution and the exact solution is given. Moreover, several numerical examples are chosen to prove the effectiveness of the quasi-boundary regularization method. Finally, our method can be used to solve high dimensional time–space fractional nonlinear diffusion equation, especially in cylindrical and spherical symmetric regions.

Multi-Scale Wake Characteristics of the Flow over a Cylinder with Different V-Groove Numbers

The near-wake structure resulting from the interaction between the water and the cylinder is researched. The wake characteristics for the smooth cylinder and the cylinder with different numbers of grooves are measured by high-speed particle image velocimetry (PIV) at a Reynolds number of 7400. From the measured data, it is observed that the v-groove increases the Reynolds shear stress and the turbulent kinetic energy; thus, the formation of the Karman-like vortices is prevented and the recirculation region is reduced. The number of grooves has a limited effect on the wake characteristics. In addition, a one-dimensional orthogonal wavelet decomposes the fluctuation velocities in the cylindrical wake region to study the multi-scale wake characteristics behind the v-groove cylinders. The large-scale structures show that the Karman-like vortices of the grooved cylinder are closer to the trailing edge of the cylinder. The intermediate-scale structures show more vortices behind the 32-groove cylinder. The small-scale structures show that the phase difference between the upper and lower oscillation positions has become smaller. Meanwhile, the large-, intermediate- and small-scale Reynolds shear stress distributions suggest that the shear layer instability in the near-wake region creates vortices, which increase the turbulent kinetic energy and narrow the wake region.

Systematic dosimetric evaluation of risk of osteoradionecrosis (DERO): First results of dose reporting for preventing teeth osteoradionecrosis after head and neck irradiation

PurposeOsteoRadioNecrosis (ORN) is a late complication of radiation for head and neck cancer. Predicting ORN is a major challenge. We developed DERO (Dosimetric Evaluation of Risk of ORN), a semi-automatic tool which reports doses delivered to tooth-bearing sectors, to guide post-therapeutic dental care. We present the method and the first results of a 125-patient prospective cohort. Material and methodsDosimetric data of patients treated with IMRT for head and neck cancer were prospectively segmented to the DERO algorithm. Four arches corresponding to 8-tooth sectors were semi-automatically generated. Thirty-two cylindrical Regions Of Interest (ROI) corresponding to each tooth and surrounding periodontium were created by linear interpolation. Mean doses (Dmean) of ROI were extracted and included in a database, along with data about primary tumor site, laterality and dose values from organs at risk. Dmean to tooth sectors were computed for molar sectors, (teeth X5 to X8) and anterior sectors (teeth X1 to X4). An individual dose map was generated and delivered to patients and dentists. ResultsDosimetric data from 125 patients treated with Tomotherapy® were prospectively collected and analyzed: 9 parotid tumors (PA), 41 Sub-Hyoid tumors (larynx, hypopharynx) (SH), 43 Oropharynx tumors (OR), 32 Oral Cavity tumors (OC). Irradiation was unilateral for 100% of PA tumors (9), 12% of OR tumors (5) and 47% of OC tumors (15). For unilateral cervical irradiation, Dmean in ipsilateral molar sectors was 54Gy for OC tumors, 45Gy for OR tumors, 20Gy for PA tumors. For Oral Cavity bilateral irradiation, Dmean was high in all tooth sectors, 49 to 55Gy. For SH tumors, Dmean in molar sectors was 27Gy. A dose gradient of 10 to 20Gy was observed between molar and anterior sectors whether radiation was uni or bilateral. ConclusionMandibular molar sectors of Oropharynx and Oral Cavity tumors were exposed to high Dmean of 40 to 50Gy. On the other hand, tooth sectors received lower doses for SH radiation. The DERO tool guide post-radiation dental care with a personalized dosimetric cartography to patient. With data update and patient follow-up, we will be able to determine ORN risk after head and neck radiation.

Spiral flows of ABC fractionalized rate type fluids in cylindrical region: an increasingly amplitude of oscillation study through complex analysis applications

The concern of the present research is to explore the fractionalized Oldroyd-B fluid with the influence of MHD effect, enclosed by two endless uniaxial circular cylinders, by utilizing Laplace transform with Antangano Baleanu factional operator and finite Hankel transform. Both cylinders are moving together about its same axis. The movement is produced by the inner and outer cylinders from rest, as a result of the rotational together with translational time-dependent velocities. The analytical outcomes of flow rate and corresponding to the tangential stress are introduced by integral and series pattern in form of the generalized function M. The solutions that have been satisfying all impose account conditions. The comparable solutions can easily be achieved for ordinary Oldroyd-B, Maxwell, second grade as well as Newtonian fluid, as exclusive cases of the generalized results. In the end, the graphical illustration depicted, to predict the impact of the relaxation time and non-integer order fractional material on the fluid flow, as well as comparison between the equations.

Secondary ultrasonic atomisation mechanisms

Liquid atomisation is the basis for various practical applications such as pharmaceuticals, cosmetics, food industry, etc. In this case, the main challenge is the development of high-performance, highly dispersed atomisation systems. Generally, high-throughput atomisation systems form aerosol with large droplet sizes, and high-disperse atomisation systems have low performance. Secondary ultrasonic atomisation can solve this problem by allowing non-contact crushing of already formed aerosol droplets with large droplet sizes by means of a high-intensity ultrasonic field. For this purpose, a pre-generated stream of liquid droplets is directed into a cylindrical region formed by an emitter in which a high-intensity ultrasonic field is generated. Ultrasonic radiator, is a tube of stepped-variable cross-section, providing the formation of bending-diametral or diametral oscillations at a frequency above 20 kHz. At sufficiently high ultrasound intensity, conditions for further crushing of liquid droplets are realised, which leads to the formation of a highly dispersed aerosol. This paper describes the proposed mathematical model of the atomisation process and finds the regularities of the process depending on the determining parameters of the ultrasonic field and physical and chemical properties of the liquid. Two mechanisms of jet destruction are revealed: direct destruction of droplets when they hit the ultrasonic wave front and cavitation mechanism of droplet and jet destruction. The dominant crushing mechanism depends on the problem parameters and, in turn, determines the minimum size of the resulting droplets. The results of this work will help to optimise the secondary ultrasonic atomisation process and improve liquid atomisation technologies in various applications.

FRACTIONAL MODEL IN THE THEORY OF GENERALIZED THERMOELASTIC DIFFUSION

A problem for thermoelastic thick plate of infinite extension and finite thickness is considered, where a permeating substance is in contact with one of the bounding planes in the context of generalized thermoelastic diffusion theory with fractional parameter. The upper surface is assumed to be traction-free, subject to time-dependent thermal shock, and the chemical potential is also assumed to be a known function of time. The lower surface of the plate is laid on an insulated rigid foundation. Laplace and Hankel transform techniques are used. Analytical solutions in the transform domain are obtained using direct methods. The inverse of the double transform is obtained using a numerical method based on the Fourier expansion technique. A general solution to the cylindrical region problem is obtained. The solution can calculate under any boundary conditions. All numerical results are in perfect agreement with earlier work in various thermoelastic theories. Numerical calculations are performed for two different time values and for three distinct fraction parameter values. Temperature, stress, displacement, concentration, and chemical potential are displayed graphically. Comparisons are made with the results of the previous theory.

Numerical investigation of MHD convective free stream nanofluid flow influenced by radiation and chemical reaction over stretching cylinder

AbstractChemically reacting magnetohydrodynamic radiative flow of convective free stream nanofluid through a stretching cylinder using Buongiorno's model is discussed. The behavior of Brownian motion and thermophoresis is also appropriate. By adopting the similarity transformation, the partial differential equation is diminished into a first‐order ordinary differential equation (ODE). Since transformed equations are highly nonlinear these ODEs are solved by using mathematical simulation. The shooting procedure has been adopted to resolve converted equations along the attendant Runge–Kutta–Fehlberg technique. The reason behind the present work is to research the effects of different parameters of fluid, namely, magnetic parameter, free stream velocity, Brownian motion, thermophoresis, chemical reaction, heat radiation, Lewis number on nanoparticle concentration, temperature, and velocity distribution. The impact of significantly participating parameters on velocity, concentration, and temperature distribution is distinguished with appropriate physical significance. The convergence of solutions for temperature, velocity, and concentration profiles is studied carefully. The measured challenges of nanofluids are scale‐up capacity, increase in nanofluid viscosity, nanoparticle dispersion, and nanofluid cost. It is observed that nanoparticle temperature rises for more value of Brownian motion parameter while it declines for higher Lewis number. The current study in the cylindrical region is related to novel free stream flow in the presence of chemical reactions along with convective conditions which find applications in electronic systems like microprocessors and in a wide variety of industries and in the field of biotechnology. The current research helps control the transport phenomena, helping production companies to find the quality of the desired product.

Performance bounds of magnetic traps for neutral particles

Knowledge of the fundamental limitations on a magnetic trap for neutral particles is of paramount interest to designers as it allows for the rapid assessment of the feasibility of specific trap requirements or the quality of a given design. In this paper, performance limitations are defined for convexity of magnetic trapping potential and bias field using a local approximation in the trapping center. As an example, the fundamental bounds are computed for current supporting regions in the form of a spherical shell, a cylindrical region, and a box. A Pareto-optimal set considering both objectives is found and compared with known designs of the Baseball trap and Ioffe-Pritchard trap. The comparison reveals a significant gap in the performance of classical trap designs from the fundamental limitations. This indicates a possibility of improved trap designs and modern techniques of shape synthesis are applied in order to prove their existence. The topologically optimized traps perform almost two times better as compared to conventional designs. Last, but not least, the developed framework might serve as a prototype for the formulation of fundamental limitations on plasma confinement in a wider sense.

The cosmic-ray induced sputtering process on icy grains

ABSTRACT In molecular cloud cores, the cosmic ray (CR) induced sputtering via CR ion-icy grain collision is one of the desorption processes for ice molecules from mantles around dust grains. The efficiency of this process depends on the incident CR ion properties as well as the physicochemical character of the ice mantle. Our main objective is the examination of the sputtering efficiency for H2O and CO ices found in molecular cloud cores. In the calculation routine, we consider a multidimensional parameter space that consists of 30 CR ion types, 5 different CR ion energy flux distributions, 2 separate ice mantle components (pure H2O and CO), 3 ice formation states, and 2 sputtering regimes (linear and quadratic). We find that the sputtering behaviour of H2O and CO ices is dominated by the quadratic regime rather than the linear regime, especially for CO sputtering. The sputtering rate coefficients for H2O and CO ices show distinct variations with respect to the adopted CR ion energy flux as well as the grain-size-dependent mantle depth. The maximum radius of the cylindrical latent region is quite sensitive to the effective electronic stopping power. The track radii for CO ice are much bigger than H2O ice values. In contrast to the H2O mantle, even relatively light CR ions (Z ≥ 4) may lead to a track formation within the CO mantle, depending on Se,eff. We suggest that the latent track formation threshold can be assumed as a separator between the linear and the quadratic regimes for sputtering.

Electronic excitation driven structural evolution in Ce0.8Zr0.2O2

The cubic phasic CeO2–ZrO2 system with the composition Ce0.8Zr0.2O2 has been synthesized at room temperature. Highly dense pellets were synthesized by standard solid-state route. Fluorite structured cubic phase was probed by X-ray diffraction along with a qualitative analysis through Rietveld refinement. A ‘pseudocubic’ phase of pristine material was noted experimentally by Raman vibrational modes corresponding to anionic displacement in cubic phase and theoretically explained as the tetragonal anionic arrangement (P42/nmc) at nanoscale embedded in framework of cubic structure (Fm3‾m). Electron microscopy accompanied by density measurement was employed to conclude that the synthesized ceramic has a very compact surface morphology with a density ∼95% of its theoretical value. The as-prepared pellets were irradiated with 100 MeV I7+ ions to mimic energy loss by fission fragment during reactor operation. A comprehensive investigation of structural damage was done through the analysis of diffraction patterns of irradiated samples. We carefully estimated the damaged regions with diameter as ∼3.18 nm and ∼2.54 nm from irradiation induced peak broadening and lattice swelling, respectively. These results are fully capable to conceptualize a model about the damaged cylindrical region along ion trajectory. A central region (∼2.54 nm) consists of extended defects revealed by lattice swelling. Moreover, an annular region (width ∼0.32 nm) consists of vacancy type simple defects accommodated in as-synthesized lattice structure. These results reveal excellent structural properties of CeO2–ZrO2 modelled system comparable to PuO2−ZrO2.

Cylindrical Rod Phosphor Structure for Laser-Driven White Lighting

In this article, a cylindrical rod phosphor structure was developed and used for laser-driven white lighting. The blue light emitting from the laser diode (LD) with limited divergence enters the cylindrical rod containing phosphor and excites the yellow phosphor particles in the cylindrical rod to generate white light. Multiple phosphor blends with yellow and red phosphors were also applied to the cylindrical rod phosphor structure to enhance the red luminescence of white light with a low correlated color temperature (CCT). An advanced structure with a surrounding transparent layer around the central cylindrical rod containing phosphors was also investigated to enhance the possibility of the blue light absorption by phosphors in the cylindrical rod region away from the LD. The cylindrical rod phosphor structures with or without the surrounding transparent layer were fabricated to produce laser-driven white lighting, and the optical characteristics of the cylindrical rod phosphor structures with different phosphor concentrations or yellow-to-red phosphor weight ratios were examined.

Repeatability and Reproducibility of Radiomic Features Produced over Time by the Fan-Beam kV-CT on a Novel Ring Gantry-Based PET/CT Linear

<h3>Purpose/Objective(s)</h3> The RefleXion® X1 is a new external-beam radiotherapy delivery system on a ring gantry with dual imaging systems fan-beam kV-CT and PET. The imaging system has the potential to be used for cancer prognosis and treatment response assessment using the radiomic features obtained from daily treatment images. The scanning variability in radiomics features and the differences between scanning protocols must be evaluated to warrant the accuracy of the prediction model. This study aims to establish the technical validation of the repeatability and reproducibility of radiomic features produced by the X1 kV-CT. <h3>Materials/Methods</h3> The Credence Cartridge Radiomics phantom was scanned 10 times on the X1 system over a 3-month time frame using the two most frequently used scanning protocols: head/medium dose/fast couch and body/medium dose/slow couch. A cylindrical region of interest of 8.0cm in diameter x 1.5cm in thickness was contoured for each of the 6 cartridges. The 6 cartridges are each comprised of different materials using acrylonitrile butadiene styrene, acrylic beads, polyvinyl chloride, hemp seeds encased in polyurethane, shredded rubber and dense cork. These materials were chosen to produce a range of radiomics feature values. 66 radiomic features were extracted using a widely available, IBSI-compliant radiomics software package. Linear regression analysis was performed to evaluate the repeatability and reproducibility over time. T-test for the difference in the mean and F-test for the difference in standard deviation was used to compare the radiomics features between scanning techniques. <h3>Results</h3> There was no significant variation of radiomic features over time. Based on linear regression analysis between the radiomic features and number of elapsed days since the initial scan, the fitted coefficient was less than 0.05 for all the radiomic features (scaled so that the mean value was unity). There was no strong linear relationship between radiomic features and elapsed days (R2 <= 0.02 in all regression analysis results). As reported in other studies, a comparison of radiomic features within each of the six cartridges demonstrated that up to 38 of the 66 radiomic features showed statistically significant differences between the fast scan and the slow scan protocols (two-tailed p value < 0.05 in paired t-tests) and up to 25 radiomic features had statistically significant differences in standard deviations between the fast and slow scan protocols (p value < 0.05 in F-tests), indicating the necessity of using consistent scan protocols to monitor radiomic features throughout the treatment course accurately. <h3>Conclusion</h3> The clinically useful CT radiomic features produced by the X1 are reproducible over time, demonstrating its utility as a quantitative imaging platform. The CT radiomic features produced by the X1 vary significantly with the scanning protocols. Evaluating radiomics feature changes over time requires image acquisition using the same scanning protocol.

Electromagnetic Wave Scattering by a Multiple Core Model of Composite Cylindrical Wires at Oblique Incidence

A complex cylindrical structure consisting of a group of parallel stratified circular lossy dielectric cylinders, embedded in a dielectric circular cylindrical region and surrounded by unbounded dielectric space, is considered in this paper. The scattering of electromagnetic (EM) plane waves by the aforementioned configuration was studied; the EM waves impinged obliquely upon the structure and were arbitrarily polarized. The formulation used was based on the boundary-value approach coupled with the generalized separation of variables method. The EM field in each region of space was expanded in cylindrical wave-functions. Furthermore, the translational addition theorem of these functions was applied in order to match the EM field components on any cylindrical interface and enforce the boundary conditions. The end result of the analysis is an infinite set of linear algebraic equations with the wave amplitudes as unknowns. The system is solved by the truncation of series and unknowns and then matrix inversion; thus, we provide a semi-analytical solution for the scattered far-field and, as a consequence, for the scattering cross section of the complex cylindrical structure. The numerical results focus on calculations of the electric- and magnetic-field intensity of the far-field as well as of the total scattering cross section of several geometric configurations that fall within the aforementioned general structure. The effect of the geometrical and electrical characteristics of the structure on the scattered field was investigated. Specifically, the cylinders’ size and spacing, their conductivity and permittivity as well as the incidence direction were modified in order to probe how these variations are imprinted on scattering. Moreover, comparisons with previously published results, as well as convergence tests, were performed; all tests and comparisons proved to be successful.

