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In this paper we investigate convergence for the Variational Iteration Method (VIM) which was introduced and described in \cite{He0},\cite{He1}, \cite{He2}, and \cite{He3}. We prove the convergence of the iteration scheme for a linear Klein-Gorden equation with a variable coefficient whose unique solution is known. The iteration scheme depends on a {\em Lagrange multiplier}, $\lambda(r,s)$, which is represented as a power series. We show that the VIM iteration scheme converges uniformly on compact intervals to the unique solution. We also prove convergence when $\lambda(r,s)$ is replaced by any of its partial sums. The first proof follows a familiar pattern, but the second requires a new approach. The second approach also provides some detail regarding the structure of the iterates.

This paper concerns the existence and properties of traveling wave solutions to reaction-diffusion-convection equations on the real line. We consider a general diffusion term involving the $p$-Laplacian and combustion-type reaction term. We extend and generalize the results established for $p=2$ to the case of singular and degenerate diffusion. Our approach allows for non-Lipschitz reaction as well. We also discuss the shape of the traveling wave profile near equilibria, assuming power-type behavior of the reaction and diffusion terms.

Let $\tau_k(\Omega)$ be the $k$-th eigenvalue of the Laplace operator in a bounded domain $\Omega$ of the form $\Omega_{\text{out}} \setminus \overline{B_{\alpha}}$ under the Neumann boundary condition on $\partial \Omega_{\text{out}}$ and the Robin boundary condition with parameter $h \in (-\infty,+\infty]$ on the sphere $\partial B_\alpha$ of radius $\alpha>0$ centered at the origin, the limiting case $h=+\infty$ being understood as the Dirichlet boundary condition on $\partial B_\alpha$. In the case $h>0$, it is known that the first eigenvalue $\tau_1(\Omega)$ does not exceed $\tau_1(B_\beta \setminus \overline{B_\alpha})$, where $\beta>0$ is chosen such that $|\Omega| = |B_\beta \setminus \overline{B_\alpha}|$, which can be regarded as a reverse Faber-Krahn type inequality. We establish this result for any $h \in (-\infty,+\infty]$. Moreover, we provide related estimates for higher eigenvalues under additional geometric assumptions on $\Omega$, which can be seen as Szeg\H{o}-Weinberger type inequalities. A few counterexamples to the obtained inequalities for domains violating imposed geometric assumptions are given. As auxiliary information, we investigate shapes of eigenfunctions associated with several eigenvalues $\tau_{i}(B_\beta \setminus \overline{B_\alpha})$ and show that they are nonradial at least for all positive and all sufficiently negative $h$ when $i \in \{2,\ldots,N+2\}$. At the same time, we give numerical evidence that, in the planar case $N=2$, already second eigenfunctions can be radial for some $h<0$. The latter fact provides a simple counterexample to the Payne nodal line conjecture in the case of the mixed boundary conditions., Comment: 36 pages, 6 figures

