# Jürgen MimkesUniversität Paderborn | UPB · Department of Physics, http://physik.uni-paderborn.de/ag/ag-mimkes/publikationen/

Jürgen Mimkes

Prof. Dr. Dipl. Phys.

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93

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April 1977 - July 2004

## Publications

Publications (93)

In the Covid-19-pandemic, the numbers of deceased do not consistently follow the number of new infections. The CFR mortality has declined in Germany from 5 % to 0.4 %. However, if we interpret the portion of positive tests as a positive rate, we find the positive rate and the numbers of deceased to run parallel with an offset of about 13 days. This...

In a disease, where all infected persons show symptoms, it is reasonable to calculate mortality by case to fatality rate CFR. Deaths follow infections by a certain time lag. However, in the Covid-19 pandemic many infectious patients show no or hardly any symptoms. The reported infections and deaths do not run parallel, but diverge with the volume o...

In Germany and other countries, a second wave of corona infections has been observed since July 2020, after the first wave has subsided. We have investigated both waves by a modified SIR-SI infection model, adapted to the data to the Robert-Koch-Institute (RKI) or the Johns- Hopkins-University (JHU).
The first wave is characterized by the SIR model...

In the first part, this chapter discusses a model of the known and unknown elements in science, by which it is possible to select or exclude various mathematical approaches to social and natural sciences. As a result, economics and physics may be formulated by various mathematical fields: differential forms, closed integrals, stochastic theory, non...

This article presents a mathematical infection model that is designed to estimate the course of coronavirus infection in Germany for several days in advance: How many people become ill or die, what is the temporal development? If the contact restriction is perfect, then the model predicts the development of the virus infection after the initial sub...

The future contains terms (V) that are valid at all times, and terms (U) that are presently unknown. In economics, (V) and (U) correspond to ex ante and ex post, in physics to conservative and not conservative, in calculus, to exact and not exact differential forms or to Riemann and Stokes integrals, and to linear or non-linear equations, in statis...

In engineering calculus of closed Stokes integrals leads to the Carnot circuit of motors or refrigerators with two levels: hot and cold. In economics calculus of closed Stokes integrals leads to capitalistic circuits with two levels: capital and labour in production and buy cheap and sell expensive in trade. There are many parallels between motors...

Thermodynamics and economics have developed independently through the last centuries. Only in the last three decades, scientists have realized the close relationship between economics and physics. The name of the new field is econophysics: In double-entry accounting, the sum of monetary and productive accounts is zero. In calculus, monetary and pro...

Economics is a field that looks into the future. We may know a few things ahead (ex ante), but most things we only know, afterwards (ex post). How can we work in a field, where much of the important information is missing? Mathematics gives two answers: 1. Probability theory leads to microeconomics: the Lagrange function optimizes utility under con...

Closed integrals in physics lead to equations for sources and vortices in fluid mechanics, electrodynamics and thermodynamics. In economics, the Stokes integral of economic circuits leads to new fundamental equations of macro-econophysics. These equations differ significantly from the laws of neoclassical theory. Entropy of markets replaces of the...

Si-doping of cubic GaN epilayers grown by an rf plasma-assisted molecular beam epitaxy on semi-insulating GaAs (001) substrates is investigated by secondary ion mass spectroscopy (SIMS), photoluminescence (PL) and by Hall-effect measurements. SIMS measurements show a homogeneous incorporation of Si in cubic GaN epilayers up to concentrations of 5*1...

We try to construct an evolutionary theory of economic and social interaction of heterogeneous agents. Modern physics is helpful
for such an attempt, as the recent flourishing of econophysics exemplifies. In this article, we are interested in a specific
or more fundamental use of physics rather than in the recent researches of econophysics. In the...

Temperature dependent Hall-Effect-measurements on unintentionally doped cubic GaN epilayers grown by molecular beam epitaxy (MBE) are reported. The cubic GaN layers have been deposited on semiinsulating (001) GaAs-substrates under N-stabilized growth conditions which were controlled by in-situ reflection high energy electron diffraction (RHEED) mea...

