Real-time multiple scattering in participating media with illumination networks

Light going through a participating medium like smoke can be scattered or absorbed by every point in the medium. To accurately render such a medium we must compute the radiance resulting at every point inside the medium because of these physical effects, which have been modeled by the radiative transfer equation. Computing the radiance at any point inside a participating medium amounts to numerically solving this radiative transport equation. Discrete Ordinate Method (DOM) is a widely used solution method. DOM is computationally intensive. Fattal [Fat09] proposed Light Propagation Maps (LPM) to expedite DOM computation. In this paper we propose a streaming based parallelization of LPM to run on SIMD graphics hardware. Our method is fast and scalable. We report more than 20x speed improvement by using our method as compared to Fattal’s original method. Using our approach we are able to render 64x64x64 dynamic volumes with multiple scattering of light at interactive speed on complex lighting, and are able to render volumes of any size independent of the GPU memory capability.

Coupling Mortar Finite Element and Boundary Element Methods for 2D Navier-Stokes Equations Courant Element: Before and After Iterative Methods for Solving Stiff Elliptic Problems Straight and Curved Finite Elements of Class C1 and Some Applications to Thin Shell Problems Exact Controllability to Solve the Helmholtz Equation with Absorbing Boundary Conditions Cubic Version of FEM in Elliptic Problems with Interfaces and Singularities Least Squares Mixed Finite Elements Turbulence Modelling in Finite Element Industrial Applications Necessary and Sufficient Conditions for the Numerical Approximation of a Partial Differential Equation Depending on a Small Parameter Efficient Solution Methods for Compressible Flow Computations Parallel Finite Volume Algorithms for Solving the Time-Domain Maxwell Equations on Nonstructured Meshes Coupling Between Nonlinear Maxwell and Heat Equations for an Induction Heating Problem: Modelling and Numerical Methods Solving the 3D Harmonic Maxwell Equations with Finite Elements, Lagrange Multipliers, and Iterative Methods Some Applications of the Hierarchic High Order MITC Finite Elements for Reissner-Mindlin Plates Domain Decomposition for Immiscible Displacement in Single Porosity Systems An Error Estimator for Nonconforming Approximations of a Nonlinear Problem Some Observations on Raviart-Thomas Mixed Finite Elements in p Extension for Parabolic Problems Mixed Finite Element Methods in Fluid Structure Systems A Black-Box Solver for the Solution of General Nonlinear Functional Equations by Mixed FEM A Remark on the Asymptotic Behaviour of Parabolic Variational Inequalities and Their Finite Element Approximation by the Courant Element Domain Decomposition vs. Adaptivity Material Optimization of Composites. Part Contents.

With increasing computer capabilities, numerical modeling of two-phase flows has developed significantly over the last few years. Although there are two main categories, namely 'one' fluid and 'two' fluid methods, the 'one' fluid methods are more commonly used for tracking or capturing the interface between two fluids. Level set (LS), volume-of-fluid (VOF), front tracking, marker-and-cell (MAC) and lattice Boltzmann (LB) methods are all 'one' fluid methods. It is clear that there is no perfect method; each method has advantages and disadvantages which make it more appropriate for one kind of problem than for others. For instance, a LS method will accurately compute the curvature and the normal to the interface, but tends to loss mass which is physically incorrect. On the other hand, a VOF method will conserve mass up to machine precision, but the computation of the curvature and normal to the interface is not as accurate. In order to minimize the disadvantages of these methods, several authors have used two or more methods together to model two-phase flows. This is the case for the CLSVOF (Couple Level Set Volume Of Fluid) method, where LS and VOF are coupled together in order to better capture the interface. In CLSVOF, the level set function is used to compute the interface curvature and normal to the interface, while the volume of fluid function is used to capture the interface. For two-phase flows in microchannels, surface tension forces play an important role in determining the dynamics of bubbles whereas gravitational forces are generally negligible. Also it is very important to consider the interaction between the boundaries and the fluids by prescribing or computing the correct contact angle between them. The commercial CFD code FLUENT allows the use of static constant angles, or the use of User Defined Functions (UDF) to compute the dynamic contact angles. It is inappropriate to use a static contact angle to model cases involving moving contact lines. For such cases a dynamic contact angle scheme should be implemented. In this study, FLUENT was used to model adiabatic and diabatic, time dependent two-phase flows. Since FLUENT already contains a VOF method, a LS method was implemented and coupled with VOF into FLUENT via UDFs. Furthermore, since the LS function, used to compute the surface tension force, ceases to be a signed distance to the interface even after one time step, a re-initialization equation was solved after each time step. This involved using a fifth order WENO (Weighted Essentially Non Oscillatory) scheme to discretize the space derivatives (otherwise oscillations of the interface occurred), and a first order Euler method for the time integration. In another part of the study, a 3D dynamic contact angle model based on volume fraction, interface reconstruction, and experimentally available advancing and receding static contact angles was also developed and implemented into FLUENT via UDFs. Several validations for the developed CLSVOF method and dynamic contact angle model are presented in this thesis, these includes a static bubble, a bubble rising in a stagnant liquid for Morton numbers ranging from 102 to 10-11, droplet deformation due to a vortex flow field, droplets spreading over a wall under the gravity effect and droplets sliding over a wall due to gravity. These validations demonstrated the high accuracy and the stability of our methods for modeling these phenomena. A heat and mass transfer model was also implemented into the commercial CFD code FLUENT for simulating of boiling (and condensation) heat transfer. Several simulations were presented with water and R134a as working fluids. The influence of the contact angle and the wall superheat was also studied.

