Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails

AAFE large deployable antenna development program: Executive summary

The large deployable antenna development program sponsored by the Advanced Applications Flight Experiments of the Langley Research Center is summarized. Projected user requirements for large diameter deployable reflector antennas were reviewed. Trade-off studies for the selection of a design concept for 10-meter diameter reflectors were made. A hoop/column concept was selected as the baseline concept. Parametric data are presented for 15-meter, 30-meter, and 100-meter diameters. A 1.82-meter diameter engineering model which demonstrated the feasiblity of the concept is described

Numerical methods of geomechanics tasks solution during coal deposits’ development

Purpose. Generalization of numerical modeling of geomechanical processes in the vicinity of mine workings by finite elements method and making recommendations for substantiation of suitable construction and behavior of rock massif physical model. Methods. Software packages SolidWorks Simulation (COSMOS/М) and ANSYS are used for geomechanical tasks solution. Findings. Solutions of geomechanical tasks dealing with topical issues of estimating stress-strain state of rock massif around underground workings of different functions are given. Data on the rock massif stress-strain state are received and recommendations on adequate and authentic reflection of its structural peculiarities (stratification and fracturing) are made. Physical model of rock condition (elastic, elastic-plastic, rheological diagrams and complete diagram of deformation taking into account weakening and fracturing) is presented. Originality. New data about the mechanism of movement processes of coal-bearing massif around mine workings considering stratification and cracks content, limit and out-of-limit deflection state in separate areas, and also the impact of rheological rock properties are received. Practical implications. Complex of geomechanical tasks solutions allow to increase credibility of rock pressure manifestations prediction and substantiate technical solutions for effective and safe operations at coal mines.Цель. Обобщение опыта численного моделирования методом конечных элементов геомеханических процессов вокруг горных выработок и формирование рекомендаций по обоснованию адекватного строения и поведения физической модели горного массива. Методика. Для решения задач геомеханики использованы пакеты прикладных программ SolidWorks Simulation (COSMOS/М) и ANSYS. Результаты. Приведены решения геомеханических задач по актуальным вопросам оценки НДС горного массива вокруг подземных выработок различного назначения. Получены закономерности поведения горного массива и даны рекомендации по адекватному и достоверному отражению его текстурных особенностей (слоистость и трещиноватость) и физической модели состояния горной породы (упругая, упруго-пластическая, реологическая, полная диаграмма деформирования с учетом разупрочнения и разрыхления). Научная новизна. Получен ряд новых закономерностей развития процессов сдвижения углевмещающего массива вокруг горных выработок с учетом его слоистости и трещиноватости, предельного и запредельного состояния в отдельных областях, а также влияния реологических свойств горных пород. Практическая значимость. Комплекс решений геомеханических задач позволяет повысить достоверность прогноза проявлений горного давления и обосновать технические решения по эффективному и безопасному ведению горных работ на угольных шахтах.Мета. Узагальнення досвіду чисельного моделювання методом скінченних елементів геомеханічних процесів навколо гірничих виробок і формування рекомендацій з обґрунтування адекватної будови й поведінки фізичної моделі гірського масиву. Методика. Для розв’язання задач геомеханіки використані пакети прикладних програм Solidworks Simulation (COSMOS/М) і ANSYS. Результати. Наведено розв’язання геомеханічних задач з актуальних питань оцінки НДС гірського масиву навколо підземних виробок різного призначення. Отримано закономірності поведінки гірського масиву й надано рекомендації з адекватного й достовірного відображення його текстурних особливостей (шаруватість і тріщинуватість) та фізичної моделі стану гірської породи (пружна, пружно-пластична, реологічна, повна діаграма деформування з урахуванням знеміцнення і розпушення). Наукова новизна. Отримано низку нових закономірностей розвитку процесів зрушення вуглевміщуючого масиву навколо гірничих виробок з урахуванням його шаруватості й тріщинуватості, граничного й позамежного станів в окремих областях, а також впливу реологічних властивостей гірських порід. Практична значимість. Комплекс розв’язань геомеханічних задач дозволяє підвищити вірогідність прогнозу проявів гірського тиску й обґрунтувати технічні розв’язання з ефективного й безпечного ведення гірничих робіт на вугільних шахтах.The materials discussed in the article were received while performing a complex of research works at the request of a number of industrial enterprises in coal mining in Donbas. The authors are grateful to M. Illiashov, M. Barabash, Yu. Cherednychenko, O. Vivcharenko, V. Chervatiuk, O. Husiev for providing mine-and-geological and technical information on features of conducting mining operations at their enterprises, and also for useful recommendations and fruitful discussion of the received results which are intended to provide an effective solution to mine-technical issues in coal mining

Eye shape and retinal shape, and their relation to peripheral refraction

Purpose: We provide an account of the relationships between eye shape, retinal shape and peripheral refraction. Recent findings: We discuss how eye and retinal shapes may be described as conicoids, and we describe an axis and section reference system for determining shapes. Explanations are given of how patterns of retinal expansion during the development of myopia may contribute to changing patterns of peripheral refraction, and how pre-existing retinal shape might contribute to the development of myopia. Direct and indirect techniques for determining eye and retinal shape are described, and results are discussed. There is reasonable consistency in the literature of eye length increasing at a greater rate than height and width as the degree of myopia increases, so that eyes may be described as changing from oblate/spherical shapes to prolate shapes. However, one study indicates that the retina itself, while showing the same trend, remains oblate in shape for most eyes (discounting high myopia). Eye shape and retinal shape are not the same and merely describing an eye shape as being prolate or oblate is insufficient without some understanding of the parameters contributing to this; in myopia a prolate eye shape is likely to involve both a steepening retina near the posterior pole combined with a flattening (or a reduction in steepening compared with an emmetrope) away from the pole