Let $\mu_2(\Omega)$ be the first positive eigenvalue of the Neumann Laplacian in a bounded domain $\Omega\subset\mathbb{R}^N$. It was proved by Szeg\H{o} for $N=2$ and by Weinberger for $N \geq 2$ that among all equimeasurable domains $\mu_2(\Omega)$ attains its global maximum if $\Omega$ is a ball. In the present work, we develop the approach of Weinberger in two directions. Firstly, we refine the Szeg\H{o}-Weinberger result for a class of domains of the form $\Omega_{\text{out}}\setminus\overline{\Omega}_{\text{in}}$ which are either centrally symmetric or symmetric of order $2$ (with respect to every coordinate plane $(x_i,x_j)$) by showing that $\mu_{2}(\Omega_{\text{out}}\setminus\overline{\Omega}_{\text{in}})\leq\mu_2(B_\beta\setminus\overline{B}_\alpha)$, where $B_\alpha, B_\beta$ are balls centered at the origin such that $B_\alpha\subset\Omega_{\text{in}}$ and $|\Omega_{\text{out}}\setminus\overline{\Omega}_{\text{in}}|=|B_\beta\setminus\overline{B}_\alpha|$. Secondly, we provide Szeg\H{o}-Weinberger type inequalities for higher eigenvalues by imposing additional symmetry assumptions on the domain. Namely, if $\Omega_{\text{out}}\setminus\overline{\Omega}_{\text{in}}$ is symmetric of order $4$, then we prove $\mu_{i}(\Omega_{\text{out}}\setminus\overline{\Omega}_{\text{in}})\leq\mu_i(B_\beta\setminus\overline{B}_\alpha)$ for $i=3,\dots,N+2$, where we also allow $\Omega_{\text{in}}$ and $B_\alpha$ to be empty. If $N=2$ and the domain is symmetric of order $8$, then the latter inequality persists for $i=5$. Counterexamples to the obtained inequalities for domains outside of the considered symmetry classes are given. The existence and properties of nonradial domains with required symmetries in higher dimensions are discussed. As an auxiliary result, we obtain the non-radiality of the eigenfunctions associated to $\mu_{N+2}(B_\beta\setminus\overline{B}_\alpha)$., Comment: 35 pages, 4 figures. A few references added, Remark 1.8 split into two, Remarks 2 and 5 of Section 6 updated, minor textual corrections incorporated according to referees' suggestions. Accepted to SIAM Journal on Mathematical Analysis

We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted $p-${L}aplacian operator with a coefficient that is {locally bounded inside the domain and satisfying certain additional integrability assumptions}. Our main result applies for boundary value problems involving continuous non-linearities having no growth restriction, but provided the existence of a sub and a supersolution is guaranteed. As an application, we present an existence result for a boundary value pro\-blem with a non-linearity $f(u)$ satisfying $f(0) \leq 0$ and having $(p-1)-$sublinear growth at infinity.

Measurements of trace-gases in planetary atmospheres help us explore chemical conditions different to those on Earth. Our nearest neighbor, Venus, has cloud decks that are temperate but hyper-acidic. We report the apparent presence of phosphine (PH3) gas in Venusian atmosphere, where any phosphorus should be in oxidized forms. Single-line millimeter-waveband spectral detections (quality up to ~15 sigma) from the JCMT and ALMA telescopes have no other plausible identification. Atmospheric PH3 at ~20 parts-per-billion abundance is inferred. The presence of phosphine is unexplained after exhaustive study of steady-state chemistry and photochemical pathways, with no currently-known abiotic production routes in Venusian atmosphere, clouds, surface and subsurface, or from lightning, volcanic or meteoritic delivery. Phosphine could originate from unknown photochemistry or geochemistry, or, by analogy with biological production of phosphine on Earth, from the presence of life. Other PH3 spectral features should be sought, while in-situ cloud and surface sampling could examine sources of this gas.

Dramatic growth of investment disputes between foreign investors and host states rises serious questions about the impact of those disputes on investors. This paper is the first to explain increased uncertainty of investors about the outcome of arbitration, which may or may not lead to compensation for damages claimed by the investor. We find robust evidence that investment disputes lead to abnormal share fluctuations of companies involved in disputes with host countries. Importantly, while a positive outcome for an investor decreases uncertainty back to original levels, we document strong increase in the volatility of companies with negative outcome for the investor. We find that several variables including size of the award, political instability, location of arbitration, country of origin of investor or public policy considerations in host country explain large portion of the investor's uncertainty.

We study the existence and multiplicity of nonnegative solutions, as well as the behaviour of corresponding parameter-dependent branches, to the equation $-\Delta u = (1-u) u^m - \lambda u^n$ in a bounded domain $\Omega \subset \mathbb{R}^N$ endowed with the zero Dirichlet boundary data, where $00$. When $\lambda > 0$, the obtained solutions can be seen as steady states of the corresponding reaction-diffusion equation describing a model of isothermal autocatalytic chemical reaction with termination. In addition to the main new results, we formulate a few relevant conjectures., Comment: 25 pages, 12 figures. Two figures and three additional references added according to referee's suggestions; several minor typos corrected. Published in Nonlinear Analysis

Many theories beyond the Standard Model postulate short-range modifications to gravity which produce deviations of Newton's gravitational potential from a strict $1/r$ dependence. It is common to analyze experiments searching for these modifications using a potential of the form $V^{\prime}(r)=-\frac{GMm}{r} [1+\alpha \exp{(-r/\lambda)}]$. The best present constraints on $\alpha$ for $\lambda <100$\,nm come from neutron scattering and often employ comparisons of different measurements of the coherent neutron scattering amplitudes $b$. We analyze the internal consistency of existing data from two different types of measurements of low energy neutron scattering amplitudes: neutron interferometry, which involves squared momentum transfers $q^{2}=0$, and neutron gravity reflectometry, which involves squared momentum transfers $q^{2}=8mV_{opt}$ where $m$ is the neutron mass and $V_{opt}$ is the neutron optical potential of the medium. We show that the fractional difference $\frac{\Delta b}{|b|}$ averaged over the 7 elements where high precision data exists on the same material from both measurement methods is $[2.2 \pm 1.4] \times 10^{-4}$. We also show that $\frac{\Delta b}{|b|}$ for this data is insensitive both to exotic Yukawa interactions and also to the electromagnetic neutron-atom interactions proportional to the neutron-electron scattering length $b_{ne}$ and the neutron polarizability scattering amplitude $b_{pol}$. This result will be useful in any future global analyses of neutron scattering data to determine $b_{ne}$ and bound $\alpha$ and $\lambda$. We also discuss how various neutron interferometric and scattering techniques with cold and ultracold neutrons can be used to improve the precision of $b$ measurements and make some specific proposals., Comment: 13 pages, 1 figure

We present the POL-2 850 $\mu$m linear polarization map of the Barnard 1 clump in the Perseus molecular cloud complex from the B-fields In STar-forming Region Observations (BISTRO) survey at the James Clerk Maxwell Telescope. We find a trend of decreasing polarization fraction as a function of total intensity, which we link to depolarization effects towards higher density regions of the cloud. We then use the polarization data at 850 $\mu$m to infer the plane-of-sky orientation of the large-scale magnetic field in Barnard 1. This magnetic field runs North-South across most of the cloud, with the exception of B1-c where it turns more East-West. From the dispersion of polarization angles, we calculate a turbulence correlation length of $5.0 \pm 2.5$ arcsec ($1500$ au), and a turbulent-to-total magnetic energy ratio of $0.5 \pm 0.3$ inside the cloud. We combine this turbulent-to-total magnetic energy ratio with observations of NH$_3$ molecular lines from the Green Bank Ammonia Survey (GAS) to estimate the strength of the plane-of-sky component of the magnetic field through the Davis-Chandrasekhar-Fermi method. With a plane-of-sky amplitude of $120 \pm 60$ $\mu$G and a criticality criterion $\lambda_c = 3.0 \pm 1.5$, we find that Barnard 1 is a supercritical molecular cloud with a magnetic field nearly dominated by its turbulent component., Comment: 22 pages, 7 figures, accepted in the Astrophysical Journal

