S-shaped Patterns Research Articles

Enhancing Accuracy and Consistency in the Valuation of Plant and Equipment through Cubic Regression Models of Physical Deterioration

The valuation of plant and equipment often involves valuers deducting physical, functional and economic depreciation from replacement cost estimates. These calculations have faced accuracy and consistency problems in the aspect of determining how much physical deterioration should be deducted. This study attempted to develop cubic regression models to resolve these accuracy and consistency problems in the basic metal, iron and steel and fabricated metal product sectors in Ogun state, Nigeria (Sango Ota and Agbara). Questionnaire surveys were administered on senior operators of plant and equipment in these sectors to draw information on the degree of physical deterioration of plant and equipment over service life, using expenditure on repairs as a proxy for physical deterioration. The questionnaire sought information on the service lives of plant and equipment, the pattern of physical depreciation over the service lives, and the degree to which the pattern is influenced by various operational factors. Data were analysed using means, standard deviations, multiple linear regressions and cubic regressions, to produce what could be the first potentially accurate and consistent valuation model of physical deterioration in Africa. The service lives of various plant and equipment were found to range at various times between 8 to 60 years. Cubic regression analyses showed that the pattern of the movement of transitions of expenditure on repairs (proxy for physical deterioration) over useful life of plant and equipment were not linear but cubic, and generally followed S-shaped patterns. Multiple regression analyses showed that the S-shaped patterns were in turn influenced by operational factors (such as intensity of use and power outages). The study concluded that valuers’ interests in accuracy and consistency in plant and equipment valuation were not served by any of the accounting methods hitherto used by valuers; accuracy in physical deterioration modelling follows an S-shaped transition over time.

Time-dependent magnetic anomaly variations in Turkey and Greece using swarm satellites: A comprehensive precursory multi-track analysis of M≥6 earthquakes from 2017 to 2020

This article presents a comprehensive multi-track analysis aimed at investigating time-dependent magnetic anomaly variations in Turkey and Greece resulting from five M ≥ 6 earthquakes occurring between January 2017 and October 2020. The study utilizes data from the Swarm satellites and employs various analytical techniques, including first-time derivative calculations, long-wavelength component removal, and moving RMS filters, to construct cumulative anomaly count graphs for each magnetic component. By eliminating the influence of the external magnetic field, we focus solely on the magnetic components (X, Y, Z, and F). The changes in magnetic anomalies before, during, and immediately after the earthquakes are carefully interpreted. The research systematically analyses the Plomari (June 12, 2017), Kos (July 20, 2017), Doğanyol (January 24, 2020), Özalp (February 23, 2020), and Karlovasion (October 30, 2020) Earthquakes, considering the mainshock and aftershock responses for each magnetic component. The findings reveal intriguing patterns, most notably the emergence of distinctive S-shaped anomalies in various magnetic components. Moreover, the study highlights the influence of significant earthquakes, such as Plomari and Kos, on cumulative anomalous tracks, providing critical insights into magnetic field behavior. Additionally, the study investigates the potential impact of the Özalp Earthquake on the magnetic anomalies observed in the Doğanyol earthquake and explores the relationship between the occurrence of the Doğanyol Earthquake and the precursory anomalies leading to the mainshock of the Özalp Earthquake. Furthermore, the analysis of the Karlovasion earthquake identifies magnetic anomalies preceding the mainshock. Finally, the research subjectively assesses the lateral and vertical scores of the five earthquakes to capability to represent the S-shaped pattern. The Plomari and Kos earthquakes score third and fourth highest, respectively, while the Doğanyol Earthquake achieves the top score and distinctly displays an S-shaped pattern, indicating its significance in the magnetic field behavior. The Özalp Earthquake scores second-best with a distinct S-shaped pattern, while the Karlovasion Earthquake receives the lowest score with no evident S-shaped pattern. Additionally, vertical scores indicate the Y and Z components with more pronounced S-shaped patterns, while the X and F components receive lower scores. Notably, the onshore Doğanyol Earthquake exhibits the most pronounced S-shaped pattern across all magnetic components, attributable to its shallow strike-slip fault at 10 km depth, while the offshore Karlovasion Earthquake, generated by a normal fault at 21 km depth, displays the most scattered pattern, providing valuable information on the influence of tectonic settings on magnetic field behaviour. In conclusion, this study provides valuable insights into the magnetic anomalies associated with seismic events in the region, significantly contributing to a better understanding of earthquake precursors and seismicity patterns, and enhancing seismic risk assessment and mitigation strategies.

Where didwergo? Lexical variation and change in third-person male adult noun referents in Old and Middle English

AbstractThe present study uses variationist quantitative methods to examine the evolution of the semantic field of third-person male adult noun referents from Old English to Middle English, covering a time depth of approximately six hundred years. Results show a shift from the favored variantwerin Old English tomanin Middle English, with the diachronic change in frequency following a prototypical s-shaped distribution. Although the replacement seems to take centuries to be complete, lexical frequency and written transmission are proposed as influential explanatory factors, and a homonymic clash is suggested to have accelerated the process of replacement in Middle English. Text type and text origin contribute to variation, with alliteration significantly influencing lexical choices in Old English verse texts. When combined with findings from recent synchronic work, this study highlights a heterogeneously structured semantic domain, which has undergone lexical replacement and change over time, providing some evidence for the applicability of s-shaped patterns for lexical change.

Effects of microtopographic patterns on plant growth and soil improvement in coastal wetlands of the Yellow River Delta.

To clarify the effects of microtopography on plant growth and soil water, salt and nutrient characteristics of saline soils in mudflats within muddy coastal zones and explore suitable microtopographic modifications. Six microtopographic modification patterns, namely, S-shaped, stripe-shaped, pin-shaped, stepshaped, dense stripe-shaped and crescent-shaped patterns, were established in the coastal mudflats of the Yellow River Delta. The soil water, salt, ion, total carbon, total nitrogen, and total phosphorus contents and their ecological stoichiometric characteristics were measured and analyzed after theimplementation of different microtopographic modification patterns, with bare mudflats as the control. The results showed that microtopographic modification significantly changed the soil water and salt contents and the soil total carbon, total nitrogen and total phosphorus contents. Compared with the bare ground, microtopographic transformation significantly promoted the growth of the pioneer plant Suaeda salsa, significantly increased the soil water and nutrient contents, and significantly decreased the soil salinity. The soil salinity was mainly reduced by Na+ and Cl- ions. The soil salinity and nutrient contents gradually decreased with increasing soil depth, indicating the occurrence of surface aggregation. Compared to that of the bare ground, the soil C/N was significantly lower and the N/P was significantly higher in the microtopographic treatments, and the overall performance suggested soil N limitation. The ions contained in the saline soil were dominated by Na+ and Cl-, followed by Mg2+ and SO4 2-, with lower contents of K+, Ca2+ and HCO3 -. Among the six microtopography modification patterns, the crescent-shaped pattern best promoted vegetation restoration. This pattern was the most effective in reducing soil salinity, with a 98.53% reduction in soil salinity compared with that of bare ground, followed by the pin-shaped pattern. Compared with that in the bare ground samples, the nutrient content in the samples from the step-shaped modification increased by 23.27%; finally, the S-shaped, step-shaped and dense stripe-shaped patterns performed poorly in terms of plant restoration and soil improvement. It is suggested that a crescent-shaped pattern should be considered first when carrying out microtopographic transformation on the beaches of the Yellow River Delta, followed by stripe-shaped and pin-shaped patterns. The dense strip-shaped should not be adopted.

