Critical Mass Threshold Research Articles

An attractive model: simulating fuzzy dark matter with attractive self-interactions

Abstract Fuzzy Dark Matter (FDM) comprised of ultralight ($m \sim 10^{-22}~\rm {eV}$) boson particles has received significant attention as a viable alternative to Cold Dark Matter (CDM), as it approximates CDM on large scales (≳ 1 Mpc) while potentially resolving some of its small-scale problems via kiloparsec-scale quantum interference. However, the most basic FDM model, with one free parameter (the boson mass), is subject to a tension: small boson masses yield the desired cores of dwarf galaxies but underpredict structure in the Lyman-α forest, while large boson masses render FDM effectively identical to CDM. This Catch-22 problem may be alleviated by considering an axion-like particle with attractive particle self-interactions. We simulate an idealized FDM halo with self-interactions parameterized by an energy decay constant $f \sim 10^{15}~\rm {GeV}$ related to the axion symmetry-breaking conjectured to solve the strong-CP problem in particle physics. We observe solitons, a hallmark of FDM, condensing within a broader halo envelope, and find that the density profile and soliton mass depend on self-interaction strength. We propose generalized formulae to extend those from previous works to include self-interactions. We also investigate a critical mass threshold predicted for strong interactions at which the soliton collapses into a compact, unresolved state. We find that the collapse happens quickly and its effects are initially contained to the central region of the halo.

The digital economy and advertising diffusion models: Critical mass and the Stalling equilibrium

In the digital economy it is frequently observed that products become more valuable the larger is the number of people that use it. To account for such network effects, we introduce a new diffusion equation in a dynamic model of the firm with the aim to obtain the advertising policy that maximizes firm profits. Also an advertising budget is introduced.First, we find that introduction of the network effect leads to a critical mass of the sales level. Only if the sales are greater or equal to this level, is it optimal for the firm to have a substantial sales level in the long run. Second, introduction of an advertising budget could result in the existence of a Stalling equilibrium. This new type of equilibrium, at which the advertising amount is at its upper bound, serves as the critical mass threshold separating growth and decline. Third, the advertising policy is continuous in the sales level either when the discount rate is large and the rate of forgetfulness is low, when the Stalling equilibrium exists, or when the rate of forgetfulness is that high that the firm is always in decline. Furthermore, existence of the Stalling equilibrium involves an important message to the management of the firm in that a slight increase of the advertising budget would open up an avenue of growth in sales.

Does the strength of women in the upper echelon influence earnings quality? The application of critical mass theory

Globally, several financial scandals were witnessed within the first decade of the 21st century that necessitated a robust corporate governance mechanism to improve financial reporting quality. Empirical evidence shows that men dominate the boards involved in these scandals. In an attempt to restore the confidence of stakeholders in the financial report, financial regulatory authorities in European Union economies recommend a well-constituted gender-diverse board where the marginalised gender is at least 40 percent of the board. However, in Nigeria, there is little research on women's participation in corporate board decisions taken into cognizance of critical mass theory. Thus, the study investigates how the critical mass of female representation on the corporate board and audit committee affects earnings quality. The study employs a longitudinal design by collecting secondary data on eleven deposit money banks from 2011-2022. The study uses data collected after testing endogeneity problems using Hausman's test. The results show that females on the board and audit committee significantly affect the quality of earnings when reaching the critical mass threshold. The study provides policy implications for supporting more significant involvement of women in board and audit committees based on business cases rather than social justice. Hence, this study proposes a mandatory thirty percent threshold compliance for board gender diversity, which the Central Bank of Nigeria voluntarily recommended.

