We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
This chapter exploresthe Fermi–Pasta–Ulam–Tsingou (FPUT) problem in the context of a one-dimensional chain of interacting point masses. We start by modelling the system as a chain of masses interacting through a force dependent on their relative displacements. Next, we simplify this system to harmonic oscillators under a linear force dependency, further developing it to describe a wave-like behaviour. The chapter discusses dispersion relations and the impact of boundary conditions leading to discretisation of allowed wave modes. A non-linear, second-order interaction is then included, complicating the system’s dynamics and necessitating the use of numerical methods for its solution. We then track the system’s evolution in a multidimensional phase space, leading to observations of seemingly chaotic motion with emerging periodicity. Energy conservation and its flow through the system are crucial aspects of the analysis. A detailed numerical procedure is provided, involving solution of initial value problems, mode projections, and energy computations to explore the complex behaviour inherent in the FPUT problem.
This project looks into the time evolution of a wave function within a two-dimensional quantum well. We start by solving the time-dependent Schrödinger equation for stationary states in a quantum well. Next, we express any wave function as a linear combination of stationary states, allowing us to understand their time evolution. Two methods are presented: one relies on decomposing the wave function into a basis of stationary states and the other on discretisation of the time-dependent Schrödinger equation, incorporating three-point formulas for derivatives. These approaches necessitate confronting intricate boundary conditions and require maintaining energy conservation for numerical accuracy. We further demonstrate the methods using a wave packet, revealing fundamental phenomena in quantum physics. Our results demonstrate the utility of these methods in understanding quantum systems, despite the challenges in determining stationary states for a given potential. This study enhances our comprehension of the dynamics of quantum states in constrained systems, essential for fields like quantum computing and nanotechnology.
Failures to reduce greenhouse gas emissions by adopting policies, technologies, and lifestyle changes have led the world to the brink of crisis, or likely beyond. Here we use Internet surveys to attempt to understand these failures by studying factors that affect the adoption of personal energy conservation behaviors and also endorsement of energy conservation goals proposed for others. We demonstrate an asymmetry between goals for self and others (“I’ll do the easy thing, you do the hard thing”), but we show that this asymmetry is partly produced by actor/observer differences: people know what they do already (and generally do not propose those actions as personal goals) and also know their own situational constraints that are barriers to action. We also show, however, that endorsement of conservation goals decreases steeply as a function of perceived difficulty; this suggests a role for motivated cognition as a barrier to conservation: difficult things are perceived as less applicable to one’s situation.
The top priority in addressing climate change is to reduce net emissions of greenhouse gases to zero as swiftly as possible. Among the policy instruments for achieving this goal: carbon markets and carbon taxes; subsidies and incentives for energy conservation and for developing renewable energy technologies; building a new network of advanced nuclear reactors to provide carbon-free energy; imposing restraints on deforestation and planting large numbers of new trees; developing powerful new technologies for removing carbon dioxide from the atmosphere; incentivizing private citizens to reduce the carbon footprint of their lifestyles; and introducing new governmental policies for decarbonizing national economies. By combining all these strategies, humankind could realistically reach net zero emissions by the middle years of this century. From that point forward, it can start actively removing existing accumulations of carbon dioxide, eventually bringing global warming to a halt and reversing some of the damage that’s already been done.
Today’s youth will inherit the brunt of climate change. Science literacy plays a critical role in raising future adults who commit to climate change mitigation by reducing daily household energy use. The objective of this study was to examine the mediating role of climate change knowledge efficacy on the positive influence of science literacy on engagement in energy conservation at home among Filipino adolescents. Data from the Program for International Student Assessment 2018 which included 7233 15-year-old high school students from 187 schools across 17 regions in the Philippines was used to address the study’s objective. Results showed that climate change knowledge efficacy fully mediated the positive association between science literacy and household energy conservation among Filipino adolescents. The study discussed the importance of emphasizing environmentalism in science education, parenting, and community programs as a viable and long-term climate change mitigation response.
Ernst Mach’s Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit is now widely regarded as occupying a pivotal position in his oeuvre. Erik C. Banks called it a ‘roman à clef’. More generally, it is safe to say that the law of energy conservation played a central role in Mach’s thought. He frequently referred to it in his publications to illustrate how science works. This chapter has a two-fold aim. First, it sets his reflections on energy conservation against the background of its nineteenth-century history. Mach appears as a particularly astute observer of his own time. Second, it relates Mach’s comments on the law to his overall philosophy. Although in the second half of the nineteenth century the importance of the law of energy conservation was generally acknowledged, there was no consensus on what the law actually meant. Its name, discoverer, formulation, justification, and implications were all subject to debate. Mach was at the same time a participant in this debate (interpreting the law of energy conservation) and a commentator on it (interpreting debates on the law of energy conservation). In the process, he developed a new understanding of scientific meaning as grounded in communication, practice, and history.
This volume presents new essays on the work and thought of physicist, psychologist, and philosopher Ernst Mach. Moving away from previous estimations of Mach as a pre-logical positivist, the essays reflect his rehabilitation as a thinker of direct relevance to debates in the contemporary philosophies of natural science, psychology, metaphysics, and mind. Topics covered include Mach's work on acoustical psychophysics and physics; his ideas on analogy and the principle of conservation of energy; the correct interpretation of his scheme of 'elements' and its relationship to his 'historical-critical' method; the relationship of his thought to movements such as American pragmatism, realism, and neutral monism, as well as to contemporary figures such as Friedrich Nietzsche; and the reception and influence of his works in Germany and Austria, particularly by the Vienna Circle.
This paper concerns the energy conservation for the weak solutions of the compressible Navier–Stokes equations. Assume that the density is positively bounded, we work on the regularity assumption on the gradient of the velocity, and establish a Lp–Ls type condition for the energy equality to hold in the distributional sense in time. We mention that no regularity assumption on the density derivative is needed any more.
This chapter illustrates the strategic importance of energy efficiency in the built environment and in industrial and agricultural sectors. It discusses the major energy end-uses within the various sectors, and outlines the types of technologies that can improve efficiency. It describes the barriers that energy efficiency implementation faces, and outlines the strategies and policies to overcome them. The chapter also underlines the synergisms that can occur by integrating energy efficiency with distributed energy strategies, and the strategic importance of creating decentralized options for accessing electricity, heating, and cooling.
The aim of this paper is to prove energy conservation for the incompressible Euler equations in a domain with boundary. We work in the domain $$\TT^2\times\R_+$$, where the boundary is both flat and has finite measure; in this geometry we do not require any estimates on the pressure, unlike the proof in general bounded domains due to Bardos & Titi (2018). However, first we study the equations on domains without boundary (the whole space $$\R^3$$, the torus $$\mathbb{T}^3$$, and the hybrid space $$\TT^2\times\R$$). We make use of somearguments due to Duchon & Robert (2000) to prove energy conservation under the assumption that $$u\in L^3(0,T;L^3(\R^3))$$ and $${|y|\to 0}\frac{1}{|y|}\int^T_0\int_{\R^3} |u(x+y)-u(x)|^3\,\d x\,\d t=0$$ or $$\int_0^T\int_{\R^3}\int_{\R^3}\frac{|u(x)-u(y)|^3}{|x-y|^{4+\delta}}\,\d x\,\d y\,\d t<\infty,\qquad\delta>0$$, the second of which is equivalent to $$u\in L^3(0,T;W^{\alpha,3}(\R^3))$$, $$\alpha>1/3$$.
We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a well known benchmark problem. We derive the analytical basis of nested force-gradient type methods and demonstrate the advantage of the proposed approach, namely reduced computational costs compared with other numerical integration schemes in HMC.
The staggered discontinuous Galerkin (SDG) method has been recently developed for the numerical approximation of partial differential equations. An important advantage of such methodology is that the numerical solution automatically satisfies some conservation properties which are also satisfied by the exact solution. In this paper, we will consider the numerical approximation of the inviscid Burgers equation by the SDG method. For smooth solutions, we prove that our SDG method has the properties of mass and energy conservation. It is well-known that extra care has to be taken at locations of shocks and discontinuities. In this respect, we propose a local total variation (TV) regularization technique to suppress the oscillations in the numerical solution. This TV regularization is only performed locally where oscillation is detected, and is thus very efficient. Therefore, the resulting scheme will preserve the mass and energy away from the shocks and the numerical solution is regularized locally near shocks. Detailed description of the method and numerical results are presented.
The first IAU Office of Astronomy for Development Task Force 3 project on light pollution is described along with evaluations and recommendations for future projects.
This paper presents the results of a study that explored the effectiveness of three intervention strategies in facilitating energy saving behaviour among resident undergraduate university students. In contrast to a dominant practice of motivating with rewards or competition this study sought to appeal to students' intrinsic motivations. An experimental design was used with two intervention groups and a control group. The interventions were the provision of real-time feedback provided by an inhouse energy consumption display unit (ecoMeter) and a targeted social marketing approach. They were evaluated using energy consumption data and self-report data from the participants via an on-line survey and focus groups. Across the three research phases the rate of reduced electricity consumption for the interventions ranged from an average of 17% to 28% less than the control group. The findings provide evidence that facilitation of intrinsically motivated behaviours can result in reduced energy use and greenhouse gas emissions.
This paper is an introduction to a conservative, positive numerical scheme which takes into account the phenomena of reflection and transmission of high frequency acoustic waves at a straight interface between two homogeneous media. Explicit forms of the interpolation coefficients for reflected and transmitted wave vectors on a two-dimensional uniform grid are derived. The propagation model is a Liouville transport equation solved in phase space.
The plane wave stability properties of the conservative schemes of Besse [SIAM J. Numer. Anal.42 (2004) 934–952] and Fei et al. [Appl. Math. Comput.71 (1995) 165–177] for the cubic Schrödinger equation are analysed. Although the two methods possess many of the same conservation properties, we show that their stability behaviour is very different.An energy preserving generalisation of the Fei method with improved stability is presented.
In long-time numerical integration of Hamiltonian systems,and especially in molecular dynamics simulation,it is important that the energy is well conserved. For symplecticintegrators applied with sufficiently small step size, thisis guaranteed by the existence of a modifiedHamiltonian that is exactly conserved up to exponentially smallterms. This article is concerned with the simplifiedTakahashi-Imada method, which is a modificationof the Störmer-Verlet method that is as easy to implement buthas improved accuracy. This integrator is symmetric andvolume-preserving, but no longer symplectic. We study itslong-time energy conservation and give theoreticalarguments, supported by numerical experiments, whichshow the possibility of a drift in the energy (linear or like a random walk).With respect to energy conservation, this article provides empiricaland theoretical data concerning the importance of using a symplecticintegrator.
The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handleeasily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes. They are applied here to DGTD methods on wave propagation problems.
Recommend this
Email your librarian or administrator to recommend adding this to your organisation's collection.