Thermal physics of the atmosphere

Thermal Physics of the Atmosphere offers a concise and thorough introduction on how basic thermodynamics naturally leads on to advanced topics in atmospheric physics. The book starts by covering the basics of thermodynamics and its applications in atmospheric science. The later chapters describe major applications, specific to more specialized areas of atmospheric physics, including vertical structure and stability, cloud formation, and radiative processes. The book concludes with a discussion of non-equilibrium thermodynamics as applied to the atmosphere. This book provides a thorough introduction and invaluable grounding for specialised literature on the subject. Introduces a wide range of areas associated with atmospheric physics Starts from basic level thermal physics Ideally suited for readers with a general physics background Self-assessment questions included for each chapter Supplementary website to accompany the book

Space physics for graduate students: an activities-based approach

The geospace environment is controlled largely by events on the Sun, such as solar flares and coronal mass ejections, which generate significant geomagnetic and upper atmospheric disturbances. The study of this Sun-Earth system, which has become known as space weather, has both intrinsic scientific interest and practical applications. Adverse conditions in space can damage satellites and disrupt communications, navigation, and electric power grids, as well as endanger astronauts. The Center for Integrated Space Weather Modeling (CISM), a Science and Technology Center (STC) funded by the U.S. National Science Foundation (see http://www.bu.edu/cism/), is developing a suite of integrated physics-based computer models that describe the space environment from the Sun to the Earth for use in both research and operations [Hughes and Hudson, 2004, p. 1241]. To further this mission, advanced education and training programs sponsored by CISM encourage students to view space weather as a system that encompasses the Sun, the solar wind, the magnetosphere, and the ionosphere/thermosphere. This holds especially true for participants in the CISM space weather summer school [Simpson, 2004].

Metrics for solar wind prediction models: Comparison of empirical, hybrid, and physics-based schemes with 8 years of L1 observations

Space weather effects on technological systems originate with energy carried from the Sun to the terrestrial environment by the solar wind. In this study, we present results of modeling of solar corona-heliosphere processes to predict solar wind conditions at the L1 Lagrangian point upstream of Earth. In particular we calculate performance metrics for (1) empirical, (2) hybrid empirical/physics-based, and (3) full physics-based coupled corona-heliosphere models over an 8-year period (1995–2002). L1 measurements of the radial solar wind speed are the primary basis for validation of the coronal and heliosphere models studied, though other solar wind parameters are also considered. The models are from the Center for Integrated Space-Weather Modeling (CISM) which has developed a coupled model of the whole Sun-to-Earth system, from the solar photosphere to the terrestrial thermosphere. Simple point-by-point analysis techniques, such as mean-square-error and correlation coefficients, indicate that the empirical coronal-heliosphere model currently gives the best forecast of solar wind speed at 1 AU. A more detailed analysis shows that errors in the physics-based models are predominately the result of small timing offsets to solar wind structures and that the large-scale features of the solar wind are actually well modeled. We suggest that additional “tuning” of the coupling between the coronal and heliosphere models could lead to a significant improvement of their accuracy. Furthermore, we note that the physics-based models accurately capture dynamic effects at solar wind stream interaction regions, such as magnetic field compression, flow deflection, and density buildup, which the empirical scheme cannot.

The role of lateral ocean physics in the upper ocean thermal balance of a coupled ocean-atmosphere GCM

The sensitivity of the upper ocean thermal balance of an ocean-atmosphere coupled GCM to lateral ocean physics is assessed. Three 40-year simulations are performed using horizontal mixing, isopycnal mixing, and isopycnal mixing plus eddy induced advection. The thermal adjustment of the coupled system is quite different between the simulations, confirming the major role of ocean mixing on the heat balance of climate. The initial adjustment phase of the upper ocean (SST) is used to diagnose the physical mechanisms involved in each parametrisation. When the lateral ocean physics is modified, significant changes of SST are seen, mainly in the southern ocean. A heat budget of the annual mixed layer (defined as the “bowl”) shows that these changes are due to a modified heat transfer between the bowl and the ocean interior. This modified heat intake of the ocean interior is directly due to the modified lateral ocean physics. In isopycnal diffusion, this heat exchange, especially marked at mid-latitudes, is both due to an increased effective surface of diffusion and to the sign of the isopycnal gradients of temperature at the base of the bowl. As this gradient is proportional to the isopycnal gradient of salinity, this confirms the strong role of salinity in the thermal balance of the coupled system. The eddy induced advection also leads to increased exchanges between the bowl and the ocean interior. This is both due to the shape of the bowl and again to the existence of a salinity structure. The lateral ocean physics is shown to be a significant contributor to the exchanges between the diabatic and the adiabatic parts of the ocean.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Well-posed boundary value problems for integrable evolution equations on a finite interval

We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

Mathematical modelling of decision making processes in construction projects

Many different individuals, who have their own expertise and criteria for decision making, are involved in making decisions on construction projects. Decision-making processes are thus significantly affected by communication, in which a dynamic performance of human intentions leads to unpredictable outcomes. In order to theorise the decision making processes including communication, it is argued here that the decision making processes resemble evolutionary dynamics in terms of both selection and mutation, which can be expressed by the replicator-mutator equation. To support this argument, a mathematical model of decision making has been made from an analogy with evolutionary dynamics, in which there are three variables: initial support rate, business hierarchy, and power of persuasion. On the other hand, a survey of patterns in decision making in construction projects has also been performed through self-administered mail questionnaire to construction practitioners. Consequently, comparison between the numerical analysis of mathematical model and the statistical analysis of empirical data has shown a significant potential of the replicator-mutator equation as a tool to study dynamic properties of intentions in communication.

An integrated mathematical model to evaluate nutrient partition in dairy cattle between the animal and its environment

In the past decade, a number of mechanistic, dynamic simulation models of several components of the dairy production system have become available. However their use has been limited due to the detailed technical knowledge and special software required to run them, and the lack of compatibility between models in predicting various metabolic processes in the animal. The first objective of the current study was to integrate the dynamic models of [Brit. J. Nutr. 72 (1994) 679] on rumen function, [J. Anim. Sci. 79 (2001) 1584] on methane production, [J. Anim. Sci. 80 (2002) 2481 on N partition, and a new model of P partition. The second objective was to construct a decision support system to analyse nutrient partition between animal and environment. The integrated model combines key environmental pollutants such as N, P and methane within a nutrient-based feed evaluation system. The model was run under different scenarios and the sensitivity of various parameters analysed. A comparison of predictions from the integrated model with the original simulation models showed an improvement in N excretion since the integrated model uses the dynamic model of [Brit. J. Nutr. 72 (1994) 6791 to predict microbial N, which was not represented in detail in the original model. The integrated model can be used to investigate the degree to which production and environmental objectives are antagonistic, and it may help to explain and understand the complex mechanisms involved at the ruminal and metabolic levels. A part of the integrated model outputs were the forms of N and P in excreta and methane, which can be used as indices of environmental pollution. (C) 2004 Elsevier B.V All rights reserved.

Use and abuse of mathematical models: an illustration from the 2001 foot and mouth disease epidemic in the United Kingdom

Foot and mouth disease (FMD) is a major threat, not only to countries whose economies rely on agricultural exports, but also to industrialised countries that maintain a healthy domestic livestock industry by eliminating major infectious diseases from their livestock populations. Traditional methods of controlling diseases such as FMD require the rapid detection and slaughter of infected animals, and any susceptible animals with which they may have been in contact, either directly or indirectly. During the 2001 epidemic of FMD in the United Kingdom (UK), this approach was supplemented by a culling policy driven by unvalidated predictive models. The epidemic and its control resulted in the death of approximately ten million animals, public disgust with the magnitude of the slaughter, and political resolve to adopt alternative options, notably including vaccination, to control any future epidemics. The UK experience provides a salutary warning of how models can be abused in the interests of scientific opportunism.

A mathematical model of the in vitro keratinocyte response to chromium and nickel exposure

A mathematical model describing the main mechanistic processes involved in keratinocyte response to chromium and nickel has been developed and compared to experimental in vitro data. Accounting for the interactions between the metal ions and the keratinocytes, the law of mass action was used to generate ordinary differential equations which predict the time evolution and ion concentration dependency of keratinocyte viability, the amount of metal associated with the keratinocytes and the release of cytokines by the keratinocytes. Good agreement between model predictions and existing experimental data of these endpoints was observed, supporting the use of this model to explore physiochemical parameters that influence the toxicological response of keratinocytes to these two metals.