Optimal Research for Cournot Oligopolists

We extend the classical Cournot model to take account of uncertainty in either the cost function or the demand function. By undertaking research, firms can acquire private (asymmetric) information to help resolve their uncertainty and make a more informed production decision. The model is a two stage game: in the first stage research levels are chosen, and in the second stage, conditional on private research outcomes, production decisions are made. We find that for a linear, continuous information structure there is a unique Nash equilibrium to the game. In the equilibrium there may be an inefficient amount of aggregate research and there may be incomplete pooling as well. The model specializes to the classical case when the cost of research is zero (and each firm gains essentially the same information by doing an infinite amount of research) or when the cost of research is so high no firm undertakes research

Impact of chromophores on colour appearance in a computational skin model

Early diagnosis of skin cancer offers the patient more favorable treatment options. Color fidelity of skin images is a major concern for dermatologists as adoption of digital dermatoscopes is increasing rapidly. Accurate color depiction of the lesion and surrounding skin are vital in diagnostic evaluation of a lesion. We previously introduced VCT-Derma, a pipeline for dermatological Virtual Clinical Trials (VCTs) including detailed and flexible models of human skin and lesions, which represent the patient in the entire dermatoscopy-based diagnostic process. However, those initial models of skin and lesions did not properly account for tissue colors. Our new skin model accounts for tissue color appearance by incorporating chromophores (e.g., melanin, blood) into the tissue model, and simulating the optical properties of the various skin layers. The physical properties of the skin and lesion were selected from clinically plausible values. The model and simulated dermatoscope images were created in open modelling software, assuming a linear camera model. We have assumed ambient white lighting, with a 6mm distance to the camera. Our model of color appearance was characterised by comparing the brightness of the lesion to its depth. The brightness of the lesion is compared through the variability of the mean gray values of a cropped region around the lesion. We compare two skin models, one without extensive chromophore content and one with. Our preliminary evaluation of increasing chromophore content shows promise based on the results presented here. Further refinement and validation of the model is ongoing

The Classical Heisenberg Model on the Centred Pyrochlore Lattice

The centred pyrochlore lattice is a novel geometrically frustrated lattice, realized in the metal-organic framework Mn(ta)$_2$ (arXiv:2203.08780) where the basic unit of spins is a five site centred tetrahedron. Here, we present an in-depth theoretical study of the $J_1-J_2$ classical Heisenberg model on this lattice, using a combination of mean-field analytical methods and Monte Carlo simulations. We find a rich phase diagram with low temperature states exhibiting ferrimagnetic order, partial ordering, and a highly degenerate spin liquid with distinct regimes of low temperature correlations. We discuss in detail how the regime displaying broadened pinch points in its spin structure factor is consistent with an effective description in terms of a fluid of interacting charges. We also show how this picture holds in two dimensions on the analogous centred kagome lattice and elucidate the connection to the physics of thin films in ($d+1$) dimensions. Furthermore, we show that a Coulomb phase can be stabilized on the centred pyrochlore lattice by the addition of further neighbour couplings. This demonstrates the centred pyrochlore lattice is an experimentally relevant geometry which naturally hosts emergent gauge fields in the presence of charges at low energies.Comment: 29 pages, 9 figures, resubmission to SciPost with minor revision

Decay modes of two repulsively interacting bosons

We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schr\"odinger equation. The solutions are analyzed according to the regions of particle presence: both particles inside the trap (in-in), one particle in and one particle out (in-out), and both particles outside (out-out). It is shown that the in-in probability is dominated by exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength the decay of in-out probability is dominated by the single particle decay mode. The decay mechanisms are adequately described by simple models.Comment: 18 pages, 13 figure

Multiple sulphur and lead sources recorded in hydrothermal exhalites associated with the Lemarchant volcanogenic massive sulphide deposit, central Newfoundland, Canada

This research is funded by the Canadian Mining Research Organization (CAMIRO) and an NSERC CRD grant. Research is also funded by the NSERC-Altius Industrial Research Chair in Mineral Deposits, funded by NSERC, Altius Resources Inc. and the Development Corporation of Newfoundland and Labrador.Metalliferous sedimentary rocks (mudstones, exhalites) associated with the Cambrian precious metal-bearing Lemarchant Zn-Pb-Cu-Au-Ag-Ba volcanogenic massive sulphide (VMS) deposit, Tally Pond volcanic belt, precipitated both before and after VMS mineralization. Sulphur and Pb isotopic studies of sulphides within the Lemarchant exhalites provide insight into the sources of S and Pb in the exhalites as a function of paragenesis and evolution of the deposit and subsequent post-depositional modification. In situ S isotope microanalyses of polymetallic sulphides (euhedral and framboidal pyrite, anhedral chalcopyrite, pyrrhotite, galena and euhedral arsenopyrite) by secondary ion mass spectrometry (SIMS) yielded δ34S values ranging from −38.8 to +14.4 ‰, with an average of ∼ −12.8 ‰. The δ34S systematics indicate sulphur was predominantly biogenically derived via microbial/biogenic sulphate reduction of seawater sulphate, microbial sulphide oxidation and microbial disproportionation of intermediate S compounds. These biogenic processes are coupled and occur within layers of microbial mats consisting of different bacterial/archaeal species, i.e., sulphate reducers, sulphide oxidizers and those that disproportionate sulphur compounds. Inorganic processes or sources (i.e., thermochemical sulphate reduction of seawater sulphate, leached or direct igneous sulphur) also contributed to the S budget in the hydrothermal exhalites and are more pronounced in exhalites that are immediately associated with massive sulphides. Galena Pb isotopic compositions by SIMS microanalysis suggest derivation of Pb from underlying crustal basement (felsic volcanic rocks of Sandy Brook Group), whereas less radiogenic Pb derived from juvenile sources leached from mafic volcanic rocks of the Sandy Brook Group and/or Tally Pond group. This requires that the hydrothermal fluids interacted with juvenile and evolved crust during hydrothermal circulation, which is consistent with the existing tectonic model that suggests a formation of the Tally Pond belt volcanic rocks and associated VMS deposits in a rifted arc environment upon crustal basement of the Ediacaran age Sandy Brook Group and Crippleback Intrusive Suite. Combined S and Pb isotope data illustrate that sulphides within the deposit that are proximal to the vent contain a higher proportion of sulphur derived from thermochemical sulphate reduction (TSR), because hydrothermal fluids are enriched in H2S derived from TSR. They also have lower radiogenic Pb contributions, than sulphides occurring distal from mineralization. Hence, the TSR S and non-radiogenic Pb composition may provide an exploration vector in exhalites associated with similar VMS environments.PostprintPeer reviewe

Wave chaos as signature for depletion of a Bose-Einstein condensate

We study the expansion of repulsively interacting Bose-Einstein condensates (BECs) in shallow one-dimensional potentials. We show for these systems that the onset of wave chaos in the Gross-Pitaevskii equation (GPE), i.e. the onset of exponential separation in Hilbert space of two nearby condensate wave functions, can be used as indication for the onset of depletion of the BEC and the occupation of excited modes within a many-body description. Comparison between the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method and the GPE reveals a close correspondence between the many-body effect of depletion and the mean-field effect of wave chaos for a wide range of single-particle external potentials. In the regime of wave chaos the GPE fails to account for the fine-scale quantum fluctuations because many-body effects beyond the validity of the GPE are non-negligible. Surprisingly, despite the failure of the GPE to account for the depletion, coarse grained expectation values of the single-particle density such as the overall width of the atomic cloud agree very well with the many-body simulations. The time dependent depletion of the condensate could be investigated experimentally, e.g., via decay of coherence of the expanding atom cloud.Comment: 12 pages, 10 figure

Rotating solenoidal perfect fluids of Petrov type D

We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure