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Accurate prediction of heat transport in porous media is important for understanding geoscience processes and properties and to design applications, for example geothermal energy systems. While heat transport is generally modelled assuming of local thermal equilibrium (LTE), i.e., instantaneous heat transfer between the fluid and solid phases, previous studies have demonstrated presence of local thermal non-equilibrium (LTNE), i.e., delayed heat transfer, in natural porous materials. However, factors that influence the rate of heat transfer between the phases and their significance for inherently heterogeneous natural systems remain unknown and untested. We develop an open-source fully coupled, finite-element application to numerically simulate heat transfer between the fluid and solid phases. This is based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) and allows massively parallel modelling of heat transport including customized transfer rates. We verify our model using an analytical solution considering LTNE and illustrate several applications. The model can be used to investigate processes that affect heat transport such as heat transfer mechanisms and their dependence on different hydrogeological conditions.

Most of the published research on goaf-hole failures are performed using 2D numerical analyses. However, 2D analyses of the goaf-hole failure mechanism, which is truly a 3D problem, often do not provide a full picture of strata movement and stress change effect. In particular such 2D models completely fail to capture the longitudinal deformation and associated shear component yielding a false sense of goaf-hole stability. This paper uses advanced 3D numerical modelling to understand the fundamentals of goaf-hole shear failure mechanism and conceptualize the transverse, longitudinal and total shears developments during longwall extraction. A mine specific geotechnical model has been developed to compare the conceptualized goaf-hole failure mechanism with the simplified representative model. The effect of geo-mechanical properties and panel widths on shear development has also been investigated. The analysis is based on a case study; however, it is expected that the results presented in this paper will be applicable to other mines with similar geological environment or will at least highlight the need for a 3D modelling to capture the true three-dimensional strata deformation behaviour and goaf-hole shearing mechanism enabling safe and stable vertical drainage hole design. In the modelled scenario, the shear increased as the face advanced, and large shears would be experienced behind 50–100 m of the face. The longitudinal shear was dominant towards the centre of the panel and the transverse shear was dominant towards the panel edges. The layered seam appeared to generate lesser shear compared to the solid seam; this could be attributed to the dissipation of shear in the layer strata of the material.

During underground longwall coal extraction, overburden strata deformation may result in vertical goaf drainage holes, which are drilled in advance of mining for tail gate gas management, to fail. The performance of these vertical goaf drainage holes is controlled by mine design parameters and local geomechanical properties. This paper investigates the use of advanced 3D finite element modelling and 2D discrete element modelling simulation techniques to understand the fundamentals of vertical goaf drainage hole failure mechanism due to strata shear at a currently operating gassy Australian mine site. Finite element modelling is used to investigate the location of high shear in the overburden strata at the vertical goaf gas drainage hole region during longwall mining and the discrete element modelling is used to examine connectivity from the goaf region to the goaf-gas drainage system.

Malaria is one of the deadliest vector-borne diseases in the world. Researchers are developing new genetic and conventional vector control strategies to attempt to limit its burden. Novel control strategies require detailed safety assessment to ensure responsible and successful deployments. Anopheles gambiae sensu stricto (s.s.) and Anopheles coluzzii, two closely related subspecies within the species complex Anopheles gambiae sensu lato (s.l.), are among the dominant malaria vectors in sub-Saharan Africa. These two subspecies readily hybridise and compete in the wild and are also known to have distinct niches, each with spatially and temporally varying carrying capacities driven by precipitation and land use factors.We model the spread and persistence of a population-modifying gene drive system in these subspecies across sub-Saharan Africa by simulating introductions of genetically modified mosquitoes across the African mainland and its offshore islands. We explore transmission of the gene drive between the two subspecies that arise from different hybridisation mechanisms, the effects of both local dispersal and potential wind-aided migration to the spread, and the development of resistance to the gene drive. Given the best current available knowledge on the subspecies’ life histories, we find that an introduced gene drive system with typical characteristics can plausibly spread from even distant offshore islands to the African mainland with the aid of wind-driven migration, with resistance taking over within a decade. Our model accounts for regional to continental scale mechanisms, and demonstrates a range of realistic dynamics including the effect of prevailing wind on spread and spatio-temporally varying carrying capacities for subspecies. As a result, it is well-placed to answer future questions relating to mosquito gene drives as important life history parameters become better understood.