Three-dimensional structures of internal solitary waves in the northern south China sea revealed by mooring array observations

The data collected from an array of five subsurface moorings, which are deployed along the direction of internal solitary wave (ISW) crests in the northern South China Sea (SCS) from October 2013 to June 2014, are used to investigate the three-dimensional structures of ISWs and their temporal variabilities. The measurements reveal that the ISWs are asymmetric along their crests, with the average amplitude in the southern portion being 70% larger than that in the northern portion. The observed three-dimensionally integrated energy and flux of ISWs are accurately calculated for the first time, reaching 53 TJ and 0.82 GW, respectively, on average. Over the whole observation period, the pattern of ISW crests was dominantly convex, accounting for 76.2% of all observed episodes. However, due to the changes in propagation speeds along the direction of ISW crests caused by either single or combined effects of mesoscale eddies and intruded Kuroshio, the ISW crests could deform into S-shaped and concave patterns, which accounted for 19.6% and 4.2%, respectively. Moreover, during November and December, the positions of the largest amplitude along ISW crests mostly shifted from the southern portion to the northern portion due to the energy refraction caused by mesoscale eddies, leading to the increase/decrease in wave intensity in the northern/southern portion. In early February, the intruded Kuroshio remarkably shifted ISW energy southward, which increased the wave amplitude in the southern portion by as much as 96%. These results clearly demonstrate that the intensities of three-dimensional ISWs could temporally vary out of phase between the northern and southern portions of crests due to the remarkable modulations by intense background processes.

Growth: From Microorganisms to Megacities by Vaclav Smil

Reviewed by: Growth: From Microorganisms to Megacities by Vaclav Smil Ruth Schwartz Cowan (bio) Growth: From Microorganisms to Megacities By Vaclav Smil. Cambridge, MA: MIT Press, 2019. Pp. 634. Growth: From Microorganisms to Megacities By Vaclav Smil. Cambridge, MA: MIT Press, 2019. Pp.634. Remember that kid in third grade? The one who memorized all the rivers in Africa, then made you feel like a jerk because she knew so much more than you? Or maybe that kid was you? Or me? Thankfully, we both grew out of it. Vaclav Smil did not. Smil, distinguished professor of environmental science emeritus at the University of Manitoba, is the author of 37 previous single-authored books, all focused on some aspect of pre-pandemic global environmental, economic, and social crises. Growth has a similar focus, but you won't find that out until you have plowed your way through 448 poorly organized pages containing dozens and dozens of graphs about the growth patterns of—the subtitle actually minimizes the scope of the enterprise—everything from microorganisms to megacities, plus empires and civilizations. In his preface, Smil tells us that he intends to examine growth quantitatively, looking for patterns in the data, particularly "S-shaped (sigmoid) growth curves" (p. xxi). He's a bit cagey, however, about whether all the data and S-shaped curves he intends to display will, or even should, lead to secure forecasts of future growth, or lack thereof. He cautions against "any simplistic embrace of even the best statistical fits for long-term forecasting," then in the next paragraph declares that "parts of the book are helpfully predictive" (p. xxiii). The pages of Growth are riddled with similarly ambivalent and protective statements about the ultimate meaning of the S-shaped growth patterns he describes. In excruciating detail. But before we get to that detail, a sixty-nine-page introductory chapter, as its title suggests, is intended to elucidate "Trajectories: or common patterns of growth." Unfortunately, much of the chapter will only be intelligible to readers who understand a "perfect power-law function (approximating the form f(x)=ax-k where a and k are constant)" (p. 60). A reader unfamiliar with the nuances of advanced statistics may well cower in frightful admiration, an effect (and affect) which strikes me as the grownup version of what that kid in third grade was hoping to achieve. Four substantive chapters, occupying 448 pages, follow the introduction: Nature, Energies, Artifacts, and Populations, Societies, Economies. Each chapter is divided into subsections with no rhyme and little reason; each subsection is filled with a miscellany of data analyses and charts. None ends with a concluding generalization that makes sense out of the very different growth patterns discussed. Historians of technology who might want to use Growth as a handy reference [End Page 916] work about growth patterns on such diverse subjects as the maximum thrust of jet engines or the total length of Chinese highways will need to be exceedingly careful. One graph, presumably based on data that I happen to know something about (adoption rates of household appliances in the U.S., 1900–2005, p. 294) is multiply fraudulent. Leaving aside the fact that there is no reliable national data for the period 1900–1960, the graph Smil publishes cannot be found in the source he cites. That source (for which Smil gives both the wrong date and wrong URL) contains data (and a graph) about something else altogether, and only the years 1973–2006. The mistakes just keep coming. P. Taylor et al. "Luxury or necessity?" is at www.pewresearch.org/wp-content/uploads/sites/3/2010/10/Luxury.pdf. One can compare the URL publication date in Growth (p. 605). Colleagues, you have been warned! Growth concludes with a sixty-page chapter "What Comes After Growth: or demise and continuity" and a five-page "Coda." Here Smil reveals that the growth trajectory he really cares about is the one for "high energy civilization." Unfortunately, after treating us to extended critiques of both pro-growth and limits-to-growth economists, as well as arguments against the concepts of sustainable growth and de-materialization, Smil concludes that everyone who has ever modeled the...

Dual-band dichroic asymmetric transmission of linearly polarized waves in terahertz chiral metamaterial

Abstract Polarization conversion dichroism is of particular interest in manipulating the polarization state of light, whereas high-performance asymmetric transmission (AT) of linearly polarized waves is still inaccessible in the terahertz range. Here, a bilayer chiral metamaterial consisting of orthogonally chained S-shaped patterns with broken symmetry along the light propagation direction is proposed and demonstrated experimentally to realize a dual-band dichroic AT effect for linearly polarized terahertz waves. The AT effects are robust across a wide range of incident angles. The observed strong AT can be theoretically explained by a multiple reflection and transmission interference model and the transfer matrix method. The proposed bilayer chiral metamaterial may have broad applications in polarization manipulation, chiral biosensing and direction-dependent information processing.

Performance analysis of perovskite solar cells in 2013–2018 using machine-learning tools

This work presents a review and analysis of a database containing 1921 solar cell device performance data points extracted from 800 publications on the (organo)-lead-halide perovskite solar cell published between 2013 and 2018. The aim is to review the literature to capture the major patterns in the past and analyze the database using machine learning tools to develop heuristics and models to predict the cell performance. The factors related to the fabrication methods of metal-halide perovskite cells like the utilization of mixed cation perovskites, solvent engineering (such as mixed DMF+DMSO solvent), use of chlorobenzene as anti-solvent, employing two or three times spinning as well as factors pertaining the device architecture like utilization of LiTFSI+TBP+FK209 as hole transport layer (HTL) additive and tin oxide (SnO2t) as electron transport layer (ETL) emerge as the significant factors leading to highly efficient device of regular (n-i-p) architecture devices. The use of poly-triarylamine (PTAA) as HTL, mixed cation perovskite and bathocuproine (BCP) as ETL interlayer seems to be important for inverted (p-i-n) cells. It is also clear that the evolution of maximum efficiencies obeys the S-shape logistic curve. Two local S-shaped patterns exist in the data; the first one seems to be completed in 2014–2015, the second curve, which apparently started due to the effective utilization of solvents and anti-solvents, covers the later years, and it is reaching its maturity; the last two records may be indicators of a new trend.

Quality evaluation of postal address datasets measuring their autocorrelation

Many spatial applications related to land and titles like land use management, registering, and utility and health service providers are using postal addresses as their main or their supplementary georeferencing method. Evaluation of postal address datasets quality is important when controlling their changes due to manipulations (like add or update), comparing them, or merging them, that is one of the main strategies of developing countries like Iran, to form a unified addressing structure and database. Despite the costly and time consuming formal methods of postal addresses qualification that are based on address matching, the method proposed in this paper provides an evaluation of a postal address quality not requiring any preprocessing like standardization or ancillary data like streets and their addressing scheme data. The proposed method is based on measuring the autocorrelation of a postal address dataset content where higher level of autocorrelation indicates more standardization and less spatial sparsity of the addresses. The method processes the adjacency graph formed measuring Damerau–Levenstein distance between records of a postal address dataset. Evaluation of 5 statistics for 4 postal address datasets of Tehran City of Iran shows that the cumulative frequency of values and the maximum size of the components (sub-graphs) in the adjacency graph could be used. These statistics both show stable S-Shaped patterns that their threshold at the first extremum of their second derivative represents the desired quality of a postal address dataset. The results show that the measured threshold of postal address dataset corresponds with its topological structure of the streets that cover its addresses. The method can define characteristics of a standard address structure for one or more postal address datasets as the results propose 5 components for the standard address of the evaluated datasets which is the same as the number of components defined for Iranian national structure of postal addresses.

Measurement of Economic Growth, Development and Under Development: New Model and Application

This paper presents a simple model to measure the relative economic growth of economic systems. The model considers S-Shaped patterns of economic growth that, represented with a linear model, measure how an economic system grows in comparison with another one. In particular, this model introduces an approach which indicates if the economic system has a process of economic growth, development or under development. The application of the model is provided for regions and macro regions of the Italian economic system.

Design and Fabrication of Micro Hemispheric Shell Resonator with Annular Electrodes.

Electrostatic driving and capacitive detection is widely used in micro hemispheric shell resonators (HSR). The capacitor gap distance is a dominant factor for the initial capacitance, and affects the driving voltage and sensitivity. In order to decrease the equivalent gap distance, a micro HSR with annular electrodes fabricated by a glassblowing method was developed. Central and annular cavities are defined, and then the inside gas drives glass softening and deformation at 770 °C. While the same force is applied, the deformation of the hemispherical shell is about 200 times that of the annular electrodes, illustrating that the deformation of the electrodes will not affect the measurement accuracy. S-shaped patterns on the annular electrodes and internal-gear-like patterns on the hemispherical shell can improve metal malleability and avoid metal cracking during glass expansion. An arched annular electrode and a hemispheric shell are demonstrated. Compared with HSR with a spherical electrode, the applied voltage could be reduced by 29%, and the capacitance could be increased by 39%, according to theoretical and numerical calculation. The surface roughness of glass after glassblowing was favorable (Rq = 0.296 nm, Ra = 0.217 nm). In brief, micro HSR with an annular electrode was fabricated, and its superiority was preliminarily confirmed.

Information Sharing and Conditional Financial Development in Africa

This study examines conditional financial development from information sharing in 53 African countries for the period 2004-2011, using contemporary and non-contemporary quantile regressions (QR) which enable the assessment of the effect of information sharing throughout the conditional distributions of financial development dynamics. The policy relevance of the QR approach builds on the motivation that blanket policies on the role of information sharing in financial development may not be effective unless they are contingent on initial levels of financial development and tailored differently across countries with low, intermediate and high levels of financial development. Information sharing is measured with private credit bureaus (PCB) and public credit registries (PCR) while financial development is proxied with dynamics of depth, efficiency, activity and size. The following findings are established. First, for financial depth, while there is a positive threshold effect from PCR in money supply and liquid liabilities, the effect from PCB is mixed. Second, for financial efficiency, there is a: (i) contemporary positive threshold from PCR and mixed effect from PCB in banking system efficiency and (ii) U-shape and positive threshold from PCR and PCB respectively in financial system efficiency. Third, for financial activity, there are consistent positive thresholds from PCR and PCB in banking system activity and financial system activity. Fourth, there are negative thresholds from PCR and PCB in financial size. Positive thresholds are consistent incremental financial development rewards from PCR and/or PCB with increasing financial development and vice-versa for negative thresholds. Mixed effects are characterised by S-shaped, Kuznets or wave-like patterns. As a main policy implication, initial conditions in financial development are essential to materialise incremental benefits from PCR and PCB. Other policy implications are discussed.

Microanatomy of the subcallosal artery: an in-vivo 7 T magnetic resonance angiography study.

To investigate in-vivo microanatomy of the subcallosal artery branching from the anterior communicating artery (ACoA) using time-of-flight (TOF) magnetic resonance angiography (MRA) at 7 Tesla. Seventy-five subjects, including 15 healthy volunteers and 60 patients, were included in this prospective study. Three raters characterized branches from ACoA in maximum intensity projections of TOF MRA at 7 Tesla acquired with 0.22 × 0.22 × 0.41mm(3) resolution. Furthermore, course patterns and anatomical features of the subcallosal artery (maximum diameter, length, and branching angle from ACoA) were measured. Branches from the anterior communicating artery were visualized in 63 of 74 (85.1%) subjects and were identified as the subcallosal artery (93.7%) and the accessory anterior cerebral artery (6.3%). The course of the subcallosal artery was classified into 3 groups; C-shaped (55.9%), straight (16.9%), and S-shaped (27.2%). There was a significant difference between the branching angles of C-shaped and straight (p < 0.0001), between C-shaped and S-shaped (p < 0.0001), as well as between straight and S-shaped (p = 0.0113) course patterns. High-resolution in-vivo 7 T TOF MRA can delineate the microanatomy of the subcallosal artery. Three main variants of course patterns and branching angles from ACoA could be identified. • In-vivo 7 Tesla TOF MRA can delineate the subcallosal artery microanatomy • Three distinct course patterns of the subcallosal artery were identified • Branching angles from ACoA significantly differed between subcallosal artery course patterns.

The Sytykanskaya kimberlite pipe: Evidence from deep-seated xenoliths and xenocrysts for the evolution of the mantle beneath Alakit, Yakutia, Russia

Mantle xenoliths (>150) and concentrates from late autolithic breccia and porphyritic kimberlite from the Sytykanskaya pipe of the Alakit field (Yakutia) were analyzed by EPMA and LAM ICP methods. In P-T-X-f(O2) diagrams minerals from xenoliths show widest variations, the trends P-Fe#-CaO, f(O2) for minerals from porphyric kimberlites are more stepped than for xenocrysts from breccia. Ilmenite PTX points mark moving for protokimberlites from the lithosphere base (7.5 GPa) to pyroxenite lens (5–3.5 GPa) accompanied by Cr increase by AFC and creation of two trends P-Fe#Ol ∼10–12% and 13–15%. The Opx-Gar-based mantle geotherm in Alakit field is close to 35 mW/m2 at 65 GPa and 600 °C near Moho was determined. The oxidation state for the megacrystalline ilmenites is lower for the metasomatic associations due to reduction of protokimberlites on peridotites than for uncontaminated varieties at the lithosphere base. Highly inclined linear REE patterns with deep HFSE troughs for the parental melts of clinopyroxene and garnet xenocrysts from breccia were influenced by differentiated protokimberlite. Melts for metasomatic xenoliths reveal less inclined slopes without deep troughs in spider diagrams. Garnets reveal S-shaped REE patterns. The clinopyroxenes from graphite bearing Cr-websterites show inclined and inflected in Gd spectrums with LREE variations due to AFC differentiation. Melts for garnets display less inclined patterns and Ba-Sr troughs but enrichment in Nb-Ta-U. The 40Ar/39Ar ages for micas from the Alakit mantle xenoliths for disseminated phlogopites reveal Proterozoic (1154 Ma) age of metasomatism in early Rodinia mantle. Veined glimmerites with richterite – like amphiboles mark ∼1015 Ma plume event in Rodinia mantle. The ∼600–550 Ma stage manifests final Rodinia break-up. The last 385 Ma metasomatism is protokimberlite-related.

The “S” curve relationship between export diversity and economic size of countries

The highly detailed international trade data among all countries in the world during 1971–2000 shows that the kinds of export goods and the logarithmic GDP (gross domestic production) of a country have an S-shaped relationship. This indicates that all countries can be divided into three stages accordingly. First, the small economies always export very few kinds of products as we expect. Second, once the economic size magnitude (log(GDP)) of a country is beyond a threshold, its export diversity may increase dramatically. However, this is not the case for large economies because a ceiling on the export diversity is observed when their logarithmic GDPs are higher than another threshold. This pattern is very stable for different years although the concrete parameters of the fitting sigmoid functions may change with time. In addition, we also discussed other relationships such as import diversity with respect to logarithmic GDP, diversity of exporters with respect to the number of export goods etc.; all of these relationships show S-shaped or power law patterns which can be derived by the “S” curve relations. Although this paper does not explain the origin of the S-shaped curve, it may provide a basic empirical fact and insights for economic diversity.

