Fluctuation-Response Relations for Multi-Time Correlations

We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control term'' added as a modification to the master equation for statistical distributions. The proof of the relations is based upon a variational characterization of the generating functional of the time-correlations. The same fluctuation-response relations are preserved within moment-closures for the statistical dynamical system, when these are constructed via the variational Rayleigh-Ritz procedure. For the 2-time correlations of the moment-variables themselves, the fluctuation-response relation is equivalent to an ``Onsager regression hypothesis'' for the small fluctuations. For correlations of higher-order, there is a new effect in addition to such linear propagation of fluctuations present instantaneously: the dynamical generation of correlations by nonlinear interaction of fluctuations. In general, we discuss some physical and mathematical aspects of the {\it Ans\"{a}tze} required for an accurate calculation of the time correlations. We also comment briefly upon the computational use of these relations, which is well-suited for automatic differentiation tools. An example will be given of a simple closure for turbulent energy decay, which illustrates the numerical application of the relations.Comment: 28 pages, 1 figure, submitted to Phys. Rev.

Simulations of protostellar collapse using multigroup radiation hydrodynamics. I. The first collapse

Radiative transfer plays a major role in the process of star formation. Many simulations of gravitational collapse of a cold gas cloud followed by the formation of a protostellar core use a grey treatment of radiative transfer coupled to the hydrodynamics. However, dust opacities which dominate extinction show large variations as a function of frequency. In this paper, we used frequency-dependent radiative transfer to investigate the influence of the opacity variations on the properties of Larson's first core. We used a multigroup M1 moment model in a 1D radiation hydrodynamics code to simulate the spherically symmetric collapse of a 1 solar mass cloud core. Monochromatic dust opacities for five different temperature ranges were used to compute Planck and Rosseland means inside each frequency group. The results are very consistent with previous studies and only small differences were observed between the grey and multigroup simulations. For a same central density, the multigroup simulations tend to produce first cores with a slightly higher radius and central temperature. We also performed simulations of the collapse of a 10 and 0.1 solar mass cloud, which showed the properties of the first core to be independent of the initial cloud mass, with again no major differences between grey and multigroup models. For Larson's first collapse, where temperatures remain below 2000 K, the vast majority of the radiation energy lies in the IR regime and the system is optically thick. In this regime, the grey approximation does a good job reproducing the correct opacities, as long as there are no large opacity variations on scales much smaller than the width of the Planck function. The multigroup method is however expected to yield more important differences in the later stages of the collapse when high energy (UV and X-ray) radiation is present and matter and radiation are strongly decoupled.Comment: 9 pages, 5 figures, accepted for publication in A&

Critical Protoplanetary Core Masses in Protoplanetary Disks and the Formation of Short-Period Giant Planets

We study a solid protoplanetary core of 1-10 earth masses migrating through a disk. We suppose the core luminosity is generated as a result of planetesimal accretion and calculate the structure of the gaseous envelope assuming equilibrium. This is a good approximation when the core mass is less than the critical value, M_{crit}, above which rapid gas accretion begins. We model the structure of the protoplanetary nebula as an accretion disk with constant \alpha. We present analytic fits for the steady state relation between disk surface density and mass accretion rate as a function of radius r. We calculate M_{crit} as a function of r, gas accretion rate through the disk, and planetesimal accretion rate onto the core \dot{M}. For a fixed \dot{M}, M_{crit} increases inwards, and it decreases with \dot{M}. We find that \dot{M} onto cores migrating inwards in a time 10^3-10^5 yr at 1 AU is sufficient to prevent the attainment of M_{crit} during the migration process. Only at small radii where planetesimals no longer exist can M_{crit} be attained. At small radii, the runaway gas accretion phase may become longer than the disk lifetime if the core mass is too small. However, massive cores can be built-up through the merger of additional incoming cores on a timescale shorter than for in situ formation. Therefore, feeding zone depletion in the neighborhood of a fixed orbit may be avoided. Accordingly, we suggest that giant planets may begin to form early in the life of the protostellar disk at small radii, on a timescale that may be significantly shorter than for in situ formation. (abridged)Comment: 24 pages (including 9 figures), LaTeX, uses emulateapj.sty, to be published in ApJ, also available at http://www.ucolick.org/~ct/home.htm

The phase shift of line solitons for the KP-II equation

The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the $L^\infty$-bound for the local phase shift of modulating line solitons for polynomially localized perturbations

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Loss associated with subtractive health service change: The case of specialist cancer centralization in England

OBJECTIVE: Major system change can be stressful for staff involved and can result in 'subtractive change' - that is, when a part of the work environment is removed or ceases to exist. Little is known about the response to loss of activity resulting from such changes. Our aim was to understand perceptions of loss in response to centralization of cancer services in England, where 12 sites offering specialist surgery were reduced to four, and to understand the impact of leadership and management on enabling or hampering coping strategies associated with that loss. METHODS: We analysed 115 interviews with clinical, nursing and managerial staff from oesophago-gastric, prostate/bladder and renal cancer services in London and West Essex. In addition, we used 134 hours of observational data and analysis from over 100 documents to contextualize and to interpret the interview data. We performed a thematic analysis drawing on stress-coping theory and organizational change. RESULTS: Staff perceived that, during centralization, sites were devalued as the sites lost surgical activity, skills and experienced teams. Staff members believed that there were long-term implications for this loss, such as in retaining high-calibre staff, attracting trainees and maintaining autonomy. Emotional repercussions for staff included perceived loss of status and motivation. To mitigate these losses, leaders in the centralization process put in place some instrumental measures, such as joint contracting, surgical skill development opportunities and trainee rotation. However, these measures were undermined by patchy implementation and negative impacts on some individuals (e.g. increased workload or travel time). Relatively little emotional support was perceived to be offered. Leaders sometimes characterized adverse emotional reactions to the centralization as resistance, to be overcome through persuasion and appeals to the success of the new system. CONCLUSIONS: Large-scale reorganizations are likely to provoke a high degree of emotion and perceptions of loss. Resources to foster coping and resilience should be made available to all organizations within the system as they go through major change

Halting Type I planet migration in non-isothermal disks

Aims: We investigate the effect of including a proper energy balance on the interaction of a low-mass planet with a protoplanetary disk. Methods: We use a three-dimensional version of the RODEO method to perform hydrodynamical simulations including the energy equation. Radiation is included in the flux-limited diffusion approach. Results: The sign of the torque depends sensitively on the ability of the disk to radiate away the energy generated in the immediate surroundings of the planet. In the case of high opacity, corresponding to the dense inner regions of protoplanetary disks, migration is directed \emph{outward}, instead of the usual inward migration that was found in locally isothermal disks. For low values of the opacity we recover inward migration, and we show that torques originating in the coorbital region are responsible for the change in migration direction.Comment: 4 pages, 5 figures, accepted for A&A letter

How to Cost the Implementation of Major System Change for Economic Evaluations: Case Study Using Reconfigurations of Specialist Cancer Surgery in Part of London, England.

BACKGROUND: Studies have been published regarding the impact of major system change (MSC) on care quality and outcomes, but few evaluate implementation costs or include them in cost-effectiveness analysis (CEA). This is despite large potential costs of MSC: change planning, purchasing or repurposing assets, and staff time. Implementation costs can influence implementation decisions. We describe our framework and principles for costing MSC implementation and illustrate them using a case study. METHODS: We outlined MSC implementation stages and identified components, using a framework conceived during our work on MSC in stroke services. We present a case study of MSC of specialist surgery services for prostate, bladder, renal and oesophagogastric cancers, focusing on North Central and North East London and West Essex. Health economists collaborated with qualitative researchers, clinicians and managers, identifying key reconfiguration stages and expenditures. Data sources (n = approximately 100) included meeting minutes, interviews, and business cases. National Health Service (NHS) finance and service managers and clinicians were consulted. Using bottom-up costing, items were identified, and unit costs based on salaries, asset costs and consultancy fees assigned. Itemised costs were adjusted and summed. RESULTS: Cost components included options appraisal, bidding process, external review; stakeholder engagement events; planning/monitoring boards/meetings; and making the change: new assets, facilities, posts. Other considerations included hospital tariff changes; costs to patients; patient population; and lifetime of changes. Using the framework facilitated data identification and collection. The total adjusted implementation cost was estimated at £7.2 million, broken down as replacing robots (£4.0 million), consultancy fees (£1.9 million), staff time costs (£1.1 million) and other costs (£0.2 million). CONCLUSIONS: These principles can be used by funders, service providers and commissioners planning MSC and researchers evaluating MSC. Health economists should be involved early, alongside qualitative and health-service colleagues, as retrospective capture risks information loss. These analyses are challenging; many cost factors are difficult to identify, access and measure, and assumptions regarding lifetime of the changes are important. Including implementation costs in CEA might make MSC appear less cost effective, influencing future decisions. Future work will incorporate this implementation cost into the full CEAs of the London Cancer MSC. TRIAL REGISTRATION: Not applicable

Instabilities in the Envelopes and Winds of Very Massive Stars

The high luminosity of Very Massive Stars (VMS) means that radiative forces play an important, dynamical role both in the structure and stability of their stellar envelope, and in driving strong stellar-wind mass loss. Focusing on the interplay of radiative flux and opacity, with emphasis on key distinctions between continuum vs. line opacity, this chapter reviews instabilities in the envelopes and winds of VMS. Specifically, we discuss how: 1) the iron opacity bump can induce an extensive inflation of the stellar envelope; 2) the density dependence of mean opacity leads to strange mode instabilities in the outer envelope; 3) desaturation of line-opacity by acceleration of near-surface layers initiates and sustains a line-driven stellar wind outflow; 4) an associated line-deshadowing instability leads to extensive small-scale structure in the outer regions of such line-driven winds; 5) a star with super-Eddington luminosity can develop extensive atmospheric structure from photon bubble instabilities, or from stagnation of flow that exceeds the "photon tiring" limit; 6) the associated porosity leads to a reduction in opacity that can regulate the extreme mass loss of such continuum-driven winds. Two overall themes are the potential links of such instabilities to Luminous Blue Variable (LBV) stars, and the potential role of radiation forces in establishing the upper mass limit of VMS.Comment: 44 pages, 13 figures. Chapter to appear in the book "Very Massive Stars in the Local Universe", Springer, J.S. Vink, e