Schell Model Research Articles

The Schelling Model of Ethnic Residential Dynamics: Beyond the Integrated - Segregated Dichotomy of Patterns

The Schelling model of segregation is an agent-based model that illustrates how individual tendencies regarding neighbors can lead to segregation. The model is especially useful for the study of residential segregation of ethnic groups where agents represent householders who relocate in the city. In the model, each agent belongs to one of two groups and aims to reside within a neighborhood where the fraction of 'friends' is sufficiently high: above a predefined tolerance threshold value F. It is known that depending on F, for groups of equal size, Schelling's residential pattern converges to either complete integration (a random-like pattern) or segregation. The study of high-resolution ethnic residential patterns of Israeli cities reveals that reality is more complicated than this simple integration-segregation dichotomy: some neighborhoods are ethnically homogeneous while others are populated by both groups in varying ratios. In this study, we explore whether the Schelling model can reproduce such patterns. We investigate the model's dynamics in terms of dependence on group-specific tolerance thresholds and on the ratio of the size of the two groups. We reveal new type of model pattern in which a portion of one group segregates while another portion remains integrated with the second group. We compare the characteristics of these new patterns to the pattern of real cities and discuss the differences.

An Algorithm to Study of the Influence of Partial-Coherent Lights through Three-Dimensional Periodic Microstructures

A transfer-matrix algorithm is presented herein as a beginning in the study of the transmission characteristics of coherent light through three-dimensional periodic microstructures, in which the structures are treated as two-dimensional layer stacks and multiple reflections are considered negligible. The spatially correlated noise is further introduced layer by layer to realize the actual partially coherence of light and allows for statistical investigation of the spatial partially coherent optics in transparent/small-birefringence media. Numerical analyses show results comparable to these obtained using the Gaussian Schell model for free-space cases, indicating the validity of the algorithms.

Dynamic models of residential segregation: An analytical solution

We propose an analytical solution to a Schelling segregation model for a relatively broad range of utility functions. Using evolutionary game theory, we provide existence conditions for a potential function, which characterizes the global configuration of the city and is maximized in the stationary state. We use this potential function to analyze the outcome of the model for three utility functions corresponding to different degrees of preference for mixed neighborhoods: (i) we show that linear utility functions is the only case where the potential function is proportional to collective utility, the latter being therefore maximized in stationary configurations; (ii) Schelling's original utility function is shown to drive segregation at the expense of collective utility; (iii) if agents have a strict preference for mixed neighborhoods but also prefer to be in the majority versus the minority, the model converges to perfectly segregated configurations, which clearly diverge from the social optimum. Departing from the existing literature, these conclusions are based on analytical results which open the way to analysis of many preference structures. Since our model is based on bounded rather than continuous neighborhoods as in Schelling's original model, we discuss the differences generated by the bounded- and continuous-neighborhood definitions and show that, in the case of the continuous neighborhood, a potential function exists if and only if the utility functions are linear. A side result is that our analysis builds a bridge between Schelling's model and the Duncan and Duncan segregation index.

Temporal and spatial coherence properties of free-electron-laser pulses in the extreme ultraviolet regime

The average temporal (longitudinal) and spatial (transverse) coherence of free-electron-laser pulses in the extreme ultraviolet at FLASH is measured by interfering two time-delayed partial beams directly on a CCD camera. Wavelengths between $\ensuremath{\lambda}=32\text{ }\text{ }\mathrm{nm}$ and $\ensuremath{\lambda}=8\text{ }\text{ }\mathrm{nm}$ are examined. A decrease of the coherence time for the fundamental wavelengths from ${\ensuremath{\tau}}_{c}=(6\ifmmode\pm\else\textpm\fi{}0.5)\text{ }\text{ }\mathrm{fs}$ at 32 nm to ${\ensuremath{\tau}}_{c}=(2.9\ifmmode\pm\else\textpm\fi{}0.5)\text{ }\text{ }\mathrm{fs}$ at 8 nm is measured. At $\ensuremath{\lambda}=8\text{ }\text{ }\mathrm{nm}$ the fundamental wavelength and the third harmonic of 24 nm are compared to each other. For 8 nm radiation as third harmonic of 24 nm a coherence time of ${\ensuremath{\tau}}_{c}=(2.5\ifmmode\pm\else\textpm\fi{}0.5)\text{ }\text{ }\mathrm{fs}$ is observed. The spatial coherence of 24 and 8 nm fundamental pulses are found to be very similar. The visibility decreases to 50% of the maximum visibility at about 3.2 mm overlap of the partial beams, which corresponds to 42% of the beam diameter at a distance of 90 m from the exit of the undulator. These results are analyzed in terms of the Gaussian Schell model resulting in six contributing modes to the total radiation. In addition, the correlation of the visibility between the fundamental radiation at 24 nm and its third harmonic at $\ensuremath{\lambda}=8\text{ }\text{ }\mathrm{nm}$ is investigated for identical shots.

