scholarly journals Three-Dimensional Enclosures

2020 ◽  
pp. 621-672
Author(s):  
Steven L. Garrett
Keyword(s):  
Separation Of Variables ◽  
Three Dimensional ◽  
Normal Modes ◽  
Sound Field ◽  
Statistical Energy Analysis ◽  
Link Type ◽  
Wave Solutions ◽  
Different Shapes ◽  
The Individual ◽  
Degenerate Modes

Abstract In this chapter, solutions to the wave equation that satisfies the boundary conditions within three-dimensional enclosures of different shapes are derived. This treatment is very similar to the two-dimensional solutions for waves on a membrane of Chap. 10.1007/978-3-030-44787-8_6. Many of the concepts introduced in Sect. 10.1007/978-3-030-44787-8_6#Sec1 for rectangular membranes and Sect. 10.1007/978-3-030-44787-8_6#Sec5 for circular membranes are repeated here with only slight modifications. These concepts include separation of variables, normal modes, modal degeneracy, and density of modes, as well as adiabatic invariance and the splitting of degenerate modes by perturbations. Throughout this chapter, familiarity with the results of Chap. 10.1007/978-3-030-44787-8_6 will be assumed. The similarities between the standing-wave solutions within enclosures of different shapes are stressed. At high enough frequencies, where the individual modes overlap, statistical energy analysis will be introduced to describe the diffuse (reverberant) sound field.

Nonlinear dynamical wave structures to the Date–Jimbo–Kashiwara–Miwa equation and its modulation instability analysis

2021 ◽  
pp. 2150300
Author(s):  
M. Younis ◽  
A. R. Seadawy ◽  
M. Bilal ◽  
S. T. R. Rizvi ◽  
Saad Althobaiti ◽  
...  
Keyword(s):  
Function Method ◽  
Modulation Instability ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Two Dimensional ◽  
Instability Analysis ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Different Shapes

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters.

scholarly journals The use of Catastrophe Theory to Analyse the Stability and Toppling of Icebergs

1980 ◽  
Vol 1 ◽  
pp. 49-54 ◽  
Author(s):  
J. F. Nye ◽  
J. R. Potter
Keyword(s):  
Catastrophe Theory ◽  
Three Dimensional ◽  
Theory Approach ◽  
Rectangular Section ◽  
Small Oscillations ◽  
Density Distributions ◽  
Conceptual Clarity ◽  
Different Shapes ◽  
The Stability ◽  
The Individual

As an iceberg melts, the resulting change of shape can cause it to list gradually or to become unstable and topple over suddenly. Similarly, when an iceberg breaks up some of the individual pieces may capsize. We have used Zeeman’s analysis of the stability of ships, which is based on catastrophe theory, to examine this problem. We deal only with statical equilibrium; dynamical effects induced by water motion are important for ships, but very large icebergs have correspondingly small oscillations and therefore dynamical aspects are ignored in this first study. The advantage of the catastrophe-theory approach over the conventional stability theory used by naval architects lies in the conceptual clarity that it provides. In particular, it gives a three-dimensional geometrical picture that enables one to see all the possible equilibrium attitudes of a given iceberg, whether they are stable or unstable, whether a stable attitude is dangerously close to an unstable one, and how positions of stable equilibrium can be destroyed as the shape of the iceberg evolves with time.By making two-dimensional computations we examine the stability of two different shapes of cross-section, rectangles and trapezia, with realistic density distributions. These shapes may list gradually or topple suddenly as a single parameter is changed. For example, we find that a conversion of the vertical sides of a rectangular section into the slightly inward-sloping sides of a trapezium has a comparatively large adverse effect on stability. The main purpose of this work is to suggest how the stability characteristics of any selected iceberg may be investigated systematically.

Semi-automated methods for 3-D reconstruction of macromolecular complexes

1995 ◽  
Vol 53 ◽  
pp. 42-43
Author(s):  
B. Carragher ◽  
M. Whittaker
Keyword(s):  
Three Dimensional ◽  
Time Saving ◽  
Macromolecular Complexes ◽  
Symmetry Properties ◽  
Dimensional Reconstruction ◽  
Experienced Operator ◽  
Projection Images ◽  
The Individual ◽  
Natural Symmetry

Techniques for three-dimensional reconstruction of macromolecular complexes from electron micrographs have been successfully used for many years. These include methods which take advantage of the natural symmetry properties of the structure (for example helical or icosahedral) as well as those that use single axis or other tilting geometries to reconstruct from a set of projection images. These techniques have traditionally relied on a very experienced operator to manually perform the often numerous and time consuming steps required to obtain the final reconstruction. While the guidance and oversight of an experienced and critical operator will always be an essential component of these techniques, recent advances in computer technology, microprocessor controlled microscopes and the availability of high quality CCD cameras have provided the means to automate many of the individual steps.During the acquisition of data automation provides benefits not only in terms of convenience and time saving but also in circumstances where manual procedures limit the quality of the final reconstruction.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

