Schell Model Research Articles

Scattering of a general partially coherent beam from a diffuse target in atmospheric turbulence

The second-order and fourth-order statistical moments of the speckle field from a diffuse target in atmospheric turbulence are studied which have great influence on the performance of lidar systems. By expanding a general rotationally symmetric beam as a sum of Gaussian—Schell model (GSM) beams, the mean intensity of the general beam propagating over a distance in an atmospheric turbulence is formulated. Expressions for the degree of coherence (DOC) and the normalized intensity variance of the scattered field of a general beam from a rough surface in turbulence are derived based on the extended Huygens—Fresnel principle. The general expressions reduce to the well-known forms for a GSM beam. Another example for the general beam used in this paper is the collimated flat-topped beam. The results of both kinds of beams show that the intensity profile on the target plane is a key factor affecting the statistical characteristics of the speckle field. A larger beam spot on the target plane induces a smaller coherence length and a smaller normalized intensity variance of the received field. As turbulence gets stronger, the coherence length becomes smaller, and the normalized intensity variance firstly increases and declines to unity finally.

How Diverse Can Spatial Measures of Cultural Diversity Be? Results from Monte Carlo Simulations on an Agent-Based Model

Cultural diversity is a complex and multi-faceted concept. Commonly used quantitative measures of the spatial distribution of culturally-defined groups – such as segregation, isolation or concentration indexes – are often only capable of identifying just one aspect of this distribution. The strengths or weaknesses of any measure can only be comprehensively assessed empirically.This paper provides evidence on the empirical properties of various spatial measures of cultural diversity by using Monte Carlo replications of agent-based modeling (MC-ABM) simulations with synthetic data assigned to a realistic and detailed geographical context of the city of Amsterdam. Schelling's classical segregation model is used as the theoretical engine to generate patterns of spatial clustering. The data inputs include the initial population, the number and shares of various cultural groups, and their preferences with respect to co-location. Our MC-ABM data generating process produces output maps that enable us to assess the performance of various spatial measures of cultural diversity under a range of demographic compositions and preferences.We find that, as our simulated city becomes more diverse, stable residential location equilibria are only possible when people, particularly minorities, become more tolerant. We test whether observed measures can be interpreted as revealing unobserved preferences for co-location of individuals with their own group and find that the segregation and isolation measures of spatial diversity are shown to be non-decreasing in increasing preference for within-group co-location, but the Gini coefficient and concentration measures are not.

Partial polarization of optical beams and near fields probed with a nanoscatterer.

We consider theoretically the detection of the spectral polarization characteristics of random, partially polarized optical beams and near fields by probing them with a dipolar nanoparticle. We show that measuring the polarization state of the scattered far field with a conventional waveplate-polarizer setup, possibly in several directions, results in the full 3×3 polarization matrix at the probe site. This allows us to deduce the distributions of the degree of polarization of the field and the Stokes parameters of the polarized part of the field with a resolution limited by the probe size. Regarding random near fields we show that, in analogy with a known result on beam fields, a degree of polarization of three-component light fields put forward in recent literature can in some cases be interpreted as a ratio of the intensity in the polarized part of the light to that of the total field. We demonstrate the technique by considering the probing of a Gaussian-Schell model beam and a thermally excited near field. The method extends the current scanning-probe techniques to the detection of partial polarization of random light fields and can find applications in nanophotonics and polarization optics.

Equivalence theorem for the spectral density of light waves on weak scattering.

The Equivalence theorem for the spectral density of light waves on weak scattering is discussed. It is shown that when a spatially coherent plane light wave is scattered from two entirely different media, the far-zone spectral density may have identical distribution provided the low-frequency antidiagonal spatial Fourier components of the correlation function of the media are the same. An example of light waves on scattering from a Gaussian Schell model medium is discussed, and the condition on which two different media may produce identical spectral densities is presented.