Adaptive gridding methods are of fundamental importance both for industry and academia. As one of the computing methods, the Boundary Element Method (BEM) is used to simulate problems whose fundamental solutions are available. The method is usually characterised as constant elements BEM or linear elements BEM depending on the type of interpolation used at the elements. Its popularity is steadily growing because of its advantages over other numerical methods most important of which being that it only involves obtaining data at the boundary and computation of the solution in the domain is merely a case of post processing through the use of an identity. This results in the reduction of the problem dimension by unity. Although there is a reduction in dimension when we use BEM, the method usually results in full matrices which can be expensive to solve. This makes the method costly for problems that require very fine grids like those with hot spots as in the example of impressed current cathodic protection systems (ICCP). The BEM is a global method in nature in that the solution in one node depends on the solutions in all the other nodes of the grid. Hence an error in one node can pollute the solution in all the other nodes. In this thesis, we first focus our attention on defining and studying both the local and global errors for the BEM. This is not a completely new study as the literature suggests, however, our approach is different. We use the basic foundations of the the method to define the errors. Since the method is a global method, first we use the interpolation error on each element to define what we have called a sublocal error. Then using the sublocal error we have defined the local error. Understanding the local errors enabled us study the global error. Theoretical and numerical results show that these errors are second order in grid size for both the constant and linear element cases. Then, having explored errors, we study a method for adaptive grid refinement for the BEM. Rather than using a truly nonuniform grid, we present a method called local defect correction (LDC) that is based on local uniform grid refinement. This method is already developed and documented for other numerical methods such as finite difference and finite volume methods but not for BEM. In the LDC method, the discretization on a composite grid is based on a combination of standard discretizations on several uniform grids with different grid sizes that cover different parts of the domain. At least one grid, the uniform global coarse grid, should cover the entire boundary. The size of the global coarse grid is chosen in agreement with the relatively smooth behaviour of the solution outside the hot spots. Then several uniform local fine grids each of which covers only a (small) part of the boundary are used in the hot spots. The grid sizes of the local grids are chosen in agreement with the behaviour of the continuous solution in that part of the boundary. The LDC method is an iterative process whereby a basic global discretisation is improved by local discretisations defined in subdomains. The update of the coarse grid solution is achieved by adding a defect correction term to the right hand side of the coarse grid problem. At each iteration step, the process yields a discrete approximation of the continuous solution on the corresponding composite grid. We have shown how this discretisation can be achieved for the BEM. We apply the discretisation to an academic example to demonstrate its implementation and later show how to use it for an application as the ICCP system. The results show that it is a cheaper method than solving on a truly composite grid and converges in a single step.

In the three-dimensional scene simulation, the realistic sense of flame simulation is of great significance to the simulation effect. Particle systems are widely used as effective simulation methods for irregularly blurred objects. This paper combines the particle system with texture mapping and proposes a more efficient method for generating flame particles. When the initial state of the particle is set, this method introduces a random function to construct a normally distributed particle distribution model. Through a reasonable analysis of the force of the particle, the motion state variation equation of the flame particle is given. On this basis, the texture particles of the flame particles are rendered using square texture sheets in different stages. Finally, the simulation of the environmental factors of the locally attenuated wind field and the dynamic vortex force field makes the flame form more flexible. The results of the study show that while meeting real-time performance, it has a more realistic flame effect.

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiency and convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partial differential equations usually needs a coordinate transformation in order to discard the singularity of the partial differential equation. Most often this transformation is not applicable and even does not exist. Therefore in this case the solution for the singular partial differential equation does not exist. In the present study the results of simulation for the singular partial differential equations with variable coefficients using the Fourier transform variational iteration method are compared with the results of simulation using the modified variational iteration method. The comparison shows that the effectiveness and accuracy of Fourier transform variational iteration method is more than that of the modified variational iteration method for the simulation of singular partial differential equations.

Numerical simulations based on Reynolds-averaged Navier Stokes (RANS) models are still the work-horse tool in engineering design involving turbulent flows. Two decades ago, when LES started gaining popularity thanks to the increasing availability of computational resources, it was widely expected that it would have gradually replaced RANS methods in industrial CFD for decades to come. In the past two decades, however, while LES-based methods gained widespread applications and the earlier hope did not diminish, the predicted time when LES would replace RANS has been significantly delayed. Most industrial users are probably decades away from any routine use of scale resolving simulations, not to mention the cost, time and user skill it take to run these computations. In brief, RANS solvers, particularly those based on standard eddy viscosity models (e.g k-e, k-ω, S-A and k-ω SST) are expected to remain the workhorse in the CFD of high Reynolds number flows for decades. However, predictions from RANS simulations are known to have large discrepancies in many flows of engineering relevance, including those with swirl, pressure gradients, or mean streamline curvature. It is a consensus that the dominant cause for such discrepancies is the RANS-modeled Reynolds stresses. In light of the long stagnation in traditional turbulence modeling, researchers explored machine learning as an alternative to improve RANS modeling by leveraging data from highfidelity simulations. The goal is to make use of vast amounts of turbulent flows data, machine learning techniques and current understanding of turbulence physics to develop models with better predictive capabilities in the context of RANS simulations. Recently, in a seminar work, Ling et al (2016) developed a neural network architecture capable of embedding invariance properties into the Reynolds stress tensor predicted in output. Such a network, named the tensor basis neural network (TBNN), was applied to a variety of flow fields with encouraging results compared to both classical turbulence models and neural networks that do not preserve Galilean invariance. Yet, as in most data driven turbulence modelling approaches, the TBNN was used as a post-processing tool to correct the Reynolds stress tensor field predicted by a RANS simulation run with standard closure models. This means that, theoretically, the network can be applied only to correct the Reynolds stress tensor for the same RANS model on which it has been trained since, in general, different turbulence models yield different results depending on the flow type. Moreover, there is no physisical insight that suggests a relation between the RANS velocity gradients - used as inputs of the machine learning model - and the true Reynolds stress tensor. Differently, in this work a network with a similar architecture to the Ling’s one was trained and tested on a database of high-fidelity data of eight different flows to learn a functional mapping between the inputs of Pope’s General Eddy Viscosity Model and the anisotropic part of the Reynolds stress tensor. Then the network was embedded into a CFD RANS solver as a replacement of the standard closure model - and therefore called at every solver’s iteration. Lasty, the RANS solver with embedded TBNN was be tested on a canonical flow case - turbulent channel flow - to evaluate its performances. As for the organization of this work: in Chapter 1 further details on the data driven turbulence modelling will be given, RANS models and equations will be introduced and also an introduction to Neural Networks will be presented. In Chapter 2, it will be given a detailedexplanation of the RANS CFD solver and the neural network’s implementation. In Chapter 3, the method will be tested on a turbulent channel flow case and the results will be discussed. Lastly, in Chapter 4, some meaningful conclusions will be drawn.

Aufgrund fallender Preise zur Speicherung von Daten kann man derzeit eine explosionsartige Zunahme in der Menge der verfügbaren Daten beobachten. Diese Entwicklung gibt Unternehmen und wissenschaftliche Institutionen die Möglichkeit empirische Daten in ungekannter Größenordnung zu analysieren. Für viele Firmen ist die Analyse der gesammelten Daten aus ihrem operationalen Geschäft längst zu einem zentralen strategischen Aspekt geworden. Im Gegensatz zu der seit längerem schon betriebenen Business Intelligence, bestehen diese Analysen nicht mehr nur aus traditionellen relationalen Anfragen. In zunehmendem Anteil kommen komplexe Algorithmen aus den Bereichen Data Mining und Maschinelles Lernen hinzu, um versteckte Muster in den Daten zu erkennen, oder Vorhersagemodelle zu trainieren. Mit zunehmender Datenmenge und Komplexität der Analysen wird jedoch eine neue Generation von Systemen benötigt, die diese Kombination aus Anfragekomplexität und Datenvolumen gewachsen sind. Relationale Datenbanken waren lange Zeit das Zugpferd der Datenanalyse im großen Stil. Grund dafür war zum großen Teil ihre deklarativen Anfragesprache, welche es ermöglichte die logischen und physischen Aspekte der Datenspeicherung und Verarbeitung zu trennen, und Anfragen automatisch zu optimieren. Das starres Datenmodell und ihre beschränkte Menge von möglichen Operationen schränken jedoch die Anwendbarkeit von relationalen Datenbanken für viele der neueren analytischen Probleme stark ein. Diese Erkenntnis hat die Entwicklung einer neuen Generation von Systemen und Architekturen eingeläutet, die sich durch sehr generische Abstraktionen für parallelisierbare analytische Programme auszeichnen; MapReduce kann hier beispielhaft genannt werden, als der zweifelsohne prominenteste Vertreter dieser Systeme. Zwar vereinfachte und erschloss diese neue Generation von Systemen die Datenanalyse in diversen neuen Anwendungsfeldern, sie ist jedoch nicht in der Lage komplexe Anwendungen aus den Bereichen Data Mining und Maschinelles Lernen effizient abzubilden, ohne sich dabei extrem auf spezifische Anwendungen zu spezialisieren. Verglichen mit den relationalen Datenbanken haben MapReduce und vergleichbare Systeme außerdem die deklarative Abstraktion aufgegeben und zwingen den Anwender dazu systemnahe Programme zu schreiben und diese manuell zu optimieren. In dieser Dissertation werden verschiedene Techniken vorgestellt, die es ermöglichen etliche der zentralen Eigenschaften von relationalen Datenbanken im Kontext dieser neuen Generation von daten-parallelen Analysesystemen zu realisieren. Mithilfe dieser Techniken ist es möglich ein Analysesystem zu beschreiben, dessen Programme gleichzeitig sowohl generische und ausdrucksstark, als auch prägnant und deklarativ sind. Im einzelnen stellen wir folgende Techniken vor: Erstens, eine Programmierabstraktion die generisch ist und mit komplexen Datenmodellen umgehen kann, aber gleichzeitig viele der deklarativen Eigenschaften der relationalen Algebra erhält. Programme, die gegen dies Abstraktion entwickelt werden können ähnlich optimiert werden wie relationale Anfragen. Zweitens stellen wir eine Abstraktion für iterative daten-parallele Algorithmen vor. Die Abstraktion unterstützt inkrementelle (delta-basierte) Berechnungen und geht mit zustandsbehafteteten Berechnungen transparent um. Wir beschreiben wie man einen relationalen Anfrageoptimierer erweitern kann so dass dieser iterative Anfragen effektiv optimiert. Wir zeigen dabei dass der Optimierer dadurch in die Lage versetzt wird automatisch Ausführungspläne zu erzeugen, die wohlbekannten, manuell erstellten Programmen entsprechen. Die Abstraktion subsumiert dadurch spezialisierte Systeme (wie Pregel) und bietet vergleichbare Performanz. Drittens stellen wir Methoden vor, um die Programmierabstraktion in eine funktionale Sprachen einzubetten. Diese Integration ermögliche es prägnante Programme zu schreiben und einfach wiederzuverwendenden Komponenten und Bibliotheken, sowie Domänenspezifische Sprachen, zu erstellen. Wir legen dar wie man die Übersetzung und Optimierung des daten-parallelen Programms mit dem Sprachübersetzer der funktionalen Sprache so integriert, dass maximales Optimierungspotenzial besteht.

This paper presents a numerical investigation for laminar forced convection flow of a radiating gas in a rectangular duct with a solid element that makes a backward facing step. The fluid is treated as a gray, absorbing, emitting and scattering medium. The governing differential equations consisting the continuity, momentum and energy are solved numerically by the computational fluid dynamics techniques. Since the present problem is a conjugate one and both gas and solid elements are considered in the computational domain, simultaneously, the numerical solution of Laplace equation is obtained in the solid element for temperature calculation in this area. Discretized forms of these equations are obtained using the finite volume method and solved by the SIMPLE algorithm. The radiative transfer equation (RTE) is also solved numerically by the discrete ordinate method (DOM) for computation of the radiative term in the gas energy equation.The streamline and isotherm plots in the gas flow and the distributions of convective, radiative and total Nusselt numbers along the solid-gas interface are presented. Besides, the effects of radiation conduction parameter and also solid to gas conduction ratio as two important parameters on thermo hydrodynamic characteristics of such thermal system are explored. It is revealed that the radiative Nusselt number on the interface surface is much affected by RC parameter but the radiation conduction parameter has not considerable effect on the convective Nusselt number. Comparison between the present numerical results with those obtained by other investigators for the case of non-conjugate problems shows good consistency.

This paper presents a fast parallel method to compute the solution of the radiative transport equation in inhomogeneous participating media. The efficiency of the method comes from different factors. First, we use a novel approximation scheme to find a good guess for both the direct and the scattered component. This scheme is based on the analytic solution for homogeneous media, which is modulated by the local material properties. Then, the initial approximation is refined iteratively. The iterative refinement is executed on a face centered cubic grid, which is decomposed to blocks according to the available simulation nodes. The implementation uses CUDA and runs on a cluster of GPUs. We also show how the communication bottleneck can be avoided by not exchanging the boundary conditions in every iteration step.

Due to the growing concern on the issues of global warming, climate change, and energy shortage, more rigorous requirements are imposed on the energy conversion process of combustion. Due to the relative safety and convenience in transportation and storage, liquid fuels are commonly used in many practical combustion systems such as diesel engines, gas turbines and industrial furnaces. In these combustion devices, turbulent spray flows are involved. The character of spray dispersion, evaporation, mixing and combustion of fuel droplets strongly determines the performance of these systems with respect to the combustion efficiency, stability, and emissions. Therefore, an improved understanding of turbulent spray combustion and the development of predictive models are needed for a better design of more efficient combustion systems. The present work focuses on the development of a computational methodology based on the transported joint probability density function (PDF) method for the modeling and simulation of two-phase turbulent spray flows without and with chemical reactions. In the non-reacting situation, the dependent variables of the joint PDF include the gas velocity and the mixture fraction. For the simulation of reacting spray flows, a three-variate joint PDF transport equation is derived and modeled in order to account for the pre-vaporization effects and partially premixed regime in turbulent spray flames. The dependent variables include the gas phase mixture fraction, the reaction progress variable and gas enthalpy. Detailed combustion chemistry is considered through an extended spray flamelet model by including a reaction progress variable in addition to the classical formulation. The dilute spray is simulated using a Lagrangian discrete parcel method for the description of droplet motion, heating and evaporation. The infinite conductivity model with consideration of non-equilibrium effects based on the Langmuir-Knudsen law is considered. The spray evolution and flame structures in the frame of the polydisperse reacting spray flows are investigated. Numerical results are compared with experimental data provided by Prof. Masri at the University of Sydney, Australia, and the test cases include three different turbulent non-reacting acetone spray flows in air and turbulent spray flames with the liquid fuel ethanol. For the acetone spray flows, computational results generally show good agreement with experimental data in terms of the droplet size and mean velocity distribution, as well as the liquid volume flux. The results show that the inflow liquid mass loading hardly affects the droplet diameter distribution, whereas the inlet turbulence level has a pronounced effect. The tendency of droplet accumulation near the jet centerline is found with a somewhat overprediction of liquid volume flux at downstream locations. A more sophisticated turbulence model is expected to eliminate this discrepancy. Moreover, the local joint PDF of the gas velocity and the mixture fraction is analyzed. A linear correlation of the gas velocity and the mixture fraction exists close to the nozzle exit outside the main spray jet, and no regions are found where statistical independence prevails. For the simulation of spray flames, computations with the newly developed spray flamelet/progress variable approach and with the previous standard spray flamelet formulation are carried out and compared with the experiments by Prof. Masri at the University of Sydney. A good agreement between the computations with the new formulation and the experiments for gas temperature and droplet size and velocity is achieved. The major spray and combustion properties are correctly captured using this new formulation, which is compared with an unphysically attached flame near the nozzle exit predicted by the previous model. A partially premixed combustion prevails in this piloted turbulent spray flame. Due to the prevaporization of the ethanol droplets near the nozzle exit, a lean premixed gas mixture is found at the inner side of spray jet. Moving downstream, the lean-sided diffusion flame is promoted towards the inner fuel-rich side by heating up the inner premixed core that is controlled by the droplet evaporation. Additionally, it is observed that in the far-field region, the diffusion flame becomes the dominant combustion mode. In summary, an efficient computational model based on the transported joint PDF method is developed to two-phase turbulent spray flows. The combined transported joint PDF and a newly proposed spray flamelet/progress variable approach shows an improved performance in the prediction of complex turbulent spray flames, and new insights on the local flame structure influenced by evaporating sprays are obtained.

Single molecule detection and fluorescence correlation spectroscopy on surfaces

Shape deformation and editing are important for animation and game design. Based on as-rigid-as-possible (ARAP) surface modeling, an efficient approach is proposed to approximately preserve the volume of an object with large-scale deformations. The classical ARAP surface modeling uses two-stage iterations to recover rotations and preserve edge lengths. However, there is no volume preserving constraint, which may cause undesired artifacts. We show that the volume can be roughly kept by leveraging the skeleton information. First a skeleton is selected, and points are evenly generated on the skeleton. Then each point is correlated with several vertices on the surface of the object. The connectivity between the skeleton and the surface is defined as skeleton edges, which can be easily added into the linear system of the ARAP method as additional rows without breaking the manifoldness or sacrificing speed. Since this linear system is able to preserve the lengths of both the surface and skeleton edges, the area of cross sections and the volume between cross sections can be approximately preserved. In our experiments, we show that the rotations are natural and volumes are roughly kept. The system achieves real time performance for surface meshes with 5k vertices.

An understanding of light and its interaction with matter is essential to produce images. As the modeling of light sources, light transport and light reflection improves, it becomes possible to render images with increasing realism. The central motivation behind this thesis is to improve realism in computer graphics images by more accurate local shading models and to assist the user to obtain the desired lighting effects with these more complex models. The first part of the thesis addresses the problem of rendering surfaces illuminated by extended (linear and area) light sources. To compute the light reflected by a surface element in a given direction, one needs to determine the unoccluded regions (shadowing) of each light source and then to compute the light reflection (shading) from each of these regions. Traditionally, point light sources are distributed on the lights to approximate both the shadowing and the shading. Instead, an efficient analytical solution is developed for the shading. Shadowing from extended light sources is a fairly expensive process. To give some insights on the complexity of computing shadows, some properties of shadows and algorithms are presented. To reduce the cost of computing shadows from linear light sources, two acceleration schemes, extended from ray tracing, are introduced and evaluated. The second part of this thesis addresses the problem of achieving a desired shading effect by building up systems of constraints. This approach is called inverse shading. It allows a user to obtain a desired lighting effect by interacting directly with the scene model. An interactive modeling system has been built to study the introduction of rendering issues into the modeling process itself. Two rendering aspects are considered: shading and shadows. By specifying a highlight position and size, the unique direction of a directional light source as well as the surface glossiness are determined. Interactively moving this highlight on the surface redefines the light direction while changing its size redefines the surface glossiness. By manipulating shadow volumes (the volume within which a particular light cannot be completely seen), the light source definition and position can be modified. By assigning colours to various points in a 3D scene, information about the colour of a surface as well as other surface characteristics can be deduced. This relatively new concept of defining the causes by manipulating the effects is expected to have a major impact on the design of future computer graphics modeling systems. It begins a new family of tools for the design of more intuitive user interfaces.

Elements, Atoms, and Electrons Matter and Elements Atoms Atomic Structure Isotopes The Periodic Table Electron Structure of Atoms Covalent Bonding and Molecules Interactions between Atoms Covalent Bonds Are Formed by Sharing Outer Electrons Formulae of Compounds Covalent Bonds Formed by Combining Atomic Orbitals Single Overlap, the Sigma-Bond Double Overlap, the Pi-Bond Molecules with s- and p-Bonds Hybrid Molecular Orbitals Forces Within and Between Molecules Ionic Bonding Polar Covalent Bonds Dipole-Dipole Forces The Hydrogen Bond van der Waals Forces The Hydrophobic Effect Coordinate Bonds Chemical Reactions Rates of Reaction Factors Affecting Rate of Reaction Rate Equations Integrated Forms of Rate Equations Zero-Order Reactions Integrated Form of the Zero-Order Rate Equation First-Order Reactions The Integrated Form of the First-Order Rate Equation Second-Order Reactions Integrated Forms of Second-Order Rate Equations Pseudo-First-Order Reactions Reversible Reactions Equilibrium Water The Water Molecule Ice Water Solutions The Mole Concept Calculating Molar Masses Molarity Colloidal Solutions Diffusion and Osmosis Acids, Bases, and Buffers Ionisation of Water The Hydrogen Ion Acids and Bases Strong Acids and Strong Bases Weak Acids and Weak Bases Ka and Kb Relationship between Ka and Kb pH, pOH, pKw, pKa, pKb Solutions of Weak Acids and Bases Salts and Salt Hydrolysis Buffer Systems Calculating the pH Values of Buffers Indicators Titrations Gases Pressure Measurement of Pressure Ideal Gas Laws Partial Pressures Solubility of Gases Diffusion in Gases Aliphatic Carbon Compounds Simple Molecules Containing Carbon Organic Compounds Alkanes and Alkyl Groups Alkenes Alcohols Thiols Aldehydes and Ketones Carboxylic Acids Amines Lipids, Sugars, and Linkages between Reactive Groups Fatty Acids Esters Glycerol Esters Hemiacetals and Hemiketals Simple Sugars Chirality in Simple Sugars Straight-Chain Sugars Spontaneously Form Rings Sugar Hydroxyls Can Be Chemically Modified Sugars Are Joined Together by Glycosidic Bonds Aromatic Carbon Compounds and Isomerism Benzene Bioactive Aromatic Compounds Isomerism Structural Isomerism Chain, Positional, and Functional Group Isomerism Tautomerism Stereoisomerism Geometrical Isomerism Optical Isomerism Organic and Biological Reaction Mechanisms Reactive Sites and Functional Groups Describing Reaction Mechanisms Bimolecular Nucleophilic Substitution Electrophilic Addition to a Nonpolar Double Bond Elimination to Form an Alkene Nucleophilic Addition to a Polar Double Bond Free Radical Reactions Carbon-Carbon Bond Formation in Biosynthesis Sulphur and Phosphorus The Electron-Shell Structure and Valency of Phosphorus and Sulphur Sulphur The Thiol Group and Thiol Esters Phosphate, Pyrophosphate, and Polyphosphate Phosphate Esters The Role of Phosphate Esters and ATP in Cellular Energy Metabolism Oxidation and Reduction Reactions Oxidation Is Linked to Reduction The Chemical Changes in the REDOX Process Splitting REDOX Reactions Standardising REDOX Half-Reactions Predicting Electron Flow Free Energy and Standard Reduction Potentials Redox Reactions and Nonstandard Conditions Metals in Biology General Properties of Metals in Biology Some Properties of Alkali Metals The Alkaline Earth Metals Transition Metals Role of Metal as Oxygen Carrier Metals Facilitate Biocatalysis The Role of Metal Ions as Charge Carriers The Toxicity of Metals Energy The First Law of Thermodynamics Units of Energy Measurement of Energy Internal Energy, U, and Enthalpy, H Calorimetry Hess's Law Enthalpies of Formation The Second Law of Thermodynamics Free Energy Interaction of DeltaH with TDeltaS Reactions and Equilibrium DeltaG and Equilibrium Activation Energy The Effect of the Temperature on Reaction Rate The Arrhenius Equation Catalysis Enzyme Catalysis Kinetics of Enzyme Reactions Finding Vmax and KM Light Light Is Part of the Electromagnetic Spectrum Wavelength and Frequency The Quantum Theory of Light The Absorption of Light The Relationship between Light Absorption and Concentration The Spectrophotometer The Fate of Absorbed Light Appendix: Derivations of Equations Index