Multiple populations and a CH star found in the 300S globular cluster stellar stream

ABSTRACT Milky Way globular clusters (GCs) display chemical enrichment in a phenomenon called multiple stellar populations (MSPs). While the enrichment mechanism is not fully understood, there is a correlation between a cluster’s mass and the fraction of enriched stars found therein. However, present-day GC masses are often smaller than their masses at the time of formation due to dynamical mass-loss. In this work, we explore the relationship between mass and MSPs using the stellar stream 300S. We present the chemical abundances of eight red giant branch member stars in 300S with high-resolution spectroscopy from Magellan/MIKE. We identify one enriched star characteristic of MSPs and no detectable metallicity dispersion, confirming that the progenitor of 300S was a GC. The fraction of enriched stars (12.5 per cent) observed in our 300S stars is less than the 50 per cent of stars found enriched in Milky Way GCs of comparable present-day mass (∼104.5 $\mathrm{\, {\rm M}_{\odot }}$). We calculate the mass of 300S’s progenitor and compare it to the initial masses of intact GCs, finding that 300S aligns well with the trend between the system mass at formation and enrichment. 300S’s progenitor may straddle the critical mass threshold for the formation of MSPs and can therefore serve as a benchmark for the stellar enrichment process. Additionally, we identify a CH star, with high abundances of s-process elements, probably accreted from a binary companion. The rarity of such binaries in intact GCs may imply stellar streams permit the survival of binaries that would otherwise be disrupted.

Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus

We study an optimal mass threshold for normalizability of the Gibbs measures associated with the focusing mass-critical nonlinear Schrödinger equation on the one-dimensional torus. In an influential paper, Lebowitz et al. (J Stat Phys 50(3–4):657–687, 1988) proposed a critical mass threshold given by the mass of the ground state on the real line. We provide a proof for the optimality of this critical mass threshold. The proof also applies to the two-dimensional radial problem posed on the unit disc. In this case, we answer a question posed by Bourgain and Bulut (Ann Inst H Poincaré Anal Non Linéaire 31(6):1267–1288, 2014) on the optimal mass threshold. Furthermore, in the one-dimensional case, we show that the Gibbs measure is indeed normalizable at the optimal mass threshold, thus answering an open question posed by Lebowitz et al. (1988). This normalizability at the optimal mass threshold is rather striking in view of the minimal mass blowup solution for the focusing quintic nonlinear Schrödinger equation on the one-dimensional torus.

Energy optimization in extrasolar planetary systems: the transition from peas-in-a-pod to runaway growth

ABSTRACT Motivated by the trends found in the observed sample of extrasolar planets, this paper determines tidal equilibrium states for forming planetary systems – subject to conservation of angular momentum, constant total mass, and fixed orbital spacing. In the low mass limit, valid for super-Earth-class planets with masses of order mp ∼ 10 M⊕, previous work showed that energy optimization leads to nearly equal mass planets, with circular orbits confined to a plane. The present treatment generalizes previous results by including the self-gravity of the planetary bodies. For systems with a sufficiently large total mass $m_{\scriptstyle \rm T}$ in planets, the optimized energy state switches over from the case of nearly equal mass planets to a configuration where one planet contains most of the material. This transition occurs for a critical mass threshold of approximately $m_{\scriptstyle \rm T}\gtrsim m_{\scriptstyle \rm C}\sim 40\,{\rm M_\oplus}$ (where the value depends on the semimajor axes of the planetary orbits, the stellar mass, and other system properties). These considerations of energy optimization apply over a wide range of mass scales, from binary stars to planetary systems to the collection of moons orbiting the giant planets in our Solar system.

Fokker--Planck Approach of Ostwald Ripening: Simulation of a Modified Lifshitz--Slyozov--Wagner System with a Diffusive Correction

We propose a well-balanced scheme for the modified Lifshitz--Slyozov equation, which incorporates a size-diffusion term. The method uses the Fokker--Planck structure of the equation. In turn, large time simulations can be performed with a reduced computational cost, since the time-step constraints are relaxed. The simulations bring out the critical mass threshold and the relaxation to equilibrium, which can be expected from the formal analogies with the Becker--Döring system.

The Spatial Concentration of Peacekeeping Personnel and Public Health During Intrastate Conflicts

ABSTRACTThe literature on the effectiveness of peacekeeping has been focused almost exclusively on conflict mitigation. This article expands the scope of this literature by developing a theory that explains how the presence of peacekeeping forces improves population health during periods of intrastate conflict. The argument is put forth that because civil conflict violence clusters geographically it undermines the herd immunity critical-mass threshold. This, in turn, leads to increased infection rates and a tragic surge in preventable deaths. Peacekeepers, because they target conflict ‘hot spots’ locally, put an end to this cycle and assist in the restoration herd immunity. Using a unique measure of peacekeeping that accounts for the area of the conflict zone, the empirical models uncover a positive relationship between peacekeeping forces and immunization rates, as vaccination rates increase when peacekeepers are deployed into violent conflicts. These findings suggest that peacekeeping missions have the potential to reduce the public health costs imposed by internal conflicts.

Board Gender Diversity in the STEM&F Sectors: The Critical Mass Required to Drive Firm Performance

This study investigates the link between board gender diversity (BGD) and firm performance (FP). The analysis is conducted using Fortune 500 firms in the Science, Technology, Engineering, Mathematics, and Finance (STEM&F) sectors covering a period of seven years, from 2007 to 2013. The theoretical framework combines several theories that give shape to the critical mass effect of BGD on FP. This shape shows that below the critical mass threshold, BGD may represent a disadvantage to the board as it may facilitate the formation of subgroups, dysfunctional conflicts, and distrust. However, at or above the critical mass threshold, BGD facilitates better monitoring of management, greater resource provisions, and divergent thinking. To ensure sound results, this study addresses endogeneity concerns regarding omitted variable bias, reverse causality, and dynamic endogeneity. These results support a significant U-shaped relationship between the number of female directors and FP in the STEM&F sectors. That is, BGD yields higher FP when there is a critical mass of women on the board. This finding remains robust when alternative proxies for BGD and FP are employed and is consistent with the predictions of our theoretical framework. Our analysis also reveals that the positive effect of BGD on FP increases when there is at least a critical mass of 30% of women on a corporate board. This finding suggests that boards that have reached a critical mass of 30% of women present a favorable environment to capitalize on innovative ideas arising from BGD.

Gendered Politics and Economic Policy Making:The Case of Public Expenditures on Family Allowances

Parliament is the place where elected politicians make laws to set the policy direction of countries. The failure of the involvement of different voices such as gender, race, ethnicity and class in policy-making may prove the existence of an unequality in political decisions. Regarding gender, there has been a sufficient amount of empirical evidence in the literature that women and men may have different policy preferences. Their common argument is that women are more likely than men give priority to public policies related to their traditional roles as care givers to children in the family. Public spending on family allowances is one of the family-specific social policies that play an important role in helping families for the childcare and the child rising. This paper, therefore, have analyzed the relationship between female political representation in the OECD parliaments and the resource allocation towards public spending on family allowances. Overall findings are driven by the fact that the fraction of female parliamentarians over the thirty years across OECD countries have not been sufficient for a possible gender effect in policy-making on family allowances. In fact, the fraction of female politicians is above a certain threshold (30%) shows a significantly different allocation of public spending on family allowances. In other words, women’s representation may need to reach a certain critical mass threshold to make an impact on the policy decision process.

Defining a Critical Mass Threshold for Agricultural Support Services

Utilizing four counties in western North Carolina as a study area, this paper examines the existence of a critical mass threshold in agricultural production below which crucial support services could be expected to close down or relocate outside the region. Twenty-two key stakeholder interviews suggest that for most support service businesses, no such critical mass threshold exists at the regional level. For those support service types most at-risk, an IMPLAN model was utilized to determine the economic impact to the region.

Impact of critical mass on the evolution of cooperation in spatial public goods games

We study the evolution of cooperation under the assumption that the collective benefits of group membership can only be harvested if the fraction of cooperators within the group, i.e., their critical mass, exceeds a threshold value. Considering structured populations, we show that a moderate fraction of cooperators can prevail even at very low multiplication factors if the critical mass is minimal. For larger multiplication factors, however, the level of cooperation is highest at an intermediate value of the critical mass. The latter is robust to variations of the group size and the interaction network topology. Applying the optimal critical mass threshold, we show that the fraction of cooperators in public goods games is significantly larger than in the traditional linear model, where the produced public good is proportional to the fraction of cooperators within the group.

Income, affordable and threshold effects on FMS in the developed and developing economies

This paper studies the effects on fixed to mobile substitution (FMS) that has evolved into an essential industry trend. Based on data from 1997 through 2005, three kinds of effects, income, affordable and threshold, are derived from various FMS patterns in developed and developing economies. The income effect is the prerequisite for the two other effects. For the G7 and new industry economies (NIE) (Taiwan, Singapore, H.K and S. Korea), the 5% income effect threshold is crossed and the mobile penetration rate climbs up rapidly. However, for Association of Southeast Asian Nations (ASEAN) and Brazil, Russia, India and China (BRIC), 1 1 ASEAN was established on 8 August 1967 in Bangkok by the five original member Countries, namely, Indonesia, Malaysia, Philippines, Singapore and Thailand. Thereafter, Brunei Darussalam, Vietnam, Lao PDR, Myanmar and Cambodia continued to join. BRIC or BRICs are terms for four brick countries used to refer to the combination of Brazil, Russia, India and China. most of these developing economies have experienced only the income effect. When mobile average revenue per user (ARPU) comes close to or drops lower than fixed line ARPU, the mobile penetration rate begins to increase and the affordable effect appears. As the mobile penetration rate begins to grow, it does not at first affect fixed line growth. The threshold effect happens only when the mobile penetration rate crosses a critical mass threshold; then the growth of fixed line penetration will decline or stop. Once mobile substitution occurs, the traditional paradigm of fixed line as the universal service obligation (USO) is no longer valid and the rules must be changed.

Where do ‘red and dead’ early-type void galaxies come from?

Void regions of the Universe offer a special environment for studying cosmology and galaxy formation, which may expose weaknesses in our understanding of these phenomena. Although galaxies in voids are observed to be predominately gas rich, star forming and blue, a sub-population of bright red void galaxies can also be found, whose star formation was shut down long ago. Are the same processes that quench star formation in denser regions of the Universe also at work in voids? We compare the luminosity function of void galaxies in the 2dF Galaxy Redshift Survey, to those from a galaxy formation model built on the Millennium Simulation. We show that a global star formation suppression mechanism in the form of low luminosity AGN heating is sufficient to reproduce the observed population of void early-types. Radio mode heating is environment independent other than its dependence on dark matter halo mass, where, above a critical mass threshold of approximately M_vir~10^12.5 M_sun, gas cooling onto the galaxy is suppressed and star formation subsequently fades. In the Millennium Simulation, the void halo mass function is shifted with respect to denser environments, but still maintains a high mass tail above this critical threshold. In such void halos, radio mode heating remains efficient and red galaxies are found; collectively these galaxies match the observed space density without any modification to the model. Consequently, galaxies living in vastly different large-scale environments but hosted by halos of similar mass are predicted to have similar properties, consistent with observations.

Sheer Numbers: Critical Representation Thresholds and Women's Political Representation

Studies of women in legislatures indicate that achieving a “critical mass” of women may have the effect of changing the legislative priorities of women, increasing the number of legislative initiatives dealing with women and the passage rate of such initiatives, and altering the legislative priorities of men. In the absence of a critical mass, “token” women may be so constrained by their minority status as to be unable to respond proactively to their environment. Popular wisdom suggests that a critical mass may be necessary for women to make a difference as women in a legislature.Yet, critical mass is both problematic and under-theorized in political science research. The critical mass threshold is debated, the mechanism of effect is unspecified, possible negative consequences are overlooked, and the potential for small numbers of elected women to effect political change on behalf of women is neglected. Beyond sheer numbers, what are the conditions that govern the ability of women legislators to make a difference? We argue that two major contextual factors beyond the sheer numbers are likely to govern the extent to which female legislators serve to represent women. Relying on the secondary literature, this article maps parliamentary and civil society contexts to sheer numbers of women to locate conditions in which female legislators are most likely to have policy successes.Karen Beckwith is the Flora Stone Mather Professor of Political Science at Case Western Research University and Editor, with Lisa Baldez, of Politics & Gender (karen.beckwith@case.edu). Her published work includes Women's Movements Facing the Reconfigured State (Cambridge 2003, with Lee Ann Banaszak and Dieter Rucht), Political Women and American Democracy (forthcoming, with Christina Wolbrecht and Lisa Baldez), and articles on gender and politics in the European Journal of Political Research, Politics & Society, and Signs, among others. Kimberly Cowell-Meyers is Assistant Professor in the Department of Government at American University (kcowell@american.edu). She is author of Religion and Politics: The Party Faithful in Ireland and Germany (Greenwood, 2002) and articles published in Women & Politics, Nationalism and Ethnic Politics, and Irish Political Studies among others. She has worked in the British Parliament and the United States Institute of Peace.

A rapid ontogenetic shift in the diet of juvenile yellowfin tuna from Hawaii

Within the tropical and subtropical oceans, tuna forage opportunistically on a wide variety of prey. However, little is known about the trophic ecology of the smallest size classes which play an important role in stock assessments and fisheries management. The for- aging behavior of yellowfin tuna, Thunnus albacares (23.5-154.0 cm FL), collected from nearshore Fish Aggregating Devices (FADs) around Oahu was stud- ied using stable isotope and stomach contents analyses. Emphasis was placed on small juveniles. Yellowfin tuna changed their diets significantly between 45 and 50 cm forklength (ca. 1.5 kg). Smallest size classes fed on planktonic organisms inhabiting the shallow mixed layer, primarily larval stomatopod and decapod crus- taceans, whereas larger tuna fed on teleosts and adult Oplophorus gracilirostris, a vertically migrating meso- pelagic species of shrimp. When interpreting the vari- ation in prey d 15 N values, we considered both their relative trophic position and d 15 N values of the nitro- gen at the base of the food web. Based on the distinct diet shift of the yellowfin tuna, demonstrated by both isotope and stomach content analyses, we propose a critical mass threshold was reached at about 45 cm FL that enabled sufficient endothermic capability to allow tuna to access prey dwelling in deeper, colder water. These ontogenetic changes in foraging range and commensurate shift in diet of small tunas would affect their vulnerability to fishing pressure.

Critical mass and economies of scale in the supply of services by business support organizations

Uses a large sample survey of businesses to demonstrate that a critical mass threshold exists for their use of business support organization services. This critical mass threshold is very marked for the two organizations examined: British case studies of chambers of commerce and government‐supported business training and advice bodies. Beyond this threshold, managers of chambers of commerce can achieve nonlinear returns to scale, while returns to scale for government‐supported bodies are almost exactly linear. Infers that this results from the very different motives of commercially based chambers and their members, compared to government‐supported bodies, which allow the benefits of service bundling for chambers while managers of government bodies have to deal with multiple discrete programmes offering few synergies. Also examines the effects of external economies of agglomeration and shows that these increase market penetration and hence reduce the catchment sizes necessary to reach critical mass only in the case of the most agglomerated urban and industrial centres.

The parabolic-parabolic Keller-Segel model in R2

This paper is devoted mainly to the global existence problem for the two-dimensional parabolic-parabolic Keller-Segel system in the full space. We derive a critical mass threshold below which global existence is ensured. Carefully using energy methods and ad hoc functional inequalities, we improve and extend previous results in this direction. The given threshold is thought to be the optimal criterion, but this question is still open. This global existence result is accompanied by a detailed discussion on the duality between the Onofri and the logarithmic Hardy-Littlewood-Sobolev inequalities that underlie the following approach.