Phonetic iconicity in the evaluative morphology of a sample of Indo-European, Niger-Congo and Austronesian languages

2010 ◽  
Vol 3 (2) ◽  
pp. 156-180 ◽  
Author(s):  
Renáta Gregová ◽  
Lívia Körtvélyessy ◽  
Július Zimmermann
Keyword(s):  
Three Dimensional ◽  
Sound Symbolism ◽  
Three Dimensional Model ◽  
Austronesian Languages ◽  
Place Of Articulation ◽  
European Languages ◽  
Phonetic Symbolism ◽  
The Individual ◽  
Core Vocabulary

Universals Archive (Universal #1926) indicates a universal tendency for sound symbolism in reference to the expression of diminutives and augmentatives. The research ( Štekauer et al. 2009 ) carried out on European languages has not proved the tendency at all. Therefore, our research was extended to cover three language families – Indo-European, Niger-Congo and Austronesian. A three-step analysis examining different aspects of phonetic symbolism was carried out on a core vocabulary of 35 lexical items. A research sample was selected out of 60 languages. The evaluative markers were analyzed according to both phonetic classification of vowels and consonants and Ultan's and Niewenhuis' conclusions on the dominance of palatal and post-alveolar consonants in diminutive markers. Finally, the data obtained in our sample languages was evaluated by means of a three-dimensional model illustrating the place of articulation of the individual segments.

scholarly journals Online biophysical predictions for SARS-CoV-2 proteins

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Luciano Kagami ◽  
Joel Roca-Martínez ◽  
Jose Gavaldá-García ◽  
Pathmanaban Ramasamy ◽  
K. Anton Feenstra ◽  
...  
Keyword(s):  
Protein Sequence ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Static Structure ◽  
Homologous Proteins ◽  
Structure Based Drug Design ◽  
Protein Protein Interaction ◽  
Link Type ◽  
Dynamics Simulations ◽  
Β Sheet

Abstract Background The SARS-CoV-2 virus, the causative agent of COVID-19, consists of an assembly of proteins that determine its infectious and immunological behavior, as well as its response to therapeutics. Major structural biology efforts on these proteins have already provided essential insights into the mode of action of the virus, as well as avenues for structure-based drug design. However, not all of the SARS-CoV-2 proteins, or regions thereof, have a well-defined three-dimensional structure, and as such might exhibit ambiguous, dynamic behaviour that is not evident from static structure representations, nor from molecular dynamics simulations using these structures. Main We present a website (https://bio2byte.be/sars2/) that provides protein sequence-based predictions of the backbone and side-chain dynamics and conformational propensities of these proteins, as well as derived early folding, disorder, β-sheet aggregation, protein-protein interaction and epitope propensities. These predictions attempt to capture the inherent biophysical propensities encoded in the sequence, rather than context-dependent behaviour such as the final folded state. In addition, we provide the biophysical variation that is observed in homologous proteins, which gives an indication of the limits of their functionally relevant biophysical behaviour. Conclusion The https://bio2byte.be/sars2/ website provides a range of protein sequence-based predictions for 27 SARS-CoV-2 proteins, enabling researchers to form hypotheses about their possible functional modes of action.

scholarly journals Validity and reliability of smartphone applications for measurement of hip rotation, compared with three‐dimensional motion analysis

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Phob Ganokroj ◽  
Nuchanun Sompornpanich ◽  
Pichitpol Kerdsomnuek ◽  
Bavornrat Vanadurongwan ◽  
Pisit Lertwanich
Keyword(s):  
Internal Rotation ◽  
Motion Analysis ◽  
Supine Position ◽  
External Rotation ◽  
Three Dimensional ◽  
Angle Measurement ◽  
Smartphone Applications ◽  
Rater Reliability ◽  
Link Type ◽  
Hip Rotation

Abstract Background Measurement of hip rotation is a crucial clinical parameter for the identification of hip problems and the monitoring of symptoms. The objective of this study was to determine whether the use of two smartphone applications is valid and reliable for the measurement of hip rotation. Methods An experimental, cross-sectional study was undertaken to assess passive hip internal and external rotation in three positions by two examiners. The hip rotational angles were measured by a smartphone clinometer application in the sitting and prone positions, and by a smartphone compass application in the supine position; their results were compared with those of the standard, three-dimensional, motion analysis system. The validities and inter-rater and intra-rater reliabilities of the smartphone applications were evaluated. Results The study involved 24 participants. The validities were good to excellent for the internal rotation angles in all positions (ICC 0.81–0.94), good for the external rotation angles in the prone position (ICC 0.79), and fair for the sitting and supine positions (ICC 0.70–0.73). The measurement of the hip internal rotation in the supine position had the highest ICC value of 0.94 (0.91, 0.96). The two smartphone applications showed good-to-excellent intra-rater reliability, but good-to-excellent inter-rater reliability for only three of the six positions (two other positions had fair reliability, while one position demonstrated poor reliability). Conclusions The two smartphone applications have good-to-excellent validity and intra-rater reliability, but only fair-to-good inter-rater reliability for the measurement of the hip rotational angle. The most valid hip rotational position in this study was the supine IR angle measurement, while the lowest validity was the ER angle measurement in the sitting position. The smartphone application is one of the practical measurements in hip rotational angles. Trial registration Number 20181022003 at the Thai Clinical Trials Registry (http://www.clinicaltrials.in.th) which was retrospectively registered at 2018-10-18 15:30:29.

scholarly journals Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

2013 ◽  
Vol 05 (01) ◽  
pp. 1350002 ◽  
Author(s):  
I. Benedetti ◽  
F. Barbe
Keyword(s):  
Three Dimensional ◽  
Constitutive Modelling ◽  
Polycrystalline Materials ◽  
High Fidelity ◽  
Computational Capability ◽  
Mechanical Models ◽  
Three Dimensional Models ◽  
The Individual ◽  
Individual Grains ◽  
Micro Structures

A survey of recent contributions on three-dimensional grain-scale mechanical modelling of polycrystalline materials is given in this work. The analysis of material micro-structures requires the generation of reliable micro-morphologies and affordable computational meshes as well as the description of the mechanical behavior of the elementary constituents and their interactions. The polycrystalline microstructure is characterized by the topology, morphology and crystallographic orientations of the individual grains and by the grain interfaces and microstructural defects, within the bulk grains and at the inter-granular interfaces. Their analysis has been until recently restricted to two-dimensional cases, due to high computational requirements. In the last decade, however, the wider affordability of increased computational capability has promoted the development of fully three-dimensional models. In this work, different aspects involved in the grain-scale analysis of polycrystalline materials are considered. Different techniques for generating artificial micro-structures, ranging from highly idealized to experimentally based high-fidelity representations, are briefly reviewed. Structured and unstructured meshes are discussed. The main strategies for constitutive modelling of individual bulk grains and inter-granular interfaces are introduced. Some attention has also been devoted to three-dimensional multiscale approaches and some established and emerging applications have been discussed.

Research on Generation Rules of Chest Width Point Curve Based on 3D Female Mannequin

2013 ◽  
Vol 796 ◽  
pp. 513-518
Author(s):  
Rong Jin ◽  
Bing Fei Gu ◽  
Guo Lian Liu
Keyword(s):  
Point Cloud ◽  
Three Dimensional ◽  
Upper Body ◽  
Secondary Development ◽  
Linear Regression Method ◽  
Point Cloud Data ◽  
Body Type ◽  
Cloud Data ◽  
Engineering Software ◽  
The Individual

In this paper 110 female undergraduates in Soochow University are measured by using 3D non-contact measurement system and manual measurement. 3D point cloud data of human body is taken as research objects by using anti-engineering software, and secondary development of point cloud data is done on the basis of optimizing point cloud data. In accordance with the definition of the human chest width points and other feature points, and in the operability of the three-dimensional point cloud data, the width, thickness, and length dimensions of the curve through the chest width point are measured. Classification of body type is done by choosing the ratio values as classification index which is the ratio between thickness and width of the curve. The generation rules of the chest curve are determined for each type by using linear regression method. Human arm model could be established by the computer automatically. Thereby the individual model of the female upper body mannequin modeling can be improved effectively.

A Numerically Efficient Method for Analysis of Very Large Articulated Floating Structures

1998 ◽  
Vol 42 (03) ◽  
pp. 174-186
Author(s):  
C. J. Garrison
Keyword(s):  
Hydrodynamic Interaction ◽  
Near Field ◽  
Three Dimensional ◽  
Computational Effort ◽  
Floating Structure ◽  
Complete Structure ◽  
Field Interaction ◽  
Floating Structures ◽  
Computing Effort ◽  
The Individual

A method is presented for evaluation of the motion of long structures composed of interconnected barges, or modules, of arbitrary shape. Such structures are being proposed in the construction of offshore airports or other large offshore floating structures. It is known that the evaluation of the motion of jointed or otherwise interconnected modules which make up a long floating structure may be evaluated by three dimensional radiation/diffraction analysis. However, the computing effort increases rapidly as the complexity of the geometric shape of the individual modules and the total number of modules increases. This paper describes an approximate method which drastically reduces the computational effort without major effects on accuracy. The method relies on accounting for hydrodynamic interaction effects between only adjacent modules within the structure rather than between all of the modules since the near-field interaction is by far the more important. This approximation reduces the computational effort to that of solving the two-module problem regardless of the total number of modules in the complete structure.

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