Spatial coherence function of partially coherent Gaussian beams in atmospheric turbulence

We introduce a new method of estimating the coherence function of a Gaussian-Schell model beam in the inertial subrange of atmospheric turbulence. It is compared with the previously published methods based on either the quadratic approximation of the parabolic equation or an assumed independence between the source's randomness and the atmosphere using effective beam parameters. This new method, which combines the results of the previous two methods to account for any random source/atmospheric coupling, was shown to more accurately estimate both the coherence radius and coherence functional shape across much of the relevant parameter space. The regions of the parameter space where one method or another is the most accurate in estimating the coherence radius are identified along with the maximum absolute estimation error in each region. By selecting the appropriate estimation method for a given set of conditions, the absolute estimation error can generally be kept to less than 5%, with a maximum error of 7%. We also show that the true coherence function is more Gaussian than expected, with the exponential power tending toward 9/5 rather than the theoretical value of 5/3 in very strong turbulence regardless of the nature of the source coherence.

Minority-Majority Relations in the Schelling Model of Residential Dynamics. 住宅动态迁移Schelling模型中的少数-多数关系

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Dynamics and complexity of the Schelling segregation model

In this paper we consider the Schelling social segregation model for two different populations. In Schelling's model, segregation appears as a consequence of discrimination, measured by the local difference between two populations. For that, the model defines a tolerance criterion on the neighborhood of an individual, indicating wether the individual is able to move to a new place or not. Next, the model chooses which of the available unhappy individuals really moves. In our work, we study the patterns generated by the dynamical evolution of the Schelling model in terms of various parameters or the initial condition, such as the size of the neighborhood of an inhabitant, the tolerance, and the initial number of individuals. As a general rule we observe that segregation patterns minimize the interface of zones of different people. In this context we introduce an energy functional associated with the configuration which is a strictly decreasing function for the tolerant people case. Moreover, as far as we know, we are the first to notice that in the case of a non-strictly-decreasing energy functional, the system may segregate very efficiently.

Average spreading of a linear Gaussian–Schell model beam array in non-Kolmogorov turbulence

The average spreading of a linear Gaussian–Schell model (GSM) beam array in non-Kolmogorov turbulence is studied, where the coherent combination is considered. The effects of the beam number, the separation distance between two adjacent beams and the generalized exponent on the root-mean-square (rms) beam width are investigated. The results indicate that the rms beam width in non-Kolmogorov turbulence is different from that in Kolmogorov turbulence, and there is an optimum beam number that leads to a minimum beam width. Further, the beam width can reach the minimum value by adopting the optimum separation distance, which decreases with the increase of beam number. Besides, the partially coherent beam array is less sensitive to the atmospheric turbulence than the fully coherent one.

Slanting propagation of stochastic electromagnetic twist anisotropic Gaussian–Schell model beams in turbulent atmosphere

Based on the extended Huygens–Fresnel diffraction integral and the unified theory of coherence and polarization, the slanting propagation properties of stochastic electromagnetic twist anisotropic Gaussian–Schell model (ETAGSM) beams in turbulent atmosphere have been investigated. Both numerical calculation and physical interpretation are obtained. The influence of the atmospheric turbulence and the source parameters on the polarization distribution, intensity distribution and coherence distribution has been studied in great detail. The investigation reveals that slanting propagation can weaken the influence of atmospheric turbulence on the spectral properties of stochastic ETAGSM beams more obviously. It is also shown that we can modulate the spectral degree of polarization in the output plane especially in the far field by simply controlling the coherence, the spot width or the twisty properties of the source beams. The distribution of the spectral degree of polarization and cross-polarization of the beams in the output plane is also given out.

The propagation of electromagnetic Gaussian–Schell model beams through atmosphericturbulence in a slanted path

Based on the extended Huygens–Fresnel principle, an analytical expression for theelements of a cross-spectral matrix for electromagnetic Gaussian–Schell model(EGSM) beams in a slanted path is derived. With the help of this expression, weinvestigate the average intensity, the degree of polarization (DOP) and the degree ofcoherence (DOC) for EGSM beams in a slanted path. Results show that thefar-zone DOP and DOC of EGSM beams in a slanted path are determined by theparameters of the source, which are different from the situations in a horizontal path.

Iterative nonlinear beam propagation using Hamiltonian ray tracing and Wigner distribution function

We present an iterative method for simulating beam propagation in nonlinear media using Hamiltonian ray tracing. The Wigner distribution function of the input beam is computed at the entrance plane and is used as the initial condition for solving the Hamiltonian equations. Examples are given for the study of periodic self-focusing, spatial solitons, and Gaussian-Schell model in Kerr-effect media. Simulation results show good agreement with the split-step beam propagation method. The main advantage of ray tracing, even in the nonlinear case, is that ray diagrams are intuitive and easy to interpret in terms of traditional optical engineering terms, such as aberrations, ray-intercept plots, etc.

Ethnic Segregation and Performance Inequality in the Swedish School System: A Regional Perspective

Sweden is today an immigrant country with more than 14% foreign born. An increasing share of the immigrants comes from non-European countries. This implies that Sweden has been transformed from an ethnically homogenous country into a country with a large visible minority. In this paper we survey the effect of this change on school segregation. Building on Schelling's model for residential segregation, we argue that establishment of a visible minority has triggered a process of school segregation that in some respects can be compared with the developments in the United States. In order to test the validity of a Schelling-type process in Swedish schools we compare segregation levels in regions with different shares of visible minority students. We use data from the PISA 2003 survey in combination with register data on the ethnic composition of student population in different parts of Sweden. We find that school segregation is higher in regions with a large visible-minority population. We also find that, controlling for student background, there are smaller differences in performance across schools in regions with low shares of minority students.

Polarization distribution control of anisotropic electromagnetic Gaussian–Schell model beams on free propagation by exploiting correlation properties at the source plane

When propagating in free space, the transversal distribution of the degree of polarization of an anisotropic electromagnetic Gaussian-Schell model (AEGSM) beam will generally undergo a complex evolution process. We find that this transversal distribution of the degree of polarization of an AEGSM beam can be controlled by exploiting the partial correlation properties of the source. The main research of our paper falls into two parts. First, the concept of analogical propagation of the transversal distribution of the degree of polarization is proposed, and the condition for an AEGSM beam having an analogical propagation is obtained. When an AEGSM beam is on analogical propagation, the distribution of the degree of polarization on any cross section of the beam is always similar to that on the source plane, except that the size of the distribution pattern will expand continuously as the propagation distance increases. Second, the far-field transversal distribution of the degree of polarization is considered, and the condition for the far-field transversal polarization distribution of an AEGSM beam to be always of circularly symmetric shape, no matter how complicated it is on the source, is obtained. Our research is expected to find applications in areas that make use of the polarization properties of random electromagnetic beams.

Low levels of ethnic intolerance do not create large ghettos a discussion about an interpretation of Schelling's model

Résumé Dans les années 1970, Thomas C. Schelling a proposé un modèle pour expliquer le lien entre ségrégation spatiale et préférences individuelles concernant cette ségrégation. Au moyen de simulations, il cherche à montrer qu’un haut niveau de ségrégation globale peut être le résultat collectif de décisions individuelles qui sont loin de viser une telle ségrégation. Cet article montre cependant que les contraintes structurelles du modèle expliquent intégralement les niveaux de ségrégation atteints. Une faible exigence individuelle pour s’entourer de voisins identiques conduit à une ségrégation collective faible et une exigence forte conduit à une ségrégation forte. Les niveaux de ségrégation correspondant à un seuil donné de satisfaction individuelle n’ont rien de surprenant en regard du hasard et de ce que chaque individu souhaite réellement. Le modèle de Schelling ne permet pas de conclure que, de manière générale, de larges ghettos naissent d’innocentes décisions.

Fast Acceptance by Common Experience: FACE-recognition in Schelling's model of neighborhood segregation

AbstractSchelling (1969, 1971a,b, 1978) observed that macro-level patterns do not necessarily reflect micro-level intentions, desires or goals. In his classic model on neighborhood segregation which initiated a large and influential literature, individuals with no desire to be segregated from those who belong to other social groups nevertheless wind up clustering with their own type. Most extensions of Schelling’s model have replicated this result. There is an important mismatch, however, between theory and observation, which has received relatively little attention. Whereas Schelling-inspired models typically predict large degrees of segregation starting from virtually any initial condition, the empirical literature documents considerable heterogeneity in measured levels of segregation. This paper introduces a mechanism that can produce significantly higher levels of integration and, therefore, brings predicted distributions of segregation more in line with real-world observation. As in the classic Schelling model, agents in a simulated world want to stay or move to a new location depending on the proportion of neighbors they judge to be acceptable. In contrast to the classic model, agents’ classifications of their neighbors as acceptable or not depend lexicographically on recognition first and group type (e.g., ethnic stereotyping) second. The FACE-recognition model nests classic Schelling: When agents have no recognition memory, judgments about the acceptability of a prospective neighbor rely solely on his or her group type (as in the Schelling model). A very small amount of recognition memory, however, eventually leads to different classifications that, in turn, produce dramatic macro-level effects resulting in significantly higher levels of integration. A novel implication of the FACE-recognition model concerns the large potential impact of policy interventions that generate modest numbers of face-to-face encounters with members of other social groups.

Scattering of scalar light wave from a Gaussian–Schell model medium

The scattering of scalar light wave from a random medium with a correlation function of Gaussian–Schell model distribution is studied. It is shown that the properties of the scattered field, i.e., the spectral density and the spectral degree of coherence of the scattered field, are closely related to the properties of the scattering medium, including the scaled effective radius and the scaled correlation length of the correlation function.

Agent-based and multi-agent simulations: coming of age or in search of an identity?

The promise of agent-based for explicating properties of social systems has not yet been fully realized. Agent models sometimes provide only a veneer of, rather than substantive engagement with, social behavior. The problem will be illustrated with Axelrod's model for evolution of ethnocentrism (a biological model) versus Schelling's model for spatial segregation based on preferences (a cultural model). The examples show the need to incorporate both the biological and cultural basis for behavior through a schema that includes behavior based on cultural/cognitive processing of information and behavior based on biological/cognitive processing of information. An example of an agent-based model that implements decision making in this manner is discussed. The model accounts for heterogeneity in behavior outcomes and leads to two main predictions: (1) small scale, hunter-gatherer societies in resource scarce environments will have stable adaptations less affected by variation in resource abundance in comparison to groups in resource rich regions where inter-group conflict is more likely and (2) the relationship between community size, population size and administrative complexity will have two distinct patterns, one for patrilineally organized societies and the other for matrilineally organized societies. Both predictions have been verified empirically.

Condition of Keeping Polarization Property Unchanged in the Circle Polarization Shift Keying System

To improve the performance of the free-space optical (FSO) system, we recently proposed circle polarization shift keying (CPolSK). In the CPolSK system, it is important to study the condition of keeping the polarization properties unchanged in the turbulent atmosphere. Based on the unified theory of coherence and polarization, three formulas are derived to describe the condition of keeping the polarization degree invariant for the Gaussian–Schell model (GSM) beam. The third formula includes all the polarization states. Consequently, it is defined as the condition of polarization invariance in CPolSK systems. If this condition is satisfied, the two parameters of the polarization ellipse will remain the values of the source during the propagation. Several GSM beams with different parameters are numerically calculated to verify the conditions. This result is helpful in designing the transmitter of the polarization modulation system.

Schelling segregation in an open city: A kinetically constrained Blume-Emery-Griffiths spin-1 system

In the 70s Schelling introduced a multiagent model to describe the segregation dynamics that may occur with individuals having only weak preferences for "similar" neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here, we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a variety of "phases" whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socioeconomic correlates.

Complex space source theory of partially coherent light wave

The complex space source theory is used to derive a general integral expression for the vector potential that generates the extended full Gaussian wave in terms of the input value of the vector potential of the corresponding paraxial beam. The vector potential and the fields are assumed to fluctuate on a time scale that is large compared to the wave period. The Poynting vector in the propagation direction averaged over a wave period is expressed in terms of the cross-spectral density of the fluctuating vector potential across the input plane. The Schell model is assumed for the cross-spectral density. The radiation intensity distribution and the power radiated are determined. The effect of spatial coherence on the radiation intensity distribution and the radiated power are investigated for different values of the physical parameters. Illustrative numerical results are provided to bring out the effect of spatial coherence on the propagation characteristics of the fluctuating light wave.