On the application of the Fourier method to solve the problem of correction of thermographic images

The work is devoted to the construction of computational algorithms implementing the method of correction of thermographic images. The correction is carried out on the basis of solving some ill-posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. This problem corresponds to the problem of the analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study towards the heat sources. The cylindrical region is bounded by an arbitrary surface and plane. On an arbitrary surface, a temperature distribution is measured (and thus is known). It is called a thermogram and reproduces an image of the internal heat-generating structure. On this surface, which is the boundary of the object under study, convective heat exchange with the external environment of a given temperature takes place, which is described by Newton’s law. This is the third boundary condition, which together with the first boundary condition corresponds to the Cauchy conditions - the boundary values of the desired function and its normal derivative. The problem is ill-posed. In this paper, using the Tikhonov regularization method, an approximate solution of the problem was obtained, stable with respect to the error in the Cauchy data, and which can be used to build effective computational algorithms. The paper considers algorithms that can significantly reduce the amount of calculations.

Thermal Friction Drilling Process Parametric Optimization for AISI 304 Stainless Steel Using an Integrated Taguchi-Pareto–Grey Wolf-Desirability Function Analysis Optimization Technique

Thermal friction estimations are presently essential on steel for manufacturing applications as they predict the aggregated energy required for the required process. However, the current thermal friction estimates are inaccurate as they exclude the optimized thresholds of both the input and output quantities. In this article, the optimization of the drilling operation process is accounted for by introducing a new method of combined Taguchi-Pareto–grey wolf-desirability function analysis applied on the AISI 304 stainless steel. An objective function was formulated using the delta values developed from the average signal-to-noise into the response table of the Taguchi method. Besides, the ranks of the parameters through the response table are taken in the reciprocal mode to evaluate the values of the linear program formulated according to the objective function and some constraints taken from the system. Six input parameters were considered tool cylindrical region diameter, friction angle, friction contact area ratio, mouthpiece thickness, feed rate and reciprocal speed. The outputs are the axial force, radial force, hole diameter dimensional error, roundness error and bushing length. These inputs and outputs were analyzed for the optimization process. Based on the results, which were solved using the C++ software, the best value converges in iteration 8 with the starting value of 1699.2. Iteration 1 drops to 11016.3 in six iterations (iterations 2 to 7) and finally converges at 11015.9 in iterations 8 through 20. The usefulness of the effort is to help process engineers to execute cost-effective energy conservation decisions in optimization that could be obtained using optimized thermal friction values.

Pairwise interaction Markov model for 3D epidermal nerve fibre endings.

In this paper, the spatial arrangement and possible interactions between epidermal nerve fibre endings are investigated and modelled by using confocal microscopy data. We are especially interested in possible differences between patterns from healthy volunteers and patients suffering from mild diabetic neuropathy. The locations of the points, where nerves enter the epidermis, the first branching points and the points where the nerve fibres terminate, are regarded as realizations of spatial point processes. We propose an anisotropic point process model for the locations of the nerve fibre endings in three dimensions, where the points interact in cylindrical regions. First, the locations of end points in are modelled as clusters around the branching points and then, the model is extended to three dimensions using a pairwise interaction Markov field model with cylindrical neighbourhood for the z-coordinates conditioned on the planar locations of the points. We fit the model to samples taken from healthy subjects and subjects suffering from diabetic neuropathy. In both groups, after a hardcore radius, there is some attraction between the end points. However, the range and strength of attraction are not the same in the two groups. Performance of the model is evaluated by using a cylindrical version of Ripley's K function due to the anisotropic nature of the data. Our findings suggest that the proposed model is able to capture the 3D spatial structure of the endpoints.

Well-tempered metadynamics applied to field-theoretic simulations of diblock copolymer melts.

Well-tempered metadynamics (WTMD) is applied to field-theoretic simulations (FTS) to locate the order-disorder transition (ODT) in incompressible melts of diblock copolymer with an invariant polymerization index of N̄=104. The polymers are modeled as discrete Gaussian chains with N = 90 monomers, and the incompressibility is treated by a partial saddle-point approximation. Our implementation of WTMD proves effective at locating the ODT of the lamellar and cylindrical regions, but it has difficulty with that of the spherical and gyroid regions. In the latter two cases, our choice of order parameter cannot sufficiently distinguish the ordered and disordered states because of the similarity in microstructures. The gyroid phase has the added complication that it competes with a number of other morphologies, and thus, it might be beneficial to extend the WTMD to multiple order parameters. Nevertheless, when the method works, the ODT can be located with impressive accuracy (e.g., ΔχN ∼ 0.01).