Scintillation of partially coherent Gaussian—Schell model beam propagation in slant atmospheric turbulence considering inner- and outer-scale effects

Based on the modified Rytov theory and the international telecommunication union-radio (ITU-R) slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian—Schell model (GSM) beam propagation in the slant path is derived from weak- to strong-turbulence regions considering inner- and outer-scale effects. The effects of wavelength of beams and inner- and outer-scale of turbulence on scintillation are analyzed numerically. Comparison between the scintillation of GSM beams under the von Karman spectrum and that of beams under the modified Hill spectrum is made. The results obtained show that the scintillation index obtained under the von Karman spectrum is smaller than that under the modified Hill spectrum. This study can find theory bases for the experiments of the partially coherent GSM beam propagation through atmospheric turbulence.

Partially coherent Gaussian—Schell model pulse beam propagation in slant atmospheric turbulence

Based on the extended Huygens—Fresnel principle, a two-frequency, two-point cross-spectral density function of partially coherent Gaussian—Schell model pulse (GSMP) beam propagation in slant atmospheric turbulence is derived. Using the Markov approximation method and on the assumption that (ω1 − ω2)/(ω1 + ω2) ≤ 1, the theory obtained is valid for turbulence of any strength and can be applied to narrow-band signals. The expressions for average beam intensity, the beam size, and the two-frequency complex degree of coherence of a GSMP beam are obtained. The numerical results are presented, and the effects of the frequency, initial pulse width, initial beam radius, zenith angle, and outer scales on the complex degree of coherence are discussed. This study provides a better understanding of the second-order statistics of a GSMP beam propagating through atmospheric turbulence in the space-frequency domain.

Spectral shifts produced by scattering of Rectangular Gaussian Schell Model sources from a deterministic medium

Within the accuracy of the first-order Born approximation, we investigate the scattering of Rectangular Gaussian Schell Model (RGSM) sources incident upon a deterministic medium. The analytical expression for the far-zone scattered spectrum is derived. Numerical results show that red shift or blue shift can be produced in the far-zone scattered spectrum, and the spectral shifts are mainly influenced by the scattering direction and the source parameters (i.e., the source width and the source correlation widths along the x and y directions).

Propagation of a twist Gaussian–Schell model beam in non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel integral, an analytical formula for the cross-spectral density (CSD) function of a twist Gaussian–Schell model (TGSM) beam propagating through non-Kolmogorov turbulence is derived. The statistical properties, such as the beam width, the radius of curvature, the transverse coherence length and the twist factor of the TGSM beam in non-Kolmogorov turbulence, are studied numerically. It is found that the TGSM beam is less affected than a GSM beam without twist phase both in non-Kolmogorov turbulence and in Kolmogorov turbulence. Our results will be useful in free-space communication.

Propagation properties of electromagnetic multi-Gaussian Schell model beams propagating through atmospheric turbulence

A model for electromagnetic multi-Gaussian Schell-model beams is introduced. An analytical expression for the cross-spectral density matrix of electromagnetic multi-Gausssian Schell-model (EMGSM) beams propagating through non-Kolmogorov turbulence is derived based on the extended Huygens-Fresnel principle. With help of this expression, the average intensity, degree of coherence (DOC) and degree of polarization (DOP) of EMGSM beams are investigated in detail. Our results show that by suitable choices of the source parameters, the distance that preserve a flat profile can be prolonged. The effects of M and exponent value α on DOC and DOP of EMGSM beams are studied in detail.

Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction

This paper shows that signal restoration methodology is appropriate for predicting the equilibrium state of certain economic systems. A formal justification for this is provided by proving the existence of finite improvement paths in object allocation problems under weak assumptions on preferences, linking any initial condition to a Nash equilibrium. Because a finite improvement path is made up of a sequence of systematic best-responses, backwards movement from the equilibrium back to the initial condition can be treated like the realisation of a noise process. This underpins the use of signal restoration to predict the equilibrium from the initial condition, and an illustration is provided through an application of maximum entropy signal restoration to the Schelling model of segregation.

Understanding with theoretical models

This paper discusses the epistemic import of highly abstract and simplified theoretical models using Thomas Schelling's checkerboard model as an example. We argue that the epistemic contribution of theoretical models can be better understood in the context of a cluster of models relevant to the explanatory task at hand. The central claim of the paper is that theoretical models make better sense in the context of a menu of possible explanations. In order to justify this claim, we introduce a distinction between causal scenarios and causal mechanism schemes. These conceptual tools help us to articulate the basis for modelers' intuitive confidence that their models make an important epistemic contribution. By focusing on the role of the menu of possible explanations in the evaluation of explanatory hypotheses, it is possible to understand how a causal mechanism scheme can improve our explanatory understanding even in cases where it does not describe the actual cause of a particular phenomenon.

What’s Wrong with Social Simulations?

/. IntroductionIn this paper I will try to answer the question: Why is the epistemic value of so many social simulations questionable? Under 'social simulations' I understand computer simulations of human interaction as they are studied in the social sciences. The reason why I consider the epistemic value of many social simulations as questionable is that many simulation studies cannot give an answer to the most salient question that any scientific study should be ready to answer: How do we know it's true? or, if specifically directed to simulation studies: How do we know that the simulation correctly simulates the phenomenon that it simulates? Answering this question requires some kind of empirical validation of the simulation. The requirement of empirical validation is in line with the widely accepted notion that science is demarcated from nonscience by its empirical testability or fal- sifiability. Many simulation studies, however, do not offer any suggestion about how they could possibly be validated empirically.A frequent reply by simulation scientists is that no simulation of empirical phenomena was intended, but that the simulation only serves a purpose. Then, however, another equally salient question should be answered: Why should we care about the results? It is my strong impression that many social simulation studies cannot answer either this or the first question. In the social sciences it is hard to find useful examples of the use of computers for purely theoretical purposes. In any case, the social sciences are empirical sciences. Therefore, social simulations should contribute either directly or indirectly to our understanding of social phenomena in the empirical world.There exist many different types of simulations but I will restrict myself to agent-based and game theoretical simulations. I do not make a sharp difference between models and simulations. For the purpose of this paper I identify computer simulations just with programmed models. Most of my criticism of the practice of these simulation types can probably be generalized to other types of simulations or models in the social sciences and maybe also to some instances of the simulation practice in the natural sciences, but it would lead us too far afield to discuss these connections here.In order to bring my point home, I rely on the survey by Heath, Hill, and Ciarallo (2009) on agent-based modeling practice for a general overview, and on two example cases that I examine in detail. I start by discussing the survey which reveals that in an important subfield of social simulations, namely, agent-based simulations, empirical validation is commonly lacking. After that I first discuss Thomas Schelling's wellknown neighborhood segregation model. This is a model that I do not consider as being devoid of epistemic value. For, unlike most social simulations, it can be empirically falsified. The discussion of the particular features that make this model scientifically valuable will help us to understand why the simulation models discussed in the following fail to be so. The simulation models that I discuss in the following section are simulations in the tradition of Robert Axelrod's Evolution of Cooperation (Axelrod 1984). Although the modeling tradition initiated by Axelrod has delivered hardly any tenable and empirically applicable results, it still continues to thrive today.Finally, the question remains why scientists continue to produce such an abundance of simulation studies that fail to be empirically applicable. In my opinion the failure to produce useful results has a lot to do with the positivist attitude prevailing in this field of the social sciences. This attitude includes the dogmatic belief in the superiority of the methods of natural sciences like physics in any area of science.2. Simulation Without Validation in Agent-Based ModelsIn this section I give my interpretation of a survey by Heath, Hill, and Ciarallo (2009) on agent-based-simulations. …

Optical binding of cylinder photonic molecules in the near field of partially coherent fluctuating Gaussian Schell model sources: a coherent mode representation

We present a theory and computation method of radiation pressure from partially coherent light by establishing a coherent mode representation of the radiation forces. This is illustrated with the near field emitted from a Gaussian Schell model source, mechanically acting on a single cylinder with magnetodielectric behavior, or on a photonic molecule constituted by a pair of such cylinders. Thus after studying the force produced by a single particle, we address the effects of the spatial coherence on the bonding and antibonding states of two particles. The coherence length manifests the critical limitation of the contribution of evanescent modes to the scattered fields, and hence to the nature and strength of the electromagnetic forces, even when electric and/or magnetic partial wave resonances are excited.

Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam

We carry out experimental measurement of the scintillation index of a partially coherent beam-carrying vortex phase (i.e., Gaussian-Schell model vortex beam) propagating through thermally induced turbulence. It is demonstrated that a Gaussian-Schell model vortex beam has appreciably smaller scintillation than a Gaussian-Schell model beam, which will be useful in free-space optical communication.

A Schelling model with switching agents: decreasing segregation via random allocation and social mobility

We study the behaviour of a Schelling-class system in which a fraction $f$ of spatially-fixed switching agents is introduced. This new model allows for multiple interpretations, including: (i) random, non-preferential allocation (\textit{e.g.} by housing associations) of given, fixed sites in an open residential system, and (ii) superimposition of social and spatial mobility in a closed residential system.\\ We find that the presence of switching agents in a segregative Schelling-type dynamics can lead to the emergence of intermediate patterns (\textit{e.g.} mixture of patches, fuzzy interfaces) as the ones described in Ref. 1. We also investigate different transitions between segregated and mixed phases both at $f=0$ and along lines of increasing $f$, where the nature of the transition changes.

Schelling-voter model: An application to language competition

In this work we analyze the language competition problem by using an interacting agent-based model which interpolates the classical Schelling and Voter models. Briefly, an agent may change its place of residence or his language when he is surrounded by more individuals of the other kind than the ones he can tolerate. We analyze this dynamic process in terms of the free space to move in, the pressure to change the language, and the propensity to change location. We identify the different regimes and the relationship with the language competition problem.

Theoretical investigation on the Schelling’s critical neighborhood demand

We derived the critical neighborhood demand in the Schelling’s segregation model by studying the conditions for which a chain reaction of migrations of unsatisfied agents occurs. The essence of Schelling dynamics was approximated in two simplified models: (1) a random walk model for the initial stage of the migrations to illustrate the power-law behavior of chain reaction lengths under critical conditions, and (2) a two-room model for the whole process to represent a non-spatial version of segregation dynamics in the Schelling model. Our theoretical results showed good agreements with numerical results obtained from agent-based simulations.

Effects of atmospheric turbulence on the orbital angular momentum of multi-Gaussian Schell model beams

The effects of multibeams and partially coherent source on the orbital angular momentum transmission of multi-Gaussian Schell model beams in an atmospheric turbulence channel are analyzed. An effective crosstalk probability model of the orbital angular momentum is derived which leads to crosstalk probability function for eigenmodes of different orbital angular momentum states and beamlets. The work shows that the evolution of the effective spatial coherence radius with growing the rms width of the correlation of the partially coherent source and the number of the beamlet in multi-Gaussian model beams. The crosstalk probability of the orbital angular momentum of an effective Gaussian-Schell model beam decreases as increasing of the degree of the spatial coherence of the partially coherent source and the beamlet number of the multi-Gaussian Schell model beams.

Entangled orbital angular momentum states of multi-Laguerre Gaussian Schell beams pumping in a Zernike tilt corrected turbulence

Based on the paraxial approximation of the beams propagation in communication system, the square approximation of the wave structure function, the Zernike polynomial expansion of the non-Kolmogorov atmospheric turbulence-aberration and the assumption of the signal photon propagation in slant Zernike tilt corrected turbulence-channel, we analyze the effect of the multi-beam on entangled orbital angular momentum states. The joint detection probability of orbital angular momentum state entangled photons is modeled. Our work shows that the correction of the Zernike tilt aberration by adaptive optics is a method to improve the joint detection probability of orbital angular momentum state entangled photons. The crosstalk probability of the entangled orbital angular momentum states decreases as increasing of the degree of the spatial coherence of the partially coherent source and the beamlet number of the multil-Laguerre Gaussian Schell model beams.

Why Sociology Should Use Agent Based Modelling

Although Agent Based Models (hereafter ABM) are now regularly reported in sociology journals, explaining the approach, describing models and reporting results leaves little opportunity to examine wider implications of ABM for sociological practice. This article uses an established ABM (the Schelling model) for this. The first part argues that ABM integrates qualitative and quantitative data distinctively, provides novel tools for understanding social causes and offers a significantly different perspective on theory building. The second part shows how the emerging ABM methodology is compatible with existing sociological practice while undermining several criticisms of ABM perceived to limit its sociological relevance.