Trajectories of faithfulness in child-specific phonology

AbstractThis paper provides new evidence and analysis of gradual and U-shaped phonological learning. Using a rich longitudinal corpus from Trevor (Compton &amp; Streeter 1977, Pater 1997b) we demonstrate that some of Trevor's consonant harmony follows a statistically significant U-shaped trajectory, in contrast to the more typical S-shaped progression of his complex onsets. We then analyse these two developmental paths using an OT model of phonological acquisition (Hayes 2004, Prince &amp; Tesar 2004, Tessier 2007, 2009), in which the learner's variation within and across stages is the effect of stored old productions rather than a variable grammar. The decrease in Trevor's faithfulness to place of articulation due to consonant harmony is attributed to the induction of a new constraint during the course of learning. Our analysis is paired with a computational implementation, showing how competition between old forms and the current grammar allows the model to derive both S-shaped and U-shaped patterns.

Application of S-shaped curves

This paper deals with the application of S-shaped curves in the contexts of inventive problem solving, innovation and technology forecasts. After explaining the origin of the logistic S-curve its application, as seen in publications from different domains, is reviewed. Despite much criticism and the failure to apply the logistic function for long-term forecasting, it continues to be a popular model for describing the evolution of systems (technological, economical, social and others) over time. This paper can help researchers and practitioners to understand the scope of application of S-shaped patterns, their limitations, and peculiarities.

Capacity Expansion in Markets with Intertemporal Consumption Externalities

This paper analyzes market capacity expansion in the presence of intertemporal consumption externalities such as consumer learning, networks, and bandwagon effects. An externality leads to an endogenous shift of market demand that responds to past market capacity. Whereas market capacity grows in waves, its magnitude depends on the degree of market concentration. The competitive environment contributes to S-shaped time patterns of market capacity expansion. On the other hand, using a low introductory price, a monopolist plans an initially larger amount of market cultivation than a competitive market capacity expansion.

CAPACITY EXPANSION IN MARKETS WITH INTER-TEMPORAL CONSUMPTION EXTERNALITIES

This paper analyses market capacity expansion in the presence of inter-temporal consumption externalities such as consumer learning, networks and bandwagon effects. An externality leads to an endogenous shift of market demand that responds to past market capacity. Whereas market capacity grows in waves, its magnitude depends on the degree of market concentration. The competitive environment contributes to S-shaped time patterns of market capacity expansion. On the other hand, using a low introductory price, a monopolist plans an initially larger amount of market cultivation than a competitive market capacity expansion.

Density structures in perturbed thin cold discs

We investigate the action of gravitational perturbers in thin cold astrophysical discs. The model includes viscous diffusion of the disc matter and gravitational scattering by the perturber as two counteracting processes. Two types of density structures are found, depending on the mass of the perturbing body and on the amount of momentum transport in the disc. A gap around the whole circumference of the disc is opened if the perturber is more massive than a certain threshold. Alternatively, a local S-shaped density modulation is generated that we call a ‘propeller’. We derive an analytic solution of the S-shaped density patterns using Green functions of the stationary problem. We find that the large-scale appearance of propellers does not depend on the details of the scattering process but mainly on the effective strength of the gravity perturbations ‐ namely the amplitudes of the Green functions. The crucial disc parameter is the kinematic viscosity describing the transport properties of the disc material. The solution provides the characteristic spatial extensions of the structures depending on the mass of the perturber and the viscosity of the disc. Furthermore, we propose a new criterion for the threshold mass of the perturber needed to open a gap. The results are applied to dense planetary rings perturbed by an embedded moonlet, and to gas‐dust discs around a protostar perturbed by a protoplanet. Concerning the rings of Saturn there is the chance to verify our findings with the high-resolution experiments of the Cassini spacecraft, which arrives at Saturn in 2004.