P-type doping with Mg and n-type doping with Si of cubic GaN (c-GaN) epilayers is reported. Cubic GaN films are grown by rf-plasma assisted MBE on semi-insulating GaAs (001) substrates at a substrate temperature of 720°C. Elemental Mg and Si are evaporated from thermal effusions cells. Secondary ion mass spectroscopy (SIMS), low temperature photolu...

In der Ökonomie lassen sich viele Funktionen wie Gewinn oder Einkommen nicht von vornherein berechnen. Diese “weichen” Funktionen heißen Putty (Lehm) und lassen sich durch Stokes-Integrale darstellen. Die Anwendung dieser Integrale auf den modernen Wirtschaftskreislauf nach Irving Fisher führt auf zwei Hauptstze der Ökonomie, die denen der Thermody...

Economic growth depends on capital and labor and two-dimensional calculus has been applied to economic theory. This leads to Riemann and Stokes integrals and to the first and second laws of production and growth. The mathematical structure is the same as in thermodynamics, economic properties may be related to physical terms: capital to energy, pro...

Econophysics is the transfer of methods from natural to socio-economic sciences. This concept has first been applied to finance1, but it is now also used in various applications of economics and social sciences [2,3]. The present paper focuses on problems
in macro economics and growth. 1. Neoclassical theory [4, 5] neglects the “ex post” property o...

So far econophysics has given contributions in four areas of economics: financial markets, wealth and income distribution,
industrial economics (firms’ size distribution, growth rates) and, more recently, networks analysis. According to Gallegati et al., 2006, there are some weakness in the approach: a lack
of awareness of work that has been done w...

The behavior of traffic agents is an important topic of recent discussions in social and economic sciences (Helbing, 2002). The methods are generally based on the Focker Planck equation or master equations (Weidlich, 1972, 2000). The present investigations are based on the statistics of binary decisions with constraints. This method is known as the...

IntroductionDifferential Forms Exact Differential FormsNot Exact Differential FormsThe Integrating FactorThe First and Second Law of Differential FormsNot Exact Differential Forms in Thermodynamics and EconomicsThe First Law of Economics The First Law: Capital Balance of ProductionWork (W)Surplus (ΔQ)Capital (E)The Second Law of Economics The Secon...

IntroductionProbability Normal DistributionConstraintsProbability with Constraints (Lagrange Principle)Elements of Societies AgentsGroupsInteractionsClassesStates: Collective vs IndividualHomogenious Societies The Three States of Homogeneous Societies Atomic Systems: H2OSocial Systems: Guided ToursEconomic Systems: CompaniesPolitical Systems: Count...

Physicists often model economic interactions like collisions of atoms in gases: by interaction one agent gains, the other loses. This leads to a Boltzmann distribution of capital, which has been observed in wealth distributions of different countries. However, economists object: no economic agent will attend a market in which he gets robbed! This c...

The Solow-Swan model of economic growth is reviewed on the basis of natural production. Natural growth is a biochemical process
based on the laws of thermodynamics. Economic production - like work in thermodynamics - is a non exact differential. The
production function Y (a, b) as a function of laborers (a) and (b) depends on the path of integratio...

Econophysics has emerged in the past 10 years as an important and active area of research for physicists and economistsl.
Within Europe, the USA and Australasia, there have been a number of important meetings dedicated to the area. We note for
example, the European Physical Society’s series of APFA meetings (Application of Physics to Financial Anal...

Economic growth is a result of production and may be calculated by a differential form δq(K, L), which depends on capital (K) and labor (L). Differential forms in two variables are generally not exact. Accordingly, a general production function q does not exist ex ante, the integral ∫ δq may not be calculated, unless the path of integration is give...

The Lagrange principle L = f + λg → maximum! is used to maximize a function f(x) under a constraint g(x). Economists regard f(x) = U as a rational production function, which has to be maximized under the constraint of prices g(x). In physics f(x) = lnP is regarded as entropy of a stochastic system, which has to be maximized under constraint of ener...

Two sets of high quality income data are analysed in detail, one set from the UK, one from the USA. It is firstly demonstrated that both a log-normal distribution and a Boltzmann distribution can give very accurate fits to both these data sets. The absence of a power tail in the US data set is then discussed. Taken in conjunction with detailed evid...

Interactions of heterogeneous agents have been calculated from probability theory with constraints (Lagrange principle): L = E + T In P
L is the Lagrange function, the constraints E are the interactions of agents, P is the probability of a distribution pattern of the agents. The laws of interaction stand for order, the entropy In P for disorder of...

Statistical models of economic distributions lead to Boltzmann distributions rather than a Pareto power law. This result is supported by two facts: 1. the distributions of income, car sales, marriages or jobs are a matter of chances and luck and not of reason! 2. Data for property, automobile sales, marriages and job markets were analyzed by two mo...

Successful p-type doping of cubic GaN epilayers by carbon using an e-beam evaporation source is reported. At room temperature Hall-effect measurements of the C-doped cubic GaN epilayer gave hole concentrations and hole mobilities as high as 6 ï¿½ 1017 cmï¿½-ï¿½3 and 200 cm2/Vs, respectively. The thermal activation energy of the C-acceptor is (215 ï...

Cubic gallium nitride epilayers were successfully doped with carbon using an e-beam evaporation source. Room temperature Hall measurements revealed hole concentrations up to 6×1017cm−3 and hole mobilities of 200cm2/Vs. Low temperature (2K) photoluminescence showed a donor–acceptor transition at 3.08eV, which could clearly be assigned to the incorpo...

Integration ist das friedliche und gleichberechtigte Zusammenleben verschiedener Gruppen in einer Gesellschaft. Dies ist kein leichter Prozess, wie wir bei der anstehenden Integration Europas und bei der Integration ausländischer Zuwanderer in Deutschland sehen, aber diese Schwierigkeiten hat es zu allen Zeiten gegeben und sie existieren auf der ga...

A vertically structured cubic GaN p–n light emitting diode was grown on n-type GaAs (001) by plasma assisted molecular beam epitaxy. Elemental Mg and Si beams were used for p- and n-type doping, respectively. Current–voltage and capacitance–voltage measurements of the cubic GaN n+–p junction are performed at room temperature. The optical properties...

Statistics: Order-disorder problems in many-particle statistics may be solved by the Lagrange principle: L=TlogP+E→maximum!
L is the Lagrange function, logP the entropy and E a special condition of order for a system of interacting objects. T is an ordering parameter: for low values of T order (E), for high values of T, disorder or chaos (logP) wil...

ZnSe diodes grown on (100) GaAs substrates by molecular beam epitaxy were investigated using cathodoluminesence (CL) measurements at sample temperatures between 50 and 300 K. The CL line scans at different photon energies were performed on cleaved p–n junctions at 50 and 300 K, respectively. Taking into account surface recombination, carrier genera...

A cubic GaN p–n diode has been grown on n-type GaAs (001) substrates by plasma assisted molecular epitaxy. For p- and n-type doping, elemental Mg and Si beams have been used, respectively. The optical properties are characterized by photoluminescence at room temperature and 2 K. Current–voltage and capacitance–voltage measurements of the cubic GaN...

Si-doping of cubic GaN epilayers grown by an rf plasma-assisted molecular beam epitaxy on semi-insulating GaAs (001) substrates is investigated by secondary ion mass spectroscopy (SIMS), photoluminescence (PL) and by Hall-effect measurements. SIMS measurements show a homogeneous incorporation of Si in cubic GaN epilayers up to concentrations of 5*1...

P-type doping with Mg and n-type doping with Si of cubic GaN (c-GaN) epilayers is reported. Cubic GaN films are grown by rf-plasma assisted MBE on semi-insulating GaAs (001) substrates at a substrate temperature of 720°C. Elemental Mg and Si are evaporated from thermal effusions cells. Secondary ion mass spectroscopy (SIMS), low temperature photolu...

Diffusion of Cu, Ag, Au, Ge and Zn in single crystal gallium antimonide has been carried out by measuring Hall effect according to van der Pauw, conductivity, energy dispersive X-ray (EDX) and surface electron microscopy. The best results have been obtained in excess of antimony. The resulting diffusion data in GaSb are diffusivity Do, activation e...

Diffusion of Cu, Ag, Au, Ge and Zn in the single crystal of gallium antimonide (GaSb) was carried out by measuring Hall effect according to van der Pauw, conductivity, energy dispersive X-ray and surface electron microscopy. The best results have been obtained with an excess of antimony. The resulting diffusion data in GaSb are difussivity D0, acti...

Temperature-dependent Hall-effect measurements are performed on cubic GaN layers grown by plasma-assisted molecular-beam epitaxy on (100) GaAs substrates. We find that under N-rich conditions, cubic GaN films are p-type with hole concentrations of ~=1013 cm-3 and mobilities of about 350 cm2/V s at room temperature. The acceptors have an activation...

The relationship betwwen diffusion and phase diagram is discussed in more detail for AgAu and AuNi alloys. For each alloy tracer diffusion and interdiffusion data have been compared with the corresponding phase diagram.Tracer diffusion is related to the solid-liquid phase transition. Ag and Au tracer diffusivities D∗(x) in AgAu alloys and meltin...

The model of regular solutions, that may be applied to binary alloys (e.g. Au−Pt, Si−Ge) has been compared to binary societies:
blacks—non-blacks in the US, catholics—non-catholics, foreigners—German citizen. The excellent agreement of phase diagrams
and intermarriage data encourages a calculation of the multicultural society by functions of thermo...

The Grüneisen-Debye equation of state (EOS) is presented for cubic solids. The Helmholtz free energy F(T,V) is obtained from the second integral of the Grüneisen relation. F(T,V) is determined by six constants: molar volume V0, cohesive energy εc, Debye temperature Θ,0, Grüneisen parameter Γ, exponent δ and constant of electronic contribution to sp...

The Grüneisen relation Γ = αpKTV/Cν has been integrated with respect to T at constant volume. This leads to a potential E(V) with the two exponents Γ = m/3 and δ = n/3. The Grüneisen constant Γ is the exponent of the repulsive term. The exponent δ of the attractive term may be determined from heat capacity, thermal expansion and cohesive energy, δ...

The enthalpy of monovalent metals is calculated as a function of electron density according to the model of nearly free electrons. The coefficient of thermal expansion of solid and liquid monovalent metals is given by heat capacity and Fermi energy, αP(T) = 2.5 × CP(T)/ϵF(T). The heat of fusion is determined by Fermi energy and relative change in v...

Diffusion of selenium and tellurium in silicon has been investigated in the temperature range 1000C to 1310C by sheet conductivity. For SiSeD
0= 0.30.1 cm2/s andh=2.60.1 eV, and for SiTeD
0=0.90.3 cm2/s and h=3.30.1eV have been obtained. The surface concentrations for both dopants were of the order of 5 1013 to 61016cm–3. The Hall coefficient leads...

Etch pit densities were compared with transmission electron microscopy investigations in silicon. The number of etch pits agrees well with the number of dislocations (about 108 cm-2). The dislocation density due to the nonperpendicular alignment of dislocations is higher by a factor of at least 3. Using this result we calculated the pipe radius fro...

Sheet conductance measurements were carried out to determine the diffusion profiles with and without p-n junctions. Diffusion of antimony and arsenic in n-Si of resistivity 5000 Ω cm was evaluated by the four-point resistivity method and the results were compared with those from tracer experiments.

Pipe diffusion of antimony in silicon was investigated by tracer and conductivity methods. The evaluation of the data reveals little dependence on the ratio of solubilities in the pipe and in the bulk. The calculated parameters of pipe diffusion depend on the real dislocation density and are in agreement with literature data.

Les mesures de profils de diffusion ont été interprétées à partir de la solution complète de l'équation de la diffusion dans le canal des dislocations. Deux paramètres ont été ajustés : la diffusivité dans le canal des dislocations D', et le rayon du canal des dislocations a. Les valeurs obtenues pour D' se trouvent en bon accord avec celles déjà d...

Low temperature specific heat measurements on a single crystal of trigonal Se result in a Debye temperature Θ
D = 186 K. This unexpected high value will be compared with the elastic Debye temperature which has been calculated from a set of the elastic constants Cik for trigonal Se. Recommended values for Cik at 300 K and 0 K, respectively, have bee...

The grain-boundary diffusion of 131I in Harshaw pure and Ca-doped NaCl was investigated in the temperature range between 430 and 560 °C. The Arrhenius plot of the grain-boundary diffusivity parameter Ddelta displays a marked dip at around 510 °C. It is proposed that this dip is due to a phase transformation occurring at the grain boundary, possibly...

The complete solution of dislocation pipe diffusion is applied to experimental data for different metals. For f.c.c. metals the mechanisms of vacancies bound to the dislocation and of diffusion in the stacking fault ribbon between dissociated dislocations are discussed. Cationic diffusion along dislocations will be obscured in the alkali halides by...

The complete solution of dislocation-pipe diffusion is applied to self-diffusion data of gold from the literature. The diffusivities reported herein are based on a fitted dislocation density of ${10}^{9}$-${10}^{10}$ lines/${\mathrm{cm}}^{2}$. The resulting diffusivities are $D=0.07\mathrm{exp}[\frac{$-${}(1.73 \mathrm{eV})}{\mathrm{kT}}]$ for the...

A heat pulse method applied to measurements of the specific heat of very small samples (≧ 10 mg) in the low temperature range is described. The accuracy of the method has been tested by determining the specific heat of sapphire and comparing it to values reported previously. Moreover, specific heat data for four samples of selenium of different str...

The dislocations are treated as an ideal array of parallel pipes of radius a and diffusivity Dp embedded in the bulk material of the diffusivity Db. The exact solution of this problem of diffusion along semi-infinite edge dislocations is presented for cubic, tetragonal, and hexagonal crystals. The solution makes it possible to evaluate the dislocat...

The rigorous solution of the grain‐boundary diffusion problem has been approximated by a series expansion method. The calculations show that higher‐order terms may be neglected in the bulk adjacent to the grain boundary. Thus, in this region Whipple's and Suzuoka's solutions represent a close approximation to the problem. Inside the grain boundary,...

Intermarriage gives information about the state of a society. Marriage data between Catholics and Non Catholics as well as natives and foreigners have been investigated in Germany and Switzerland. Integration and intermarriage depend on group size, nationality, language and religion of the groups as well as emotional interactions between the groups...

In stochastic systems (markets) with constraints (prices) all interactions may be derived from the Lagrange principle: L = E + λ ln w → maximum! Data for the "markets" property, automobile sales, marriage and jobs were analyzed by two models: the Cobb Douglas production function and the entropy function ln w. All results are in favor of entropy. As...

A model of human behaviour is derived from intermarriage data of ethnic, religious and national groups in Germany, Switzerland and the US. The resulting model society of sympathetic or antipathetic groups depends on three parameters: group size, sympathy and tolerance. A society will be stable, if the mutual satisfaction of all groups is at a maxim...

Thermodynamics is a statistical theory for large atomic systems under constraints of energy. An economy is a large system of economic agents and goods under the constraints of capital. Both systems may be handled by the Lagrange principle, the law of statistics for large systems under constraints. Thermodynamics and economics are expected to follow...

Investors would like to calculate profits in advance, "ex ante", like the path of a flying ball. But income can only be given "ex post", after the money is earned. The properties "ex ante" and "ex post" have never been investigated in economic theory by a mathematical tool. According to this paper the tool is given by exact and not exact differenti...

Calculus in two dimensions leads to two different types of integrals: Riemann integrals of exact differential forms (df) are path independent, fixed, "clay". Stokes integrals of not exact forms (δf) are path dependent, flexible, "putty". Productive and financial cycles may be represented by Stokes integrals. The resulting differential equations may...

The Lagrange principle L = f + λ g → maximum! is used to maximize a function f(x) under a constraint g(x). Economists regard f(x) = U as a rational production function, which has to be maximized under the constraint of prices g(x). In physics f(x) = ln P is regarded as entropy of a stochastic system, which has to be maximized under constraint of en...

Berlin, T. U., F. f. allg. Ingenieurwiss., Diss. v. 24. April 1967.

## Projects

Project (1)

Science contains two elements, the known of today (teaching), and the unknown of tomorrow (research). In natural sciences these elements are called conservative and non-conservative, in social sciences they are called ex ante and ex post. How can we catch these terms by science, by mathematics? The terms correspond to exact and not exact differentials, to path independent Riemann and path dependent Stokes integrals, to real constraints and probable results, and to solvable linear and not solvable non-linear equations. Accordingly, we may handle economics and social science by calculus, stochastic theory and by complexity. calculations.