Exit problems associated with affine reflection groups

We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type \~A case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, observing that the `Hot Spots' conjecture of J. Rauch is true for alcoves.Comment: 34 pages. Rewritten in some places to improve presentation. To appear in Probability Theory and Related Field

Anti-Swarming: Structure and Dynamics of Repulsive Chemically Active Particles

Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a `chemical' coupling parameter $\Gamma_c$ that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic One Component Plasma (OCP) system. When confined to a constant-volume domain, Body-Centered Cubic crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-Centered Cubic crystals may also be stable. The `melting point' of the `liquid-to-crystal transition' occurs at $\Gamma_c\approx140$ for both BCC and FCC lattices

Anisotropic swim stress in active matter with nematic order

Active Brownian Particles (ABPs) transmit a swim pressure $\Pi^{swim}=n\zeta D^{swim}$ to the container boundaries, where $\zeta$ is the drag coefficient, $D^{swim}$ is the swim diffusivity and $n$ is the uniform bulk number density far from the container walls. In this work we extend the notion of the isotropic swim pressure to the anisotropic tensorial swim stress $\mathbf{\sigma}^{swim} = - n \zeta \mathbf{D}^{swim}$, which is related to the anisotropic swim diffusivity $\mathbf{D}^{swim}$. We demonstrate this relationship with ABPs that achieve nematic orientational order via a bulk external field. The anisotropic swim stress is obtained analytically for dilute ABPs in both 2D and 3D systems, and the anisotropy is shown to grow exponentially with the strength of the external field. We verify that the normal component of the anisotropic swim stress applies a pressure $\Pi^{swim}=-(\mathbf{\sigma}^{swim}\cdot\mathbf{n})\cdot\mathbf{n}$ on a wall with normal vector $\mathbf{n}$, and, through Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. Since ABPs have no friction with a wall, the difference between the normal and tangential stress components -- the normal stress difference -- generates a net flow of ABPs along the wall, which is a generic property of active matter systems

The curved kinetic boundary layer of active matter

The finite reorient-time of swimmers leads to a finite run length $\ell$ and the kinetic accumulation boundary layer on the microscopic length scale $\delta$ on a non-penetrating wall. That boundary layer is the microscopic origin of the swim pressure, and is impacted by the geometry of the boundary [Yan \& Brady, \textit{J. Fluid. Mech.}, 2015, \textbf{785}, R1]. In this work we extend the analysis to analytically solve the boundary layer on an arbitrary-shaped body distorted by the local mean curvature. The solution gives the swim pressure distribution and the total force (torque) on an arbitrarily shaped body immersed in swimmers, with a general scaling of the curvature effect $\Pi^{swim}\sim\lambda\delta^2/L$

Instability of Dynamic Inventory Systems

We show in this paper that instability is an intrinsic cause of production variability in a dynamic inventory system. We first show that a unique stationary optimal policy exists for both full-backlog and lost-sales case and under the policy a firm replenishes its inventory to a constant target level. We then express the constant inventory target as the unique steady state of the Euler’s equation governing the dynamics of target inventories. We finally show that the Euler’s equation is locally instable at the steady state but a sufficiently large refund to unsold inventory in lost-sales case can stabilize the inventory system.stability, production variability, dynamic inventory system, full-backlog, lost-sales

CARBON, TRADE POLICY, AND CARBON FREE TRADE AREAS

This paper discusses both the potential contribution that trade policy initiatives can make towards the achievement of significant global carbon emissions reduction and the potential impacts of proposals now circulating for carbon reduction motivated geographical trade arrangements, including carbon free trade areas. We first suggest that trade policy is likely to be a relatively minor consideration in climate change containment. The dominant influence on carbon emissions globally for next several decades will be growth more so than trade and its composition, and in turn, the size of trade seemingly matters more than its composition given differences in emission intensity between tradables and nontradables. We also note that differences in emissions intensity across countries are larger than across products or sectors and so issues of country discrimination in trade policy (and violations of MFN) arises. We next discuss both unilateral and regional carbon motivated trade policy arrangements, including three potential variants of carbon emission reduction based free trade area arrangements. One is regional trade agreements with varying types of trade preferences towards low carbon intensive products, low carbon new technologies and inputs to low carbon processes. A second is the use of joint border measures against third parties to counteract anti-competitive effects from groups of countries taking on deeper emission reduction commitments. A third is third country trade barriers along with free trade or other regional trade agreements as penalty mechanisms to pressure other countries to join emission reducing environmental agreements. We differentiate among the objectives, forms and possible impacts of each variant. We also speculate as to how the world trading system may evolve in the next few decades as trade policy potentially becomes increasingly dominated by environmental concerns. We suggest that the future evolution of the trading system will likely be with environmentally motivated arrangements acting as an overlay on prevailing trade and financial arrangements in the WTO and IMF, and eventually movement to linked global trade and environmental policy bargaining.carbon, trade policy, WTO, Regional Trade Agreements, trade barriers, anti-competitive effects

A Third Benefit of Joint Non-OPEC Carbon Taxes: Transferring OPEC Monopoly Rent

This paper highlights the potential for joint OECD (or non-OPEC) carbon taxes to reduce OPEC’s monopoly rent and provide benefit to non-OPEC countries provided jointly agreed trigger strategies are adhered to. In traditional economic theory, the primary purpose of a carbon tax is to internalize a global negative externality. A second benefit for individual countries is that the revenue raised by carbon tax can be used to reduce other tax rates and so lower the deadweight loss of tax system. In this paper, we discuss a third benefit of carbon taxes: transferring rents from OPEC to the oil importing countries.We develop a multi-region general equilibrium structure with endogenously determined oil supply for the purpose in which emissions are endogenously determined. We calibrate our model to 2006 data. Our analytics and numerical simulation results highlight how a uniform carbon tax used by all non-OPEC countries will increase the buyer’s price of oil but decrease the supplier’s price of oil, thus decreasing non-OPEC countries’ oil demand, and transferring OPEC monopoly rent to non-OPEC countries. Carbon taxes reduce the welfare of OPEC and increase the welfare of non-OPEC countries. Results also show how carbon taxes reduce global emissions, but the effect is small.carbon taxes, OECD, monopoly rent

Improvement of indoor VLC network downlink scheduling and resource allocation

Indoor visible light communications (VLC) combines illumination and communication by utilizing the high-modulation-speed of LEDs. VLC is anticipated to be complementary to radio frequency communications and an important part of next generation heterogeneous networks. In order to make the maximum use of VLC technology in a networking environment, we need to expand existing research from studies of traditional point-to-point links to encompass scheduling and resource allocation related to multi-user scenarios. This work aims to maximize the downlink throughput of an indoor VLC network, while taking both user fairness and time latency into consideration. Inter-user interference is eliminated by appropriately allocating LEDs to users with the aid of graph theory. A three-term priority factor model is derived and is shown to improve the throughput performance of the network scheduling scheme over those previously reported. Simulations of VLC downlink scheduling have been performed under proportional fairness scheduling principles where our newly formulated priority factor model has been applied. The downlink throughput is improved by 19.6% compared to previous two-term priority models, while achieving similar fairness and latency performance. When the number of users grows larger, the three-term priority model indicates an improvement in Fairness performance compared to two-term priority model scheduling