We present the first release of the data and compact-source catalogue for the JCMT Large Program SCUBA-2 Continuum Observations of Pre-protostellar Evolution (SCOPE). SCOPE consists of 850-um continuum observations of 1235 Planck Galactic Cold Clumps (PGCCs) made with the Submillimetre Common-User Bolometer Array 2 on the James Clerk Maxwell Telescope. These data are at an angular resolution of 14.4 arcsec, significantly improving upon the 353-GHz resolution of Planck at 5 arcmin, and allowing for a catalogue of 3528 compact sources in 558 PGCCs. We find that the detected PGCCs have significant sub-structure, with 61 per cent of detected PGCCs having 3 or more compact sources, with filamentary structure also prevalent within the sample. A detection rate of 45 per cent is found across the survey, which is 95 per cent complete to Planck column densities of $N_{H_{2}}$ $>$ 5 $\times$ 10$^{21}$ cm$^{-2}$. By positionally associating the SCOPE compact sources with YSOs, the star formation efficiency, as measured by the ratio of luminosity to mass, in nearby clouds is found to be similar to that in the more distant Galactic Plane, with the column density distributions also indistinguishable from each other., Comment: 16 pages, 13 figures, 1 table. Accepted for publication in MNRAS

We report 850~$\mu$m dust polarization observations of a low-mass ($\sim$12 $M_{\odot}$) starless core in the $\rho$ Ophiuchus cloud, Ophiuchus C, made with the POL-2 instrument on the James Clerk Maxwell Telescope (JCMT) as part of the JCMT B-fields In STar-forming Region Observations (BISTRO) survey. We detect an ordered magnetic field projected on the plane of sky in the starless core. The magnetic field across the $\sim$0.1~pc core shows a predominant northeast-southwest orientation centering between $\sim$40$^\circ$ to $\sim$100$^\circ$, indicating that the field in the core is well aligned with the magnetic field in lower-density regions of the cloud probed by near-infrared observations and also the cloud-scale magnetic field traced by Planck observations. The polarization percentage ($P$) decreases with an increasing total intensity ($I$) with a power-law index of $-$1.03 $\pm$ 0.05. We estimate the plane-of-sky field strength ($B_{\mathrm{pos}}$) using modified Davis-Chandrasekhar-Fermi (DCF) methods based on structure function (SF), auto-correlation (ACF), and unsharp masking (UM) analyses. We find that the estimates from the SF, ACF, and UM methods yield strengths of 103 $\pm$ 46 $\mu$G, 136 $\pm$ 69 $\mu$G, and 213 $\pm$ 115 $\mu$G, respectively. Our calculations suggest that the Ophiuchus C core is near magnetically critical or slightly magnetically supercritical (i.e. unstable to collapse). The total magnetic energy calculated from the SF method is comparable to the turbulent energy in Ophiuchus C, while the ACF method and the UM method only set upper limits for the total magnetic energy because of large uncertainties., Comment: 22 pages, 12 figures

We show that the elliptic equation with a non-Lipschitz right-hand side, $-\Delta u = \lambda |u|^{\beta-1}u - |u|^{\alpha-1}u$ with $\lambda>0$ and $0<\alpha<\beta<1$, considered on a smooth star-shaped domain $\Omega$ subject to zero Dirichlet boundary conditions, might possess a nonnegative ground state solution which violates Hopf's maximum principle only on a nonempty subset $\Gamma$ of the boundary $\partial\Omega$ such that $\Gamma \neq \partial\Omega$., Comment: 6 pages, 1 figure. Published in Applied Mathematics Letters

We present the 850 $\mu$m polarization observations toward the IC5146 filamentary cloud taken using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) and its associated polarimeter (POL-2), mounted on the James Clerk Maxwell Telescope (JCMT), as part of the B-fields In STar forming Regions Observations (BISTRO). This work is aimed at revealing the magnetic field morphology within a core-scale ($\lesssim 1.0$ pc) hub-filament structure (HFS) located at the end of a parsec-scale filament. To investigate whether or not the observed polarization traces the magnetic field in the HFS, we analyze the dependence between the observed polarization fraction and total intensity using a Bayesian approach with the polarization fraction described by the Rice likelihood function, which can correctly describe the probability density function (PDF) of the observed polarization fraction for low signal-to-noise ratio (SNR) data. We find a power-law dependence between the polarization fraction and total intensity with an index of 0.56 in $A_V\sim$ 20--300 mag regions, suggesting that the dust grains in these dense regions can still be aligned with magnetic fields in the IC5146 regions. Our polarization maps reveal a curved magnetic field, possibly dragged by the contraction along the parsec-scale filament. We further obtain a magnetic field strength of 0.5$\pm$0.2 mG toward the central hub using the Davis-Chandrasekhar-Fermi method, corresponding to a mass-to-flux criticality of $\sim$ $1.3\pm0.4$ and an Alfv\'{e}nic Mach number of $<$0.6. These results suggest that gravity and magnetic field is currently of comparable importance in the HFS, and turbulence is less important., Comment: 24 pages, 15 figures, accepted for publication in ApJ

Radio observations of cool stellar systems provide unique information on their magnetic fields, high-energy processes, and chemistry. Buoyed by powerful new instruments (e.g. ALMA, JVLA, LOFAR), advances in related fields (e.g., the Gaia astrometric revolution), and above all a renewed interest in the relevant stellar astrophysics, stellar radio astronomy is experiencing a renaissance. In this splinter session, participants took stock of the present state of stellar radio astronomy to chart a course for the field's future., Comment: Splinter session summary, to appear in the proceedings of the 20th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (ed. S. J. Wolk)

The anti-maximum principle for the homogeneous Dirichlet problem to $-\Delta_p u = \lambda |u|^{p-2}u + f(x)$ with positive $f \in L^\infty(\Omega)$ states the existence of a critical value $\lambda_f > \lambda_1$ such that any solution of this problem with $\lambda \in (\lambda_1, \lambda_f)$ is strictly negative. In this paper, we give a variational upper bound for $\lambda_f$ and study its properties. As an important supplementary result, we investigate the branch of ground state solutions of the considered boundary value problem in $(\lambda_1,\lambda_2)$., Comment: 17 pages, 1 figure. A reference added, minor typos corrected, minor textual changes incorporated according to referee's suggestions. Published in Journal of Differential Equations

We present the results of dust emission polarization measurements of Ophiuchus-B (Oph-B) carried out using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) camera with its associated polarimeter (POL-2) on the James Clerk Maxwell Telescope (JCMT) in Hawaii. This work is part of the B-fields In Star-forming Region Observations (BISTRO) survey initiated to understand the role of magnetic fields in star formation for nearby star-forming molecular clouds. We present a first look at the geometry and strength of magnetic fields in Oph-B. The field geometry is traced over $\sim$0.2 pc, with clear detection of both of the sub-clumps of Oph-B. The field pattern appears significantly disordered in sub-clump Oph-B1. The field geometry in Oph-B2 is more ordered, with a tendency to be along the major axis of the clump, parallel to the filamentary structure within which it lies. The degree of polarization decreases systematically towards the dense core material in the two sub-clumps. The field lines in the lower density material along the periphery are smoothly joined to the large scale magnetic fields probed by NIR polarization observations. We estimated a magnetic field strength of 630$\pm$410 $\mu$G in the Oph-B2 sub-clump using a Davis-Chandeasekhar-Fermi analysis. With this magnetic field strength, we find a mass-to-flux ratio $\lambda$= 1.6$\pm$1.1, which suggests that the Oph-B2 clump is slightly magnetically supercritical., Comment: 17 pages, 10 figures, Accepted for publication in ApJ

We investigate the following eigenvalue problem \begin{align*} \begin{cases} -\operatorname{div}\left( L(x) |\nabla u| ^{p-2}\nabla u\right)=\lambda K(x)|u|^{p-2}u \quad \text{in } A_{R_1}^{R_2} , u=0\quad \text{on } \partial A_{R_1}^{R_2} , \end{cases} \end{align*} where $A_{R_1}^{R_2}:=\{x\in\mathbb{R}^N: R_1<|x|0$ is a parameter, the weights $L$ and $K$ are measurable with $L$ positive a.e. in $A_{R_1}^{R_2}$ and $K$ possibly sign-changing in $A_{R_1}^{R_2}$. We prove the existence of the first eigenpair and discuss the regularity and positiveness of eigenfunctions. %apriori bounds of any eigenfunction as well as local boundedness. The asymptotic estimates for $u(x)$ and $\nabla u(x)$ as $|x|\to R_1^+$ or $R_2^-$ are also investigated.

We present 850 $\mu$m imaging polarimetry data of the $\rho$ Oph-A core taken with the Submillimeter Common-User Bolometer Array-2 (SCUBA-2) and its polarimeter (POL-2), as part of our ongoing survey project, BISTRO (B-fields In STar forming RegiOns). The polarization vectors are used to identify the orientation of the magnetic field projected on the plane of the sky at a resolution of 0.01 pc. We identify 10 subregions with distinct polarization fractions and angles in the 0.2 pc $\rho$ Oph A core; some of them can be part of a coherent magnetic field structure in the $\rho$ Oph region. The results are consistent with previous observations of the brightest regions of $\rho$ Oph-A, where the degrees of polarization are at a level of a few percents, but our data reveal for the first time the magnetic field structures in the fainter regions surrounding the core where the degree of polarization is much higher ($> 5 \%$). A comparison with previous near-infrared polarimetric data shows that there are several magnetic field components which are consistent at near-infrared and submillimeter wavelengths. Using the Davis-Chandrasekhar-Fermi method, we also derive magnetic field strengths in several sub-core regions, which range from approximately 0.2 to 5 mG. We also find a correlation between the magnetic field orientations projected on the sky with the core centroid velocity components., Comment: 22 pages, 11 figures, accepted for publication in ApJ

We consider a one-dimensional reaction-diffusion equation of Fisher-Kolmogoroff-Petrovsky-Piscounoff type. We investigate the effect of the interaction between the nonlinear diffusion coefficient and the reaction term on the existence and nonexistence of travelling waves. Our diffusion coefficient is allowed to be degenerate or singular at both equilibrium points, 0 and 1, while the reaction term need not be differentiable. These facts influence the existence and qualitative properties of travelling waves in a substantial way., Comment: 20 pages, 5 figures

We present 850 and 450 micron observations of the dense regions within the Auriga-California molecular cloud using SCUBA-2 as part of the JCMT Gould Belt Legacy Survey to identify candidate protostellar objects, measure the masses of their circumstellar material (disk and envelope), and compare the star formation to that in the Orion A molecular cloud. We identify 59 candidate protostars based on the presence of compact submillimeter emission, complementing these observations with existing Herschel/SPIRE maps. Of our candidate protostars, 24 are associated with young stellar objects (YSOs) in the Spitzer and Herschel/PACS catalogs of 166 and 60 YSOs, respectively (177 unique), confirming their protostellar nature. The remaining 35 candidate protostars are in regions, particularly around LkHalpha 101, where the background cloud emission is too bright to verify or rule out the presence of the compact 70 micron emission that is expected for a protostellar source. We keep these candidate protostars in our sample but note that they may indeed be prestellar in nature. Our observations are sensitive to the high end of the mass distribution in Auriga-Cal. We find that the disparity between the richness of infrared star forming objects in Orion A and the sparsity in Auriga-Cal extends to the submillimeter, suggesting that the relative star formation rates have not varied over the Class II lifetime and that Auriga-Cal will maintain a lower star formation efficiency., Comment: 39 pages (54 including the Appendix), 9 figures, 3 tables, in press in ApJ

We study the solvability of the Zakharov equation $$\Delta^2 u + (\kappa-\omega^2)\Delta u - \kappa \,\text{div} \left(e^{-|\nabla u|^2} \nabla u\right) = 0$$ in a bounded domain under homogeneous Dirichlet or Navier boundary conditions. This problem is a consequence of the system of equations derived by Zakharov to model the Langmuir collapse in plasma physics. Assumptions for the existence and nonexistence of a ground state solution as well as the multiplicity of solutions are discussed. Moreover, we consider formal approximations of the Zakharov equation obtained by the Taylor expansion of the exponential term. We illustrate that the existence and nonexistence results are substantially different from the corresponding results for the original problem., Comment: 17 pages

Saturn's moon Enceladus has vents emerging from a sub-surface ocean, offering unique probes into the liquid environment. These vents drain into the larger neutral torus in orbit around Saturn. We present a methanol (CH3OH) detection observed with IRAM 30-m from 2008 along the line-of-sight through Saturn's E-ring. Additionally, we also present supporting observations from the Herschel public archive of water (ortho-H2O; 1669.9 GHz) from 2012 at a similar elongation and line-of-sight. The CH3OH 5(1,1)-4(1,1) transition was detected at 5.9 sigma confidence. The line has 0.43 km/s width and is offset by +8.1 km/s in the moon's reference frame. Radiative transfer models allow for gas cloud dimensions from 1750 km up to the telescope beam diameter ~73000 km. Taking into account the CH3OH lifetime against solar photodissociation and the redshifted line velocity, there are two possible explanations for the CH3OH emission: methanol is primarily a secondary product of chemical interactions within the neutral torus that (1) spreads outward throughout the E-ring or (2) originates from a compact, confined gas cloud lagging Enceladus by several km/s. We find either scenario to be consistent with significant redshifted H2O emission (4 sigma) measured from the Herschel public archive. The measured CH3OH:H2O abundance (> 0.5 per cent) significantly exceeds the observed abundance in the direct vicinity of the vents (~0.01 per cent), suggesting CH3OH is likely chemically processed within the gas cloud with methane (CH4) as its parent species., Comment: 16 pages, 4 figures, accepted for publication in the International Journal of Astrobiology (IJA)

Most protostars have luminosities that are fainter than expected from steady accretion over the protostellar lifetime. The solution to this problem may lie in episodic mass accretion -- prolonged periods of very low accretion punctuated by short bursts of rapid accretion. However, the timescale and amplitude for variability at the protostellar phase is almost entirely unconstrained. In "A JCMT/SCUBA-2 Transient Survey of Protostars in Nearby Star Forming Regions", we are monitoring monthly with SCUBA-2 the sub-mm emission in eight fields within nearby (<500 pc) star forming regions to measure the accretion variability of protostars. The total survey area of ~1.6 sq.deg. includes ~105 peaks with peaks brighter than 0.5 Jy/beam (43 associated with embedded protostars or disks) and 237 peaks of 0.125-0.5 Jy/beam (50 with embedded protostars or disks). Each field has enough bright peaks for flux calibration relative to other peaks in the same field, which improves upon the nominal flux calibration uncertainties of sub-mm observations to reach a precision of ~2-3% rms, and also provides quantified confidence in any measured variability. The timescales and amplitudes of any sub-mm variation will then be converted into variations in accretion rate and subsequently used to infer the physical causes of the variability. This survey is the first dedicated survey for sub-mm variability and complements other transient surveys at optical and near-IR wavelengths, which are not sensitive to accretion variability of deeply embedded protostars., Comment: ApJ, accepted

The mass of a protoplanetary disk limits the formation and future growth of any planet. Masses of protoplanetary disks are usually calculated from measurements of the dust continuum emission by assuming an interstellar gas-to-dust ratio. To investigate the utility of CO as an alternate probe of disk mass, we use ALMA to survey $^{13}$CO and C$^{18}$O J = $3-2$ line emission from a sample of 93 protoplanetary disks around stars and brown dwarfs with masses from 0.03 -- 2 M$_{\odot}$ in the nearby Chamaeleon I star-forming region. We detect $^{13}$CO emission from 17 sources and C$^{18}$O from only one source. Gas masses for disks are then estimated by comparing the CO line luminosities to results from published disk models that include CO freeze-out and isotope-selective photodissociation. Under the assumption of a typical ISM CO-to-H$_2$ ratios of $10^{-4}$, the resulting gas masses are implausibly low, with an average gas mass of $\sim$ 0.05 M$_{Jup}$ as inferred from the average flux of stacked $^{13}$CO lines. The low gas masses and gas-to-dust ratios for Cha I disks are both consistent with similar results from disks in the Lupus star-forming region. The faint CO line emission may instead be explained if disks have much higher gas masses, but freeze-out of CO or complex C-bearing molecules is underestimated in disk models. The conversion of CO flux to CO gas mass also suffers from uncertainties in disk structures, which could affect gas temperatures. CO emission lines will only be a good tracer of the disk mass when models for C and CO depletion are confirmed to be accurate., Comment: accepted for publication in ApJ

We present the first results from the B-fields In STar-forming Region Observations (BISTRO) survey, using the Sub-millimetre Common-User Bolometer Array 2 (SCUBA-2) camera, with its associated polarimeter (POL-2), on the James Clerk Maxwell Telescope (JCMT) in Hawaii. We discuss the survey's aims and objectives. We describe the rationale behind the survey, and the questions which the survey will aim to answer. The most important of these is the role of magnetic fields in the star formation process on the scale of individual filaments and cores in dense regions. We describe the data acquisition and reduction processes for POL-2, demonstrating both repeatability and consistency with previous data. We present a first-look analysis of the first results from the BISTRO survey in the OMC 1 region. We see that the magnetic field lies approximately perpendicular to the famous 'integral filament' in the densest regions of that filament. Furthermore, we see an 'hour-glass' magnetic field morphology extending beyond the densest region of the integral filament into the less-dense surrounding material, and discuss possible causes for this. We also discuss the more complex morphology seen along the Orion Bar region. We examine the morphology of the field along the lower-density north-eastern filament. We find consistency with previous theoretical models that predict magnetic fields lying parallel to low-density, non-self-gravitating filaments, and perpendicular to higher-density, self-gravitating filaments., Comment: 12 pages, 8 figures, accepted for publication in ApJ

We investigate the Fredholm alternative for the $p$-Laplacian in an exterior domain which is the complement of the closed unit ball in $\mathbb{R}^N$ ($N\geq 2$). By employing techniques of Calculus of Variations we obtain the multiplicity of solutions. The striking difference between our case and the entire space case is also discussed., Comment: 34 pages

We present 450 and 850 micron submillimetre continuum observations of the IC5146 star-forming region taken as part of the JCMT Gould Belt Survey. We investigate the location of bright submillimetre (clumped) emission with the larger-scale molecular cloud through comparison with extinction maps, and find that these denser structures correlate with higher cloud column density. Ninety-six individual submillimetre clumps are identified using FellWalker and their physical properties are examined. These clumps are found to be relatively massive, ranging from 0.5to 116 MSun with a mean mass of 8 MSun and a median mass of 3.7 MSun. A stability analysis for the clumps suggest that the majority are (thermally) Jeans stable, with M/M_J < 1. We further compare the locations of known protostars with the observed submillimetre emission, finding that younger protostars, i.e., Class 0 and I sources, are strongly correlated with submillimetre peaks and that the clumps with protostars are among the most Jeans unstable. Finally, we contrast the evolutionary conditions in the two major star-forming regions within IC5146: the young cluster associated with the Cocoon Nebula and the more distributed star formation associated with the Northern Streamer filaments. The Cocoon Nebula appears to have converted a higher fraction of its mass into dense clumps and protostars, the clumps are more likely to be Jeans unstable, and a larger fraction of these remaining clumps contain embedded protostars. The Northern Streamer, however, has a larger number of clumps in total and a larger fraction of the known protostars are still embedded within these clumps., Comment: 30 pages, 11 figures, 8 tables, accepted by ApJ