Realistic modelling of tightly coupled hydro-geomechanical processes is relevant for the assessment of many hydrological and geotechnical applications. Such processes occur in geologic formations and are influenced by natural heterogeneity. Current numerical libraries offer capabilities and physics couplings that have proven to be valuable in many geotechnical fields like gas storage, rock fracturing and Earth resources extraction. However, implementation and verification of full heterogeneity of subsurface properties using high resolution field data in coupled simulations has not been done before. We develop, verify and document RHEA (Real HEterogeneity App), an open-source, fully coupled, finite-element application capable of including element-resolution hydro-geomechanical properties in coupled simulations. We propose a simple, yet powerful workflow to allow the incorporation of fully distributed hydro-geomechanical properties. We then verify the code with analytical solutions in one and two dimensions, and propose a benchmark semi-analytical problem to verify heterogeneous systems with sharp gradients. Finally, we demonstrate RHEA's capabilities with a comprehensive example including realistic properties. With this we demonstrate that RHEA is a verified open-source application able to include complex geology to perform scalable, fully coupled, hydro-geomechanical simulations. Our work is a valuable tool to assess challenging real world hydro-geomechanical systems that may include different levels of complexity like heterogeneous geology with several time and spatial scales and sharp gradients produced by contrasting subsurface properties.

Realistic modelling of tightly coupled hydro-geomechanical processes is relevant for the assessment of many hydrological and geotechnical applications. Such processes occur in geological formations and are influenced by natural heterogeneities. Current numerical libraries offer capabilities and physics coupling, that have proven to be valuable in simulating various applications in geotechnical fields such as underground gas storage, rock fracturing, land subsidence and Earth resources extraction. However, implementation and verification of full heterogeneity of subsurface properties using high resolution field data in coupled simulations has not been done yet. Hence, we develop, verify and document RHEA (Real HEterogeneity App), an open-source fully coupled finite element application capable of including node-resolution hydro-geomechanical properties in coupled simulations. We propose a simple, yet powerful workflow to allow the integration of fully distributed hydro-geomechanical properties. We then verify the code with analytical solutions in one and two dimensions and propose a benchmark semi-analytical problem to verify heterogeneous systems with sharp gradients. Finally, we exemplify RHEA's capabilities with a comprehensive example integrating realistic properties. With this we demonstrate that RHEA is a verified open-source application able to integrate complex geology to perform scalable fully coupled hydro-geomechanical simulations. Our work is a valuable tool to assess real world hydro-geomechanical challenging systems that may include different levels of complexity like heterogeneous geology with several time and spatial scales and sharp gradients produced by contrasting subsurface properties.

The CO2CRC Otway Stage 3 project is developing low-impact methods for near-continuous monitoring of storage sites. This paper reports on the design, drilling, instrumenting, and early results from an array of an injector and five monitoring wells, spread over a km2. Highlights include the deployment and use of distributed acoustic sensors on casing, and baseline injections and interpretation of pressure tomography.

Aquifer Thermal Energy Storage (ATES) uses excess thermal energy to heat water which is stored in an aquifer until it is needed, at which time the hot water is recovered and the heat used for some purpose e.g. electricity generation. The recovery efficiency (i.e. the ratio of heat energy recovered to heat energy injected, R ) is one of the most important factors dictating the viability of ATES systems. The variation of R with various aquifer properties and operating parameters is explored for high temperature (HT) ATES systems with injection temperatures ≥ 90 ∘ C , extending the results of previous studies to higher temperatures and a broader range of aquifer properties and operating conditions. R values are calculated using numerical models of a single-well ATES system, which is validated by comparison with previous field and modelling studies. The results show that HT-ATES may be viable with injection temperatures as high as 300 ∘ C , depending on the aquifer properties and operating parameters. Daily cycles are very efficient over a broad range of conditions, whereas the efficiency of annual cycles is much more variable. The most important parameters governing R are aquifer thickness, injection temperature, horizontal and vertical permeability, and dispersion length. The R values are used to derive an improved version of the Rayleigh number relationship proposed by Schout et al. (2014), extending the applicability of this relationship to daily cycles and improving its accuracy for annual cycles. An alternative method for estimating R using a convolutional neural network is proposed. The calculated R values may be considered best-case because aspects such as background groundwater flow and geochemical effects are ignored. Practical factors such as energy supply/demand requirements, reservoir and above-ground engineering, financial or regulatory aspects, and public acceptance are not considered. Nevertheless, the results of this study can be used for rapid screening of large areas for potential HT-ATES sites, defining requirements for potential sites, and estimating R values for specific sites, before performing detailed feasibility studies.

Numerical-simulation studies of transport and flow in porous media are essential in many practical fields of research. Including the coupling of different physical processes allows accurate modelling of the effects of fluid flow and temperature changes on the subsurface reservoir structure, and conversely, the effects of reservoir-structure changes on fluids and heat. In this study, we introduce the development of a physics module for non-isothermal, multicomponent, multiphase flow in porous media, as part of the open-source, multiphysics simulation framework MOOSE. Through tight interfaces with existing physics modules for solid mechanics and aqueous geochemistry, massively parallel, fully implicit, fully coupled thermo-hydro-mechanical-chemical simulations are possible. MOOSE and the porous flow module are freely available under an open-source license, making MOOSE a platform for collaborative efforts in this field of research.

The geomechanical response of a porous reservoir due to injection of fluid can result from a complex interplay between the changes in porepressure and temperature near the wellbore. As a result, predictions are usually made using either simplified analytical models, which may apply unrealistic assumptions in order to produce a tractable model, or detailed numerical simulations that can be computationally expensive. LaForce et al. (2014a, 2014b) developed a semi-analytical model for the geomechanical response of a reservoir to nonisothermal, multi-phase fluid injection, which has been used in studies of CO 2 sequestration. We demonstrate that a numerical solution using the MOOSE software precisely matches the analytical formulae. We then include various effects in the numerical model that relax the simplifying assumptions made in the analytical derivation. We find the analytic and numerical solutions for the fluid and temperature fronts still agree reasonably, while only qualitative agreement is observed for other quantities such as stress and displacement. We conclude the LaForce, Ennis-King, Paterson, 2014a , LaForce, Mijic, Ennis-King, Paterson, 2014b solutions are useful for rapid investigation of projects involving injection of cold fluid into warm aquifers. However, the enhancements afforded by MOOSE, such as high-precision fluid equations of state and the ability to more accurately capture geological complexity, along with its computational scalability which greatly reduces runtimes, means that MOOSE should be preferred for more sophisticated analyses. Because validating complex coupled codes is challenging, we propose that the model contained herein can be used as a benchmark for other coupled codes.

This paper presents an assessment of the hydrological impacts of proposed coal mines and coal seam gas (CSG) developments in the Gloucester, Hunter, Namoi and Galilee subregions of eastern Australia. Surface water and groundwater modelling was carried out to assess the cumulative regional-scale hydrological impacts of multiple coal and coal seam gas developments. The hydrological metrics assessed were groundwater drawdown and changes in low-flow characteristics as measured by the number of low-flow or zero flow days per year. Uncertainty in the modelling was also considered, and the results are presented as the median and plausible range (5th to 95th percentile) from many simulations which attempt to capture a wide range of uncertainty. The results indicate that under the best-case (5th percentile) scenario, the impact of additional/proposed coal resource developments on groundwater drawdown and surface water characteristics can be quite small. However, under the worse-case (95th percentile), groundwater drawdown is very likely for up to 5 km from the coal resource developments, but unlikely beyond 20 km. Altered surface water characteristics can extend for many kilometres downstream, particularly in unregulated systems. The cumulative hydrological impact is enhanced where there are multiple developments in close proximity. The results are being used to inform policy and the approval process for coal resource developments.

Summary Three new contributions to the field of multisurface plasticity are presented for general situations with an arbitrary number of nonlinear yield surfaces with hardening or softening. A method for handling linearly dependent flow directions is described. A residual that can be used in a line search is defined. An algorithm that has been implemented and comprehensively tested is discussed in detail. Examples are presented to illustrate the computational cost of various components of the algorithm. The overall result is that a single Newton-Raphson iteration of the algorithm costs between 1.5 and 2 times that of an elastic calculation. Examples also illustrate the successful convergence of the algorithm in complicated situations. For example, without using the new contributions presented here, the algorithm fails to converge for approximately 50% of the trial stresses for a common geomechanical model of sedementary rocks, while the current algorithm results in complete success. Because it involves no approximations, the algorithm is used to quantify the accuracy of an efficient, pragmatic, but approximate, algorithm used for sedimentary-rock plasticity in a commercial software package. The main weakness of the algorithm is identified as the difficulty of correctly choosing the set of initially active constraints in the general setting. Copyright © 2016 John Wiley & Sons, Ltd.