Three-dimensional analysis of mandibular landmarks, planes and shape, and the symphyseal changes associated with growth and orthodontic treatment

OBJECTIVE: To test reliability of 3D mandibular landmarks, planes of reference and surfaces and assess their correlation to conventional 2D cephalometric measurements. To analyze changes in three-dimensional shape of the symphysis due to growth and orthodontic treatment. METHODS: This was a retrospective analysis of CBCTs of healthy orthodontic patients. 32 subjects were included, 16 males and 16 females. Mean ages of 10.6 ± 1.5 years and 15.0 ± 0.9 years before and after treatment, respectively. The mean follow up time was 4.3 years. Subjects free of any craniofacial anomalies, and no observable pathology on panoramic radiograph were. 15 subjects had CVM 1 and 17 subjects had CVM 2 before orthodontic treatment. All subjects had CVM 5 after orthodontic treatment. For the first phase, 3D mandibular landmark identifications were digitized. Planes and landmarks were constructed and compared with conventional 2D mandibular measurements. For the second phase, mandibles were isolated by removing surrounding structures. Pearson correlation and paired t-test were performed to test for correlation and differences between 2D and 3D measurements, respectively. Statistical analysis was performed using SAS 9.4. Software. MorphoJ software (Version 2.0, www.flywings.org.uk) was used for symphysis shape analysis; and Discriminant Function Analysis (DFA) between pre-treatment and post-treatment was used for statistical analysis of the symphysis. RESULTS: We found statistical significant positive correlation between 2D and 3D pre-treatment ramus height (P-value =0.01), post-treatment ramus height (P-value < 0.0001), pre-treatment corpus length (P-value 0.0003), post-treatment corpus length (P-value 0.04), pre-treatment gonial angle (P-value <0.0001), and post-treatment gonial angle (P-value=0.05). Also, statistically significant differences in 2D ramus height (P=0.001), 3D ramus height (P-value=0.002), 2D corpus length (P-value <0.01), and 3D corpus length (P-value <0.01). For symphysis shape comparing between pre-treatment and post-treatment, we found that there is no statistically significant difference between them (P-value= 0.99). CONCLUSION: These results demonstrated statistically significant positive correlation between certain 2D and 3D measurements, pre-treatment and post-treatment differences in 2D and 3D measurements showed consistent results. Symphysis shapes do break out as distinctly separate groups, but the differences between the means is small

How Filaments are Woven into the Cosmic Web

Observations indicate galaxies are distributed in a filament-dominated web-like structure. Numerical experiments at high and low redshift of viable structure formation theories also show filament-dominance. We present a simple quantitative explanation of why this is so, showing that the final-state web is actually present in embryonic form in the overdensity pattern of the initial fluctuations, with nonlinear dynamics just sharpening the image. The web is largely defined by the position and primordial tidal fields of rare events in the medium, with the strongest filaments between nearby clusters whose tidal tensors are nearly aligned. Applications of the cosmic web theory to observations include probing cluster-cluster bridges by weak gravitational lensing, X-rays, and the Sunyaev-Zeldovich effect and probing high redshift galaxy-galaxy bridges by low column density Lyman alpha absorption lines.Comment: 9 pages, gzipped uuencoded postscript file, 4 figures in separate files. The text + figures are also available from anonymous ftp site: ftp://ftp.cita.utoronto.ca/ftp/cita/bond/bkp_natur

Improvement of irregular dtm for sph modelling of flow-like landslides

Irregular topography of real slopes largely affects the propagation stage of flowlike landslides and accurate digital terrain models (DTMs) are absolutely necessary for realistic simulations and assessments. In this paper a simple yet effective method is proposed to improve the accuracy of existing DTMs which is applied to the topographical models used in well equipped laboratory experiments. Aimed at evaluating the effects of different DTMs in the results of the propagation modelling, a depth-integrated SPH model is used to simulate two series of laboratory tests referring to a frictional rheological model while using either the available DTM or the DTM improved through the proposed procedure. The obtained results show that the proposed method provides a more accurate topographical model for all the analyzed cases. Particularly, the new topographical model allows better reproducing the laboratory evidences in terms of run-out distances, inundated areas and geometrical characteristics of the final deposits. Furthermore, SPH analyses with progressively finer topographical inputs outline the role of DTM’s precision towards the accuracy of the numerical simulations

Optimal boundary geometry in an elasticity problem: a systematic adjoint approach

p. 509-524In different problems of Elasticity the definition of the optimal geometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables. Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.Garcia-Palacios, J.; Castro, C.; Samartin, A. (2009). Optimal boundary geometry in an elasticity problem: a systematic adjoint approach. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654

Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography

A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver. Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography. Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function. An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion