Reiner Kümmel

Optimization of solar district heating systems: seasonal storage, heat pumps, and cogeneration☆

The dynamic energy, emission, and cost optimization model deeco is further developed and applied to the analysis of solar district heating systems with seasonal storage in a pilot project of the Bavarian Research Foundation. The optimum integration of condensing boilers, compression and absorption heat pumps, and cogeneration of heat and power is computed for 100 well insulated housing units with an annual total heat demand of 616 MWh. Collector areas between 1 and 2.5 m2 per MWh heat demand and water storage volumes between 1.2 and 4.2 m3 per m2 collector area satisfy between 32 and 95 per cent of the total heat demand by solar thermal heat. Compared with a reference case with individual condensing boilers and electricity taken from the public grid, selected scenarios achieve (non-renewable primary) energy savings between 15 and 35% associated with cost increases between −20% and 140%; cogeneration turns out to be quite attractive from an economical point of view. With cogeneration and a solar contribution to the heat supply of 80%, emission reductions of CO2-equivalents by 33%, SO2 by 20%, and NOx by 22% can be achieved at cost increases of 120%. Fossil fuel savings of more than 40% are possible if electricity is produced from non-fossil energy sources.

Capital, labor, energy and creativity: modeling innovation diffusion ☆

Abstract Economic growth in the USA, Japan, and Germany during three decades and the recessions during the energy crises are well reproduced by production functions that depend on capital, labor, energy and three technology parameters. Time changes of these parameters model innovation diffusion, driven by creativity. In all three countries the time-averaged elasticities of production of energy exceed the share of energy cost in total factor cost by about an order of magnitude, and those of labor are much less than labors cost share. Only for capital; elasticities and shares are roughly in equilibrium.

Thermodynamic laws, economic methods and the productive power of energy

Abstract Energy plays only a minor role in orthodox theories of economic growth, because standard economic equilibrium conditions say that the output elasticity of a production factor, which measures the factors productive power, is equal to the factors share in total factor cost. Having commanded only a tiny cost share of about 5 percent so far, energy is often neglected altogether. On the other hand, energy conversion in the machines of the capital stock has been the basis of industrial growth. How can the physically obvious economic importance of energy be reconciled with the conditions for economic equilibrium, which result from the maximization of profit or overall welfare? We show that these equilibrium conditions no longer yield the equality of cost shares and output elasticities, if the optimization calculus takes technological constraints on the combinations of capital, labor, and energy into account. New econometric analyses of economic growth in Germany, Japan, and the USA yield output elasticities that are for energy much larger and for labor much smaller than their cost shares. Social consequences are discussed.

Theory of valley-splitting in surface quantum states of Silicon MOSFETS

The experimentally observed removal of valley degeneracy along the (100)-axis in the surface quantum states of Silicon MOSFETS is explained as an effect due to the electric field and spin-orbit interaction. A combination of crystal momentum representation and effective mass theory is used from which results that within the one-band approximation a magnetic field normal to the Si surface and the electric gate field act upon the electrons independently from each other.

How energy conversion drives economic growth far from the equilibrium of neoclassical economics

Energy conversion in the machines and information processors of the capital stock drives the growth of modern economies. This is exemplified for Germany, Japan, and the USA during the second half of the 20th century: econometric analyses reveal that the output elasticity, i.e. the economic weight, of energy is much larger than energy?s share in total factor cost, while for labor just the opposite is true. This is at variance with mainstream economic theory according to which an economy should operate in the neoclassical equilibrium, where output elasticities equal factor cost shares. The standard derivation of the neoclassical equilibrium from the maximization of profit or of time-integrated utility disregards technological constraints. We show that the inclusion of these constraints in our nonlinear-optimization calculus results in equilibrium conditions, where generalized shadow prices destroy the equality of output elasticities and cost shares. Consequently, at the prices of capital, labor, and energy we have known so far, industrial economies have evolved far from the neoclassical equilibrium. This is illustrated by the example of the German industrial sector evolving on the mountain of factor costs before and during the first and the second oil price explosion. It indicates the influence of the ?virtually binding? technological constraints on entrepreneurial decisions, and the existence of ?soft constraints? as well. Implications for employment and future economic growth are discussed.

The Impact of Entropy Production and Emission Mitigation on Economic Growth

Entropy production in industrial economies involves heat currents, driven by gradients of temperature, and particle currents, driven by specific external forces and gradients of temperature and chemical potentials. Pollution functions are constructed for the associated emissions. They reduce the output elasticities of the production factors capital, labor, and energy in the growth equation of the capital-labor-energy-creativity model, when the emissions approach their critical limits. These are drawn by, e.g., health hazards or threats to ecological and climate stability. By definition, the limits oblige the economic actors to dedicate shares of the available production factors to emission mitigation, or to adjustments to the emission-induced changes in the biosphere. Since these shares are missing for the production of the quantity of goods and services that would be available to consumers and investors without emission mitigation, the “conventional” output of the economy shrinks. The resulting losses of conventional output are estimated for two classes of scenarios: (1) energy conservation; and (2) nuclear exit and subsidies to photovoltaics. The data of the scenarios refer to Germany in the 1980s and after 11 March 2011. For the energy-conservation scenarios, a method of computing the reduction of output elasticities by emission abatement is proposed.

Ehrenfest theorem for inhomogeneous superconductors and supercurrent force on Andreev reflected quasiparticles

Quasiclassical equations of motion are derived for quasiparticle wave packets in inhomogeneous superconductors with electromagnetic fields. Besides the Lorentz forces on electrons and holes there are two off-diagonal pair potential forces. The first one is due to gradients of the modulus of the pair potential and responsible for electron-hole scattering from inhomogeneities of the pair potential. The second one results from interactions with the ground state condensate and is proportional to the gauge invariant Cooper pair velocity of surface supercurrents in the interfaces between normal and superconducting regions. The most favorable experimental conditions for the observation of this new force may be found inN-S junctions composed of clean normal metals and type II superconductors with high critical fields, large London penetration depths, and large energy gaps.

Excitation spectrum of a paramagnetic-superconducting contact

A calculation of the bound states in a paramagnetic-superconducting contact, valid at any temperature belowTc, is performed by using a recently developed method of solving the Bogoliubov equations. The problem of self-consistency of the pair-potentialΔ(x) is being avoided by leaving open the detailed form ofΔ(z), introducing instead the characteristic lenghth for the spatial variation of the pair-potential,d=O∫D(1−Δ(z)/Δ)dz, as a fit parameter. The energies, the quasiparticle wave-functions and the density of the bound states are calculated for negligible impurity scattering. The energy gap of the excitation spectrum reduces from about one third of its bulk value to practically zero as the thicknessa of the normal film increases froma≪d toa≫d.ZusammenfassungDie gebundenen Zustände in einem Kontakt zwischen einem paramagnetischen Metall und einem Supraleiter werden mit Hilfe einer kürzlich entwickelten Methode zur Lösung der Bogoliubov-Gleichungen für beliebige Temperaturen unterhalbTc berechnet. Unter Umgehung des Problems der Selbstkonsistenz des PaarpotentialsΔ(z) wird die charakteristische Länge für die räumliche Änderung des Paarpotentials,d=O∫D(1−Δ(z)/Δ)dz, als Anpaßparameter eingeführt. Die Energien, die Quasitelchen-Wellenfunktionen und die Dichte der gebundenen Zustände werden unter Vernachlässigung der Streuung an Verunreinigungen berechnet. Die Energielücke des Anregungsspektrums nimmt von einem Drittel ihres Wertes für einen unendlich ausgedehnten Supraleiter auf Null ab, wenn die Dickea des normalen Films vona≪d aufa≫d anwächst.RésuméOn calcule les états liés d’un contact paramagnétique — supra-conducteur en utilisant une méthode récemment développée pour la solution des équations de Bogoliubov, valable pour toute température inférieure àTc. Afin d’éviter le problème de la self-consistence du potentiel de pairesΔ(z), la présente description fait intervenir comme paramètre ajustable la longueur caractéristique pour la variation spatiale de ce potential,d=O∫D(1−Δ(z)/Δ)dz. Les énergies, les fonctions d’onde des quasi-particules et la densité des états liés sont exprimées en négligeant la diffusion par des impuretés. On trouve que la largeur de la bande interdite du spectre d’excitations dépend de l’épaisseura de la couche normale, valant environ le tiers de celle d’un supraconducteur massif poura≪d, elle tend vers zéro poura≫d.

Prologue: Time Travel with Abel

Traveling in time and space from the Big Bang to the Sun and through the ages of the Earth we note that energy conversion is the prime mover in the evolution of life and the universe. We are witness to two revolutionary changes in the development of civilization when humans enhanced their access to the energy sources produced by the Sun. First, they increased their use of living biomass by the invention of farming and cattle breeding in the Neolithic Revolution after the climate had warmed and stabilized. About 10, 000 years later, humans started to exploit fossil energies by with the invention of the steam engine during the Industrial Revolution. Even without heat engines, Europeans had already conquered the world with firearms and sailing ships, which utilized the chemical energy of gunpowder and the kinetic energy of the wind. European dominance was shattered by World Wars I and II, which could not have gone global without fossil-fuel-powered heat engines. Since then, heat engines and transistors have decisively assisted the increasing production of material wealth. The resulting resource depletion and environmental pollution must be mitigated by a careful observation of the natural laws governing energy and entropy.

Epilogue: Decisions Under Uncertainty

The easily accessible fossil energy sources are drying up, pollution is creating ecological problems on a global scale, and the increasing costs of providing energy contribute to the growing instability of the global financial system. The very uneven distribution of wealth that has resulted on national and global scales is likely to create social tensions and breakdowns that are dangerous in a world of growing population and nuclear weapons. All technical and social actions that may avoid a Dark Age of battles for diminishing resources bear risks, whose assessments by individuals and nations differ substantially. The first decision to be taken under these uncertainties should concern the legal framework of the market and its adjustment to the challenges of a future ruled more clearly than ever by energy and entropy. This adjustment should stimulate energy conservation and emission mitigation. Furthermore, it should invigorate those sectors of the economy where humans cannot be easily pushed aside by energy-powered machines, and observe simultaneously that the production of material wealth rests on the conversion of nature’s gift of energy into physical work. Whether the appropriate instrument is a social-ecological tax reform that shifts the burden of taxes and levies from labor to energy according to the productive power of these factors is a question that voters and governments will have to decide. Their decisions may well depend on the general acceptance of old and seemingly trite rules of conduct that serve to promote a minimum level of equity for all.