Synthetic rock mass modelling is based on estimating the mass scale properties of rock directly from properties of the intact material and observed jointing geometry and strength. This technique explicitly represents characteristics of the rock mass that are implicit in the widely applied, empirical Hoek–Brown strength criterion. We demonstrate here that the two approaches converge in mass strength and the strength envelope when the necessary conditions for the empirical method are satisfied. However, the synthetic rock mass approach is advantageous whenever the necessary conditions of the empirical method are not satisfied. As an example, we use the synthetic rock mass method to describe an anisotropic strength envelope for a rock mass with four independent joint sets, where the orientation-specific strength has a significant impact on rock mass stability. In addition we show that rock mass strength is controlled strongly by joint persistence and the resultant connectivity of discontinuities, and only weakly by joint density and intensity.

Microseismic monitoring in mining can potentially forecast catastrophic disasters, and help in the optimization of day-to-day operational and safety issues. However, it is difficult to fully utilize microseismic data due to the large quantity of small microseismic events and because automatically detecting events is frustrated by the pollution of the microseismic signal by instrument noise and mining activities. Recent research has demonstrated that convolutional neural networks (CNNs) trained on vast seismic data sets can accurately detect seismic events. We train a CNN on hand-labeled, modestly sized, multi-channel microseismic data from a coal mine. We make the labeled data available as part of this paper. Using a k -fold cross validation approach, we demonstrate that the CNN surpasses the accuracy of a human microseismic expert, both in picking more true events and in eliminating more spurious (false) events. This demonstrates the feasibility of including a CNN in an automated system to detect, classify and locate microseismic events, for use in mine safety and operation.

The geographic niches of many species are dramatically changing as a result of environmental and anthropogenic impacts such as global climate change and the introduction of invasive species. In particular, genetically compatible subspecies that were once geographically separated are being reintroduced to one another. This is of concern for conservation, where rare or threatened subspecies could be bred out by hybridising with their more common relatives, and for commercial interests, where the stock or quality of desirable harvested species could be compromised. It is also relevant to disease ecology, where disease transmission is heterogeneous among subspecies and hybridisation may affect the rate and spatial spread of disease. We develop and investigate a mathematical model to combine competitive effects via the Lotka-Volterra model with hybridisation effects via mate choice. The species complex is structured into two classes: a subspecies of interest (named x), and other subspecies including any hybrids produced (named y). We show that in the absence of limit cycles the model has four possible equilibrium outcomes, representing every combination: total extinction, x-dominance (y extinct), y-dominance (x extinct), and at most a single coexistence equilibrium. We give conditions for which limit cycles cannot exist, then further show that the “total extinction” equilibrium is always unstable, that y-dominance is always stable, and that the other equilibria have stability depending on the model parameters. We demonstrate that both x-dominance and coexistence are achievable under a wide range of parameter values and initial conditions, which corresponds with empirical evidence of known competing-hybridising systems. We then briefly examine bifurcation behaviour. In particular, we note that a subcritical bifurcation is possible in which a “catastrophic” transition from x-dominance to y-dominance can occur, representing an invasion event. Finally, we briefly examine the common complication of time-varying carrying capacity, showing that such a case can make coexistence more likely.

The Liu-Elsworth (1997) formalism that predicts permeability in deformed fractured rock has been highly useful and successful in numerous engineering situations involving mining, coal-bed methane and shale gas extraction. The formalism assumes the rock's fractures are aligned with three orthogonal axes and that the rock is subjected to strains along these three directions only. Here we relax these assumptions: our proposed formula yields the permeability tensor for an anisotropic arbitrarily-fractured rock subjected to arbitrary deformations. Unlike the original Liu-Elsworth approach, our formula may therefore be used confidently in situations involving any stress and strain states, including those that are non-diagonal, and with rocks with any distribution of fracture orientations , including those that are non-orthogonal. This is advantageous in numerical simulation and in mining situations that frequently involve such situations. Our formula adds no discernible computational load to numerical simulations. Our proposal agrees with lab and in-situ direct and indirect tests of permeability.

Underground longwall mining in multi-seam gassy conditions induces a large volume of methane emissions, which not only presents a threat to mining safety but also contributes significantly to greenhouse gas emissions. Effective methane extraction from the longwall is the most effective way to control gas emissions. However, this requires a clear delineation of optimal methane drainage zone within the longwall goaf where consistently high flow and high purity methane can be captured. This paper presents a numerical-modelling based method to delineate the 3D distribution of the optimal methane drainage zone. A factor, named Stress Relief Ratio (SRR), is found to be well correlated with known fracture patterns particularly the “O” shaped fracture zone. The SRR has enabled the delineation of the Annual Overlying Zone for longwalls where comprehensive field investigations are not available.

We demonstrate that care must be taken in a finite-element discretisation of multi-phase compressible Darcy flow, otherwise constraints of non-negativity of fluid mass can become violated. Generalising a technique pioneered by Dalen, a lumped, finite-difference-inspired approximation with upstream weighting is described. This is numerically cheap, physically elegant, and the fluid mass at all nodes remains non-negative.

The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young’s modulus in tension is lower than in compression.

Plastic yield criteria for porous ductile materials are explored numerically using the finite-element technique. The cases of spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple-cubic and body-centred cubic arrays - in contrast to the famous Gurson-Tvergaard-Needleman (GTN) formula - while there is no such dependence for face-centred cubic arrays within the accuracy of the finite-element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield-function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body-centred and face-centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.

Mechanistic models of pilling are discussed in general terms, and a framework for pilling simulations is thereby created. A fundamental flaw in earlier models of pilling is revealed. A more comprehensive model of fibre diffusion and withdrawal from the fabric is proposed, and this is solved in general terms to find the rate of fuzz growth. Fuzz wear-off and entanglement into pills are discussed. Fibre fatigue is introduced, and it is demonstrated that this potentially increases the rate of withdrawal of anchor fibres.

A one-dimensional computational model of pilling of a fibre assembly has been created. The model follows a set of individual fibres, as free ends and loops appear as fuzz and arc progressively withdrawn from the body of the assembly, and entangle to form pills, which eventually break off or are pulled out. The time dependence of the computation is given by ticks, which correspond to cycles of a wear and laundering process. The movement of the fibres is treated as a reptation process. A set of standard values is used as inputs to the computation. Predictions arc given of the change with a number Of cycles of mass of fuzz, mass of pills, and mass removed from the assembly. Changes in the standard values allow sensitivity studies to be carried out.

Finite-element simulations are used to obtain many thousands of yield points for porous materials with arbitrary void-volume fractions with spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic three-dimensional arrays. Multi-axial stress states are explored. We show that the data may be fitted by a yield function which is similar to the Gurson-Tvergaard-Needleman (GTN) form, but which also depends on the determinant of the stress tensor, and all additional parameters may be expressed in terms of standard GTN-like parameters. The dependence of these parameters on the void-volume fraction is found. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Previous studies of the mechanics of fiber assemblies have neglected fiber movements that are due to perturbations of the assembly. Axial movements, which are treated in the paper, are important in pilling, bagging, felting, and incremental drafting of yarns in weaving, but lateral movements may also occur. A dynamical model is analogous to molecular statistical mechanics. Both a diffusion model and a driven model are presented. The resistance to movement is due to gripping forces, which may be externally imposed or caused by structural features, such as twist; both are easy to take into account. The geometric forms of entanglements and the way in which they add to frictional resistance are discussed in more detail.

The dynamics of fibre slippage within general non-bonded fibrous assemblies is studied in the situation where the assembly is subjected to general small cyclic loads. Two models are proposed. The first is applicable when the general cyclic loading is complemented by an occasional tugging force on one end of a fibre, which causes it to gradually withdraw from the assembly, such as might occur during the pilling of a textile. The second considers the situation in which the cyclic perturbations act around a constant background load applied to the assembly. The dynamics is reminiscent of self-organized critical behaviour. This model is applied to predict the progressive elongation of a single yarn during weaving.

We show how a theorem of Sullivan provides a precise mathematical statement of a 3D holographic principle, that is, the hyperbolic structure of a certain class of 3D manifolds is completely determined in terms of the corresponding Teichm\"uller space of the boundary. We explore the consequences of this theorem in the context of the Euclidean Ba\~nados-Teitelboim-Zanelli black hole in three dimensions.

We compute the effective action for scattering of three well-separated extremal brane solutions, in 11d supergravity, with zero p_ transfer and small transverse velocities. Using an interpretation of the conjecture of Maldacena, following Hyun, this can be