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

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

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

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

/pdf/computer-vision-algorithms-and-applications-25dn6wu83j.pdf

Computer Vision: Algorithms and Applications

In 1997, Azuma published a survey on augmented reality (AR). Our goal is to complement, rather than replace, the original survey by presenting representative examples of the new advances. We refer one to the original survey for descriptions of potential applications (such as medical visualization, maintenance and repair of complex equipment, annotation, and path planning); summaries of AR system characteristics (such as the advantages and disadvantages of optical and video approaches to blending virtual and real, problems in display focus and contrast, and system portability); and an introduction to the crucial problem of registration, including sources of registration error and error-reduction strategies.

https://www.cc.gatech.edu/~blair/papers/ARsurveyCGA.pdf

Recent advances in augmented reality

Granular materials are ubiquitous in the world around us. They have properties that are different from those commonly associated with either solids, liquids, or gases. In this review the authors select some of the special properties of granular materials and describe recent research developments.[S0034-6861(96)00204-8]

/pdf/granular-solids-liquids-and-gases-4s2hurss9b.pdf

Granular solids, liquids, and gases

Interparticle forces in granular media form an inhomogeneous distribution of filamentary force chains. Understanding such forces and their spatial correlations, specifically in response to forces at the system boundaries, represents a fundamental goal of granular mechanics. The problem is of relevance to civil engineering, geophysics and physics, being important for the understanding of jamming, shear-induced yielding and mechanical response. Here we report measurements of the normal and tangential grain-scale forces inside a two-dimensional system of photoelastic disks that are subject to pure shear and isotropic compression. Various statistical measures show the underlying differences between these two stress states. These differences appear in the distributions of normal forces (which are more rounded for compression than shear), although not in the distributions of tangential forces (which are exponential in both cases). Sheared systems show anisotropy in the distributions of both the contact network and the contact forces. Anisotropy also occurs in the spatial correlations of forces, which provide a quantitative replacement for the idea of force chains. Sheared systems have long-range correlations in the direction of force chains, whereas isotropically compressed systems have short-range correlations regardless of the direction.

Contact force measurements and stress-induced anisotropy in granular materials.

1. Introduction.- 1.1 Some Orders of Magnitude Defining the Problem.- 1.2 Economic Implications and Industrial Problems.- 1.2.1 Industrial Processing of Granulars.- Construction Materials.- Processing Industries.- An Example: Casting by Sacrificial Polystyrene.- The Agriculture Industry.- 1.2.2 Flow Problems.- 1.2.3 Problems of Segregation.- 1.3 Granular Materials and Geophysics.- 1.4 A Brief Historical Review.- 1.5 Prerequisites and Selected Bibliography.- 2. Interactions in Granular Media.- 2.1 A Single Particle and Its Environment.- Laminar Drag.- Turbulent Drag.- Granular Dendrites.- Humidity, Electrostatic Interactions, and Other Perturbations.- Classification of Granular Materials and Definitions.- 2.2 Interactions between Two Particles.- 2.2.1 The Laws of Friction between Solids.- The Three Fundamental Laws of Solid Friction.- A Microscopic Explanation.- Gliding and Rotations: Frustrated Rotations.- Rolling without Gliding.- Gliding without Rolling.- Transition from One Regime to the Other.- Stick-Slip Motion.- 2.2.2 Collisions and Deformations of Elastic Spheres.- Frontal Elastic Collision.- Nonfrontal Elastic Collision and Rotation of Particles.- A Ball Thrown Against a Wall.- Nonfrontal Collision Between Two Elastic Spheres with Friction.- The Tangential Restitution Coefficient.- Penetration During Frontal Collision:Hertz's Problem.- Inhomogeneous Spheres: The Soft Crust Model.- 2.3 A Single Particle on Top of a Granular Medium.- 2.4 Interactions Between Several Particles.- 2.4.1 The Laws of Friction in a Granular Medium.- 2.4.2 Bagnold's Number.- 3. Fluidization, Decompaction, and Fragmentation.- 3.1 The Static Properties of a Granular Pile.- 3.1.1 First Principle: The Role of Friction.- The Stacking of Cannon Balls.- Indetermination of Solid Friction: Hysteresis.- Distribution of Stresses in a Granular Medium.- Arch in Equilibrium Under its Own Weight.- Arch Supporting an Evenly Distributed Load.- 3.1.2 Stress-Strain Relations.- Identical Spherical Granules.- Granules of Different Sizes: Power Law and Electrical Analogy.- 3.1.3 Second Principle: Reynolds's Dilatancy.- Deformation of a Simple Parallelogram.- Deformation of a Row of Parallelograms Placed Between Two Walls.- 3.1.4 Cylindrical Container: Janssen's Model.- Generic Model: The Silo Problem.- Specific Applications.- Cylindrical Container of Diameter D.- Two-Dimensional Container.- 3.2 Dynamic Properties of a Granular Pile.- 3.2.1 A Column of Spheres Subjected to a Vertical Vibration.- Some Orders of Magnitude.- Mathematical Analysis of the Problem.- Results: Fluidized Phase and Condensed Phase.- Fluidization and Condensation as Functions of Acceleration.- Fluidization and Condensation as Functions of Height.- 3.2.2 Two-Dimensional Stack of Frictionless Spheres.- Some Comments on Scaling.- 3.2.3 Two-Dimensional Stack of Spheres with Friction.- Generic Model.- Levitation of Cylindrical Stacks.- Levitation of Two-Dimensional Stacks.- Experimental Observation of Decompaction and Convection in a Two-Dimensional Granular Structure.- Experimental Technique: Image Processing.- Measurements of the Velocity of Moving Particles.- Measurements of the Relative Motion of Particles.- Convection and Pile Formation.- Threshold of Pile Formation and Decompaction.- Dynamics of Pile Formation in Two Dimensions.- Experimental Verifications of the Decompaction Model.- Short-Term Decompaction: Fragmentation.- 3.2.4 Fragmentation of a Stack in Guided Fall.- Two-Dimensional Experiment.- Theoretical Modeling.- Fall Without Fragmentation.- Where Do Fractures Initially Appear'?.- Numerical Simulation of a Stack in Guided Fall.- Distribution of Pressure in a Stack: Arch Effects.- Self-Organization of Rotations.- 3.2.5 Surface Instabilities in an Extended Granular Medium.- Extended Three-Dimensional Stacks.- Wavelength Dependence on Vibration Frequency.- Extended Two-Dimensional Stacks.- Summary.- 4. Granular Media in a State of Flow.- 4.1 A Sand Pile in Equilibrium: The Angle of Repose.- The Embankment Angle of a Pile Made of a Small Number of Particles.- Transition from Intermittent to Continuous Regime-Power Laws.- Power Law for a Newtonian Fluid.- Power Law for a Granular Surface.- 4.2 Avalanche Models.- 4.2.1 Cellular Automaton Model (CAM).- The Principle.- Implementations of the Cellular Automaton Model (CAM).- Lifetime and 1/f Noise.- The Statistics of Avalanches.- Piles Involving Large Numbers of Particles.- Piles Involving Small Numbers of Particles.- Relaxation of the Critical Angle-Granular Temperature.- 4.2.2 Stick-Slip Model of Avalanches.- Different Friction Models.- Burridge-Knopoff (BK) Pads.- Other Friction Laws F(v).- A Few Remarks Concerning the Stick-Slip Model of Avalanches.- 4.2.3 Avalanche Models Based on Coupled Variables.- Upward Propagation of Perturbations.- Simulation of Avalanches.- De Gennes's Modified Model.- Rotating Drum Experiment.- 5. Mixing and Segregation.- 5.1 Introduction.- 5.1.1 Oyama's Cylindrical Drum.- 5.1.2 Potential Energy of a Heterogeneous Pile.- Superposition of Stacks-Two Compact Stacks.- Where Are the Defects Concentrated?.- 5.2 Segregation by Vibration.- 5.2.1 Simulation of Segregation by Size.- Two-Dimensional Model.- Three-Dimensional Model.- 5.2.2 Experiments on Segregation by Vibration.- Experiments on Continuous and Intermittent Ascent.- Convection or Arch Effect?.- Convection and Segregation in Three Dimensions.- Convection and Segregation in Two Dimensions.- 5.3 Segregation by Shearing.- 5.3.1 A Single Particle in a Uniform Medium.- 5.3.2 Segregation of Two Populations of Particles of Different Size.- Segregation Speed and Particle Size.- Segregation Speed and Rotation Velocity.- Fractal Growth of the Central Cluster.- 5.4 Segregation in Oyama's Three-Dimensional Drum.- 5.4.1 Experimental Observations.- 5.4.2 Savage's Model.- 6. Numerical Simulations.- 6.1 Introduction.- 6.1.1 The Challenges of Numerical Simulation.- 6.1.2 The Different Simulation Methods.- Hard Spheres and Soft Spheres.- Duration of Collisions and Chronology Problems.- 6.1.3 The Transition from a Discrete to a Continuous Description.- 6.2 Simulations of Collisions.- 6.2.1 Introduction.- 6.2.2 One-Dimensional LRV Procedure.- 6.3 Molecular Dynamics (MD) Simulations.- 6.3.1 Elastic and Friction Forces.- Linear and Nonlinear Equations.- Mechanical Analogies.- 6.3.2 MD Collision Model.- Linear Model of a Binary Collision.- Nonlinear Model of a Binary Collision.- The Detachment Effect.- 6.4 Simulation of the Dynamics of Contacts.- 6.5 Monte Carlo (MC) Simulations.- Monte Carlo Technique for Stacking and Relaxation.- 6.6 Sequential Model of a Pile.

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1383168

Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials

A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu-Nagel jamming concept has attracted intensive theoretical and modelling interest but has prompted less experimental effort. In the Liu-Nagel framework, jammed states of athermal systems exist only above a certain critical density. Although numerical simulations for particles that do not experience friction broadly support this idea, the nature of the jamming transition for frictional grains is less clear. Here we show that jamming of frictional, disk-shaped grains can be induced by the application of shear stress at densities lower than the critical value, at which isotropic (shear-free) jamming occurs. These jammed states have a much richer phenomenology than the isotropic jammed states: for small applied shear stresses, the states are fragile, with a strong force network that percolates only in one direction. A minimum shear stress is needed to create robust, shear-jammed states with a strong force network percolating in all directions. The transitions from unjammed to fragile states and from fragile to shear-jammed states are controlled by the fraction of force-bearing grains. The fractions at which these transitions occur are statistically independent of the density. Jammed states with densities lower than the critical value have an anisotropic fabric (contact network). The minimum anisotropy of shear-jammed states vanishes as the density approaches the critical value from below, in a manner reminiscent of an order-disorder transition.

Robert Behringer

Papers

Recent advances in augmented reality

Granular solids, liquids, and gases

Contact force measurements and stress-induced anisotropy in granular materials.

Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials

Jamming by shear