There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

http://nathan.instras.com/ResearchProposalDB/doc-109.pdf

A review on polymer nanofibers by electrospinning and their applications in nanocomposites

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Table Of Integrals Series And Products

Nanofibers of polymers were electrospun by creating an electrically charged jet of polymer solution at a pendent droplet. After the jet flowed away from the droplet in a nearly straight line, it bent into a complex path and other changes in shape occurred, during which electrical forces stretched and thinned it by very large ratios. After the solvent evaporated, birefringent nanofibers were left. In this article the reasons for the instability are analyzed and explained using a mathematical model. The rheological complexity of the polymer solution is included, which allows consideration of viscoelastic jets. It is shown that the longitudinal stress caused by the external electric field acting on the charge carried by the jet stabilized the straight jet for some distance. Then a lateral perturbation grew in response to the repulsive forces between adjacent elements of charge carried by the jet. The motion of segments of the jet grew rapidly into an electrically driven bending instability. The three-dimensional paths of continuous jets were calculated, both in the nearly straight region where the instability grew slowly and in the region where the bending dominated the path of the jet. The mathematical model provides a reasonable representation of the experimental data, particularly of the jet paths determined from high speed videographic observations.

/pdf/bending-instability-of-electrically-charged-liquid-jets-of-4s8cl7dcfj.pdf

Bending instability of electrically charged liquid jets of polymer solutions in electrospinning

The review deals with drop impacts on thin liquid layers and dry surfaces. The impacts resulting in crown formation are referred to as splashing. Crowns and their propagation are discussed in detail, as well as some additional kindred, albeit nonsplashing, phenomena like drop spreading and deposition, receding (recoil), jetting, fingering, and rebound. The review begins with an explanation of various practical motivations feeding the interest in the fascinating phenomena of drop impact, and the above-mentioned topics are then considered in their experimental, theoretical, and computational aspects.

Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ...

Electrospinning jets and polymer nanofibers

Compound core-shell polymer nanofibers by co-electrospinning

Introduction The expression: "analytical work", often connotes an effort in which basic expressions are combined to analyze a given problem and to derive new information and insight from the resulting mathematical steps of the analysis. Specifically, having started with the appropriate relationships and bringing appropriate mathematical manipulations to the task, the analyst is able to create new information to address the motivating question(s). A central organizing theme of this handbook is that 'experimental fluid mechanics" can be understood as a parallel activity to that described above. The motivating questions will set the context for the experiment. The experiment will be established as a boundary value problem in which the experimentalist will address all aspects of the boundary conditions that will influence the "solution." If a transient or an evolving solution is sought, the appropriate initial conditions will similarly be addressed. Having established these conditions, the solution to the boundary value problem will be revealed in the experimental data that will - ideally - not be contaminated by unintended or unknown perturbing effects and that will be fully converged if statistical average values are sought. Part A Experiments in Fluid Mechanics The objective of Part A is to establish the fundamental concepts and equations that undergird experimental fluid mechanics. The first chapter: addresses both the governing equations and the constitutive equations for Newtonian and non-Newtonian fluids. Chapter 2 provides the systematic bases for model testing and the scaling of experimental results. Sections 2.1 through 2.7 derive similitude parameters (Reynolds number, Froude number, etc.) from the governing equations and the boundary conditions. Dimensional analysis (Sect. 2.2) provides a rational approach for the organization and interpretation of experimental data Sect. 2.3, self-similarity, documents known flow fields that exhibit this condition and it provides guidance on what other flows may exhibit this behavior. The encyclopedic presentation of examples will allow the reader to comprehend the universal features of both complete and incomplete self-similarity. Chap. 1 The Experiment as a Boundary-Value Problem Chap. 2 Nondimensional Representation of the Boundary-Value Problem Part B Measurement of Primary Quantities The objective of Part B is to provide specific information to the reader on the following primary quantities: material properties (Chap. 3), flow field properties (Chap. 4 - pressure, Chap. 5 - velocity, vorticity, Mach number, Chap. 6 - spatial density variations and Chap. 7 - temperature and heat flux) and forces and moments (Chap. 8). Chapter 3 is focused on providing quantitative information for the material properties, the sources of this information and the associated confidence levels for the given data. Chapters 4 through 8 provide comprehensive guidance to the reader on: i) the objectives, ii) the available equipment, iii) the utilization techniques, and iv) the post-processing of the primitive information for the stated quantities. Chap. 3 Material Properties: Measurement and Data Chap. 4 Pressure Measurement Systems Chap. 5 Velocity, Vorticity and Mach Number Chap. 6 Spatial Density Variations Chap. 7 Temperature, Concentration and Heat Flux Chap. 8 Forces and Moments Part C Specific Experimental Approaches Building on the previous two parts of this Springer Handbook, which have dealt with the fundamental concepts and equations that undergrid experimental fluid mechanics and the measurement of primary quantities, respectively, Part C addresses experimental fluid mechanics from an application point of view. According to application, often unique and specific forms of equipment, experimental procedure, or analysis and interpretation of results have been developed. It is the purpose of Part C to elucidate a selection of such application areas, in particular measurements of non-Newtonian flows, turbulence, flow visualization, wall-bounded flows, surface topology, turbomachines, hydraulics, aerodynamics, atmospheric and oceanographic measurements, combustion diagnostics and electrohydrodynamic systems. Chap. 9 Non-Newtonian Flows Chap. 10 Measurement of Turbulent Flows Chap. 11 Flow Visualization Chap. 12 Wall-Bounded Flows Chap. 13 Surface Topology Chap. 14 Turbomachines Chap. 15 Hydraulics Chap. 16 Aerodynamics Chap. 17 Atmospheric Measurements Chap. 18 Oceanographic Measurements Chap. 19 The No-Slip Boundary Condition Chap. 20 Combustion Diagnostics Chap. 21 Electrohydrodynamic Systems Part D Analyses and Post-Processing of Data This final part of the Springer Handbook is actually meant to be a reference source about single and data processing techniques commonly encountered in fluid mechanics. These topics have been complemented by a section discussing data acquisition by imaging detectors, a topic becoming increasingly important for optical measurement techniques. These are all subjects, which in their development are not naturally associated with fluid mechanics hence Part D attempts to collect information from many diverse sources and present them conveniently to the fluid mechanic researcher. Topics covered in this part include fundamental topics of signal and data processing transforms (Fourier, Hilbert, wavelet), proper orthogonal decomposition and stochastic estimation. This is followed by a discussion of estimator expectation and variance and the influence of noise on these quantities. The Cramer-Rao Lower Bound (CRLB) is introduced and developed for several common signal processing examples from fluid mechanics. Imaging detectors and measures of their performance are then discussed in detail before closing with a chapter on image processing and motion analysis, two topics especially relevant for the Particle Image Velocity (PIV) measurement technique. Chap. 22 Review of Some Fundamentals Chap. 23 Fundamentals of Data Processing Chap. 24 Data Acquisition Chap. 25 Data Analyses About the Authors Subject Index

Alexander L. Yarin

Papers

Bending instability of electrically charged liquid jets of polymer solutions in electrospinning

Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ...

Electrospinning jets and polymer nanofibers

Compound core-shell polymer nanofibers by co-electrospinning

Springer Handbook of Experimental Fluid Mechanics