A Brief Introduction to Classical Mechanics with Illustrative Problems

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Based on the lecture notes for a course on Classical Mechanics, students with a basic knowledge of calculus should be able to follow this book. Unlike other textbooks, exercises are not included because the main goal is to equip students with the skills to problem-solve. An old-fashioned yet efficient method has been to provide a step-by-step derivation of the fundamental formulas, giving students an overview of the subject through various illustrative examples and showing how to apply the general results to relevant problems in Classical Mechanics. Sample Chapter(s) Preface Chapter 1: Force and Energy Contents: Force and Energy Newtonian Gravity Scattering and Systems of Particles Non-Inertial Frames Extended Rigid Bodies Lagrangian Formulation Hamiltonian Formulation Variational Problems Appendices: Derivation of the Lagrange Equations Prolate and Oblate Coordinates Laplace Equation Readership: Graduate students in Classical Mechanics with a basic knowledge of Calculus.

PHYSICS AND MECHANICS OF NEW MATERIALS AND THEIR A

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This book explores new materials, composites, and devices, examining the physics and mechanics behind them, as well as processing techniques and applications. The research presented in this book aims to enhance material characteristics through chemical, physical, and mechanical studies. Modern numerical approaches, mathematical modelling, and physical experiments are utilized to understand and evaluate the intricate technological processes and property transformations involved in manufacturing these materials. Sample Chapter(s) Foreword Repetitive recycling of 3D printing PLA filament as renewable resources on mechanical and thermal loads Contents: Influence of Rare Earth on the Microstructure and Mechanical Properties of Al–Zn Alloy (Bui Thi Ngoc Mai, Nguyen Xuan Dong, Pham Mai Khanh and Tran Duc Huy) Visible-Light Photocatalytic Activity of Fe@TiO2 Core–Shell Composite Synthesized by Sol–Gel Method (Min Yen Yeh, Tzu Yuan Yang, Tsung Chi Wu, Shiow Yueh Lee and Shun Hsyung Chang) A Research on Relevance Between Photoplethysmography Signal and Perceptual Stimulation (Chih-Hsueh Lin, Zhi-Hao Wang and Gwo-Jia Jong) Comparison of Water Uptake Behavior on Tensile Property of Epoxy Impregnated Continuous Basalt and Slag Filament Composites (Se-Yoon Kim, Soo-Jeong Park, Chang-Wook Park and Yun-Hae Kim) Properties of the Interface Between the As-Built Ti–6Al–4V Sample and the Ti Substrate in Selective Laser Sintering (Minh-Thuyet Nguyen, Hoang-Viet Nguyen, Thai-Hung Le, Quoc-Khanh Dang and Jin-Chun Kim) Automatic Mantispid Egg Detection and Counting Using Image Nature (Pei-Ying Yang, Chin-Dar Tseng, Tai-Lin Huang, Chao-Hong Liu, I-Hsing Tsai, Wei-Chun Lin, Chin-Shiuh Shieh, Shyh-An Yeh, Stephen Wan Leung and Tsair-Fwu Lee) Study on the Effects of Tooth Profile Design Parameters of Rotor to Performance of Vacuum Pump (Van-The Tran, Bui Trung Thanh, Banh Tien Long, Hoang Quoc Tuan and Duc Toan Nguyen) Comparative Study of Low-Frequency Vibrations Assigned to a Workpiece in EDM and PMEDM (Quang Dung Le, Huu Phan Nguyen, Tien Long Banh and Duc Toan Nguyen) Repetitive Recycling of 3D Printing PLA Filament as Renewable Resources on Mechanical and Thermal Loads (Jeong-Hyo Hong, Tianyu Yu, Soo-Jeong Park and Yun-Hae Kim) Investigations of the Characteristics and Chemical Bonds of Al and F Co-Doped ZnO Films as a Function of F2 Flow Rate (Guo-Xiang Peng, Fang-Hsing Wang, Chun-Chi Lin and Cheng-Fu Yang) The Structural Correlation and Mechanical Properties in Amorphous Hafnium Oxide Under Pressure (Nguyen-Hoang Thoan, Nguyen-Trung Do, Nguyen-Ngoc Trung and Le-Van Vinh) Vehicle Speed Estimation Using Two Roadside Passive Infrared Sensors (Van Quang Vu, Van Linh Ngo, Toan Thang Vu and Van Phuc Doan) Effects of Removing Temperature of Reduction Gas on the Luminescence Characteristics of Li2BaSiO4:0.003EU2+ Green Phosphor (Jie Li, Yang-Ming Lu, Qing-Hao Yang and Cheng-Fu Yang) CNT/Epoxy Interleaves for Strengthening Performance of Filament Wound Composite Structures (Soo-Jeong Park and Yun-Hae Kim) Carbon Nanotubes Produced from Rubber Fruit Shell Activated Carbon (Suhdi and Sheng-Chang Wang) Fabrication of Strong Macrofibers from Plant Fiber Bundles (Antonio Norio Nakagaito, Hitoshi Takagi and Yusuke Katsumoto) A Study on the Removal of Paint and Oxide Layer on the Steel Surface by Laser Beam Scanning Method (Ji-Eon Kim and Jong-Do Kim) Laser Assisted Synthesis of WS2 Nanorods by Pulsed Laser Ablation in Liquid Environment (Pankaj Koinkar, Kohei Sasaki, Tetsuro Katayama and Akihiro Furube) Development of Multi-Layered Sewer Pipe Plug — 1st Report: Ruptured Test and Stress Analysis of Protective Sheet (Nao-Aki Noda, Hisanori Tottori, Geng Gao, Rei Takaki, Yoshikazu Sano and Akira Kai) Development of Multi-Layered Sewer Pipe Plug — 2nd Report: Tensile Strength of Protective Sheet Bonded by Seams (Nao-Aki Noda, Geng Gao, Hisanori Tottori, Rei Takaki, Yoshikazu Sano and Akira Kai) Effect of Focal Position on Cut Surface Quality in Laser Cutting of 50-mm Thick Stainless Steel (Moo-Keun Song, Jong-Do Kim, Dong-Sig Shin, Su-Jin Lee and Dae-Won Cho) Stress Due to Interfacial Slip Causing Sleeve Fracture in Shrink-Fitted Work Roll (Nao-Aki Noda, Rahimah Abdul Rafar and Yoshikazu Sano) Experimental Prediction of Internal Defects According to Defect Area on NDI via Water Absorption Behavior (Kyo-Moon Lee, Soo-Jeong Park, Tianyu Yu, Seong-Jae Park and Yun-Hae Kim) Photographic Image Processing to Predict Radiation Dermatitis in Breast Cancer Patients Using Machine Learning Algorithms (Chou-Hsien Lee, Chen-Lin Kang, Chin-Dar Tseng, Chi-Ming Chou, Chin-Shiuh Shieh, Chih-Hsueh Lin, I-Hsing Tsai, Bo-Sheng Li, Jia-Hong Ren, Pei-Ju Chao and Tsair-Fwu Lee) Mechanical Properties of Large-Scale Composite Structures According to Process Conditions (Chang Wook Park and Sung Won Yoon) How to Estimate Fatigue Strength of Wood Material (Kinjirou Saitou and Nao-Aki Noda) Study of the Micro/Nano-Texture Design to Improve the Friction Properties of DLC Thin Films (Young Woo Kwon, Mun Ki Bae, Ri-Ichi Murakami, Tae Hwan Jang and Tae Gyu Kim) Accurate Stress Intensity Factors for Kinked Interface Crack in Bonded Dissimilar Half-Plane (Kazuhiro Oda and Nao-Aki Noda) Quantitative Analysis of Surfaces of Cross-Section in Butt Welding of Aluminum Alloy 5083 Using Laser–Arc Hybrid Welding (Ji-Sung Kim and Jong-Do Kim) Photo-Enhanced Field-Emission Behavior of CdSSe Microflowers (Amol B Deore, Mahendra A More, Bhausaheb B Musmade, Sachin D Nerkar, Padmakar G Chavan and Pankaj M Koinkar) Study on Structural Design and Analysis of 18 Ft CFRP Leisure Boat (Sung-Youl Bae and Yun-Hae Kim) Laminated Design for the Application of Composite Materials for Ship Radar Mast (Sung Won Yoon and Chang Wook Park) Fabrication and Evaluation of CA-Doped SrTiO3 Thermoelectric Materials by Molten Salt Method (Kei-Ichiro Murai, Takuya Nishiura, Ryutaro Nagata and Toshihiro Moriga) Applications of a Novel Detector for Pencil Beam Scanning Proton Therapy Beam Quality Assurance (Pei-Ying Yang, Yang-Wei Hsieh, Chen-Lin Kang, Chin-Dar Tseng, Chih-Hsueh Lin, Chin-Shiuh Shieh, Pei-Ju Chao and Tsair-Fwu Lee) Multi-Layer Thin-Film Deposition for High-Performance X-Ray Field-Emission Characteristics (Tae Hwan Jang, Tae Gyu Kim, Mun Ki Bae, Kyuseok Kim and Jaegu Choi) Investigation of Electrical Properties of PEALD-Deposited Ti/Al2O3/Al/Si MIM Capacitors (Sumit Patil, Viral Barhate, Ashok Mahajan, Haoyu Xu, Mohammad Rasadujjaman and Jing Zhang) Effects of Water pH and Immersion Time on Water Absorption Behavior and Mechanical Properties of Carbon Fiber-Reinforced Bioplastic Composites (Ri-Ichi Murakami and Wahyu Solafide Sipahutar) Electrophoretic Deposition of Non-Conductive Halloysite Nanotubes onto Glass Fabrics with Improved Interlaminar Properties of Glass/Epoxy Composites (Tianyu Yu, Zixuan Chen, Soo-Jeong Park and Yun-Hae Kim) Readership: Researchers, academics, and graduate students in materials science and related fields. Also, industry professionals in manufacturing and engineering sectors would benefit from this book.

ANALYTICAL FLUID DYNAMICS IN LAGRANGIAN VARIABLES

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The monograph focuses on the analytical challenges of describing incompressible fluid flows using Lagrangian variables. The Lagrangian method is presented as a complementary approach to the Eulerian method for studying fluid motion. The fundamental nature of fluid dynamics is linked to tracing the trajectories of individual fluid particles, which is precisely what the Lagrangian method facilitates. The purpose of this publication is to reflect as fully as possible the achievements of analytical fluid dynamics in Lagrangian variables. A significant part of it consists of original articles by the author. Considerable attention is paid to the subtleties of the Lagrangian description and its popularization among experts in fluid dynamics, students, postgraduates, and anyone interested in problems of fluid mechanics. The book can be considered, among other things, as a tutorial on Lagrangian fluid dynamics. The book covers issues of the general description of the movement of incompressible fluid, problems of classical hydrodynamics and geophysical hydrodynamics. Fundamental topics include free-boundary motion, vortices in fluids, and water waves. The book includes a number of problems that take into account the stratification and viscosity of fluids, as well as the rotation of the Earth. Sample Chapter(s) Preface Chapter 7: Two-Dimensional Vortex Flow Contents: Description of Basics: Ideal Fluid Equations Potential Motion Vortex Motion Waves on Water: Potential Approximation Gerstner Wave Weakly Vortex Waves Exact Solutions in Vortex Dynamics: Two-Dimensional Vortex Flow Localized Two-Dimensional Vortices in the External Flow Spatial Vortex Flows Generalized Gerstner Waves: Waves on Water at Unstable Pressure Vortex Model of Rogue Waves Breaking of the Surface Gravity Wave Non-Stationary Edge Waves Viscous Fluid Flows: Basic Equations and Examples Gravity Waves on the Surface of a Viscous Fluid The Earth's Rotation Effect: Exact Solutions for Waves Vortices in a Rotating Fluid Readership: This book can be targeted by a various levels of researchers from undergraduate and beginner to graduate and professional levels for both industry and academic sectors in green and sustainable energy.

COMPREHENSIVE SUMMARY OF THE BENFORD\'S LAW PHENOME

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Numbers are written in our digital language system by conveniently and efficiently utilizing the ten digits 0 to 9 in much the same way as sentences and books are written in the English language system by conveniently utilizing the 26 letters A to Z. Surprisingly, and against all common sense or intuition, the spread of these ten digits within numbers of random data is not uniform, but rather highly uneven. Benford's Law predicts that the first digit on the left-most side of numbers is proportioned between all possible digits 1 to 9 approximately according to LOG(1 + 1/digit), so that occurrences of low digits such as {1, 2, 3} in the first position are much more frequent than occurrences of high digits such as {7, 8, 9}. Remarkably, Benford's Law is found to be valid in almost all real life statistics, from data relating to physics, astronomy, chemistry, geology, and biology to data relating to economics, accounting, finance, engineering, and governmental census information. Therefore, Benford's Law stands as the only common thread running through and uniting all scientific disciplines! This book represents an intense and concentrated effort by the author to narrate this digital, numerical, and quantitative story of the Benford's Law phenomenon as briefly and as concisely as possible, while still ensuring a comprehensive coverage of all its aspects, results, causes, explanations, and perspectives. The most recent research results and discoveries in this field are included within this book in such a way as to be comprehensible and engaging to readers of all proficiencies. Errata(s) Errata (177 KB) Sample Chapter(s) Sample of Section I: The Digits Phenomenon Contents: About the Author Introduction The Digits Phenomenon: The First Digit on the Left Side of Numbers Benford's Law and the Predominance of Low Digits Second-Digits and Third-Digits Distributions The Quantitative Origin of the Digital-Numerical Phenomenon The Scale Invariance Principle The Base Invariance Principle Physical Order of Magnitude of Data Robust Measure of Physical Order of Magnitude Two Essential Requirements for Benford Behavior Sum of Squared Deviations Measure The Mistaken Use of the Chi-Square Test in Benford's Law Causes and Explanations: Multiplication Processes Lead to Positive Skewness and Often to Benford Addition Processes Lead to the Symmetrical Normal away from Benford The Multiplicative Central Limit Theorem and Lognormal Distribution Multiplications are More Prevalent than Additions in Real-Life Data Tugs of War between Addition and Multiplication Partitions Typically Lead to Positive Skewness and Often to Benford One-Dimensional Random Staged Partition One-Dimensional Chaotic Repeated Partition One-Dimensional Random Real Partition Two-Dimensional Random Partition The General Requirements for Partitions to Converge to Benford Benford Model for Planet and Star Formations Consolidation and Fragmentation Processes Random Exponential Growth Leads to Positive Skewness and Benford Data Aggregation Leads to Positive Skewness and Often to Benford Chains of Statistical Distributions and Benford's Law Meta-Explanation or the Explanation of all Explanations The Logarithmic Perspective: Benford's Law as Uniformity of Mantissa Rising or Falling Mantissa Distributions Uniqueness of k/x Distribution and Its Central Role in Benford's Law Related Log Conjecture The Random and Deterministic Flavors in Benford's Law The Great Prevalence of the Digital Development Pattern in Data The Absence of the Digital Development Pattern in k/x Distribution Benford's Law in Its Purest Form Constant Base Raised to a Random Power General Results: General Results in Benford's Law First Two Digits versus Last Two Digits The Law of Relative Quantities: The Relating Concepts of Digits, Numbers, and Quantities The Arbitrariness of our Positional Number System Two Radically Different Interpretations of the Benford Phenomenon The Quest for a Universal and Number-System-Invariant Measure The Shape and Nature of Histograms are Number-System Invariant Constructing a Three-Bin Histogram Signifying Small, Medium, and Big Constructing a Set of Infinitely Expanding Histograms Numerical Consistency in Bin Schemes for 15 Real-Life Data Sets The Postulate on Relative Quantities Application of the Postulate via Generic Bin Scheme on k/x The Infinite Sequence Result for the Bin Scheme on k/x The General Law of Relative Quantities Benford's Law as a Special Case and Direct Consequence of GLORQ The Universal Law of Relative Quantities Benford Second-Order Digits Interpreted as an Irregular Bin Scheme Concluding Historical and Conceptual Perspectives Appendices: Infinite Sequence Reduction Data Sets Glossary of Frequently Used Abbreviations First Two Digits versus Last Two Digits Index Readership: This book is suitable for expert mathematicians, statisticians, and scientists, as well as university students of these disciplines. This book is also suitable for the layman, the non-expert, and the educated general public, who are not necessarily proficient in mathematics, statistics, and the sciences, but who have enough interest to still be able to understand the topic on the whole.