Preface: Seismic imaging is the process through which seismograms recorded on the Earth surface are mapped into representations of its interior properties // Imaging methods are nowadays applied to a broad range of seismic observations from near surface environ mental studies to oil and gas exploration even to long period earthquake seismology // The characteristic length scales of the features imaged by these techniques range over many orders of magnitude // Yet there i...

Abstract: The present paper gives an overview of the CALPHAD method and recent progress made. A brief history is given then the scope of phase diagram calculations is described. Thermodynamic descriptions most commonly used in the Calphad method are described and the methods used to obtain the numerical values for these descriptions are outlined. Extrapolation to higher-component systems is explained and recent progress in the quality of assessments is demonstrated. A br...

Excerpt: The previous edition, which was the first, of this National Institute of Standards and Technology (NIST) Technical Note (TN 1297) was initially published in January 1993. A second printing followed shortly thereafter, and in total some 10 000 copies were distributed to individuals at NIST and in both the United States at large and abroad - to meteorologists, scientists, engineers, statisticians, and others who are concerned with measurement and the evaluation an...

Introduction: Physics can be defined as the science of predicting the motion of objects. A science is supposed to be quantitative: the goal of physics is to predict the function x(t) that gives the position of an object as a function of time. (More precisely, in a three-dimensional space we need the three functions x(t), y(t), and z(t) that determine the three coordinates of our object) The possibility of a physical science is obvious from our daily observation of regula...

Introduction: In this brief chapter we review some elementary topics in the physics of systems of particles with the idea of applying these concepts to the study of systems with many particles, where thermodynamic concepts such as temperature can be defined ...

Introduction: The study of systems of many particles is facilitated by the introduction of the concept of temperature. We will do this by successive approximations. We will start with a definition of temperature that is not very rigorous. With the help of this definition, however, we will be able to study a number of systems and improve our definition of temperature. Eventually, we will provide the most rigorous definition, but this will have to await the introduction of...

Introduction: When we discussed the ideal gas, we were able to justify the empirical equation of state pV = NkT from the point of view of Newtonian mechanics. We achieved this by defining certain intuitive ideas, such as temperature, in terms of precise mechanical concepts and by making reasonable assumptions concerning the statistical distribution of velocities in the gas. We also showed that our definition of temperature as proportional to the average kinetic energy is...

Introduction: The problem of a mass attached to a spring was discussed in previous physics courses. As you remember, the mass oscillates around the point where the spring is not stretched. The reason we are reviewing this problem here is that we want to study waves, which are the oscillations of a system of many masses connected by many springs. As you will see, the generalization to many masses is surprisingly straightforward once you understand the problem of a single oscillating mass.

Introduction: Our Chapter 2 discussion of the oscillations of a single mass attached to a spring was a review of material you learned in previous physics courses. In this chapter, we would like to start with a specific PHY 241 topic: the oscillations of several - perhaps many - masses connected by springs. Ultimately, this will lead to the concept of waves.

Introduction: Our discussion in the previous chapter shows that the calculation of normal modes in a vibrating system becomes more and more difficult as the number of masses increases. It appears that for real systems such as crystals, which have as many as 1023 atoms/cm3, no supercomputer will ever be able to calculate the normal modes of vibration. However, we hinted at a possible solution of this problem for systems that have some type of symmetry. Crystals do display...

Introduction: The method we developed in the previous chapter makes it possible to study the vibrations of any real system. Let us discuss for example a guitar?s string. We can consider the string as a chain of masses. The masses of the chain correspond to the atoms in the string. Because there are zillions of atoms in a string, there is a correspondingly huge number of normal modes. However, the modes we excite when we play the guitar are a few modes for which the wavel...

Introduction: The standing waves we found as solutions to the wave equation can be used to explain any type of vibration in continuous media, since they represent the most general solution to the problem. Any arbitrary set of initial conditions can be taken care of by appropriately selecting the adjustable parameters in the expression for the standing waves. On the other hand, these standing waves are particularly inappropriate to illustrate certain kind of very common w...

Introduction: A fundamental property of the solutions to the continuum wave equation is the linear relationship w = ck between frequency and wave number, or, equivalently, the famous in = c relationship. The most important implication of this relationship is the following: if a certain perturbation is imposed on a medium, the perturbation travels without distortion. You have already found one such case in Problem 2, Chapter 5, where you started with a rectangular shape a...

Introduction: The basic laws of electromagnetism were established in the nineteenth century. Initially, the electric and magnetic interaction were considered to be independent, each of them governed by its own Gauss-like law. Ampere?s law provided the first hint of a linkage, since it acknowledged the fact that moving charges produce magnetic fields. The link between electric and magnetic fields was further clarified by Faraday?s induction law. Finally, James Clerck Maxw...

Introduction: When you solved Problem 5.2 using the standing-wave approach, you found a rather curious behavior as the wave propagates and meets the boundary. A new wave emerges from the boundary, traveling in the opposite direction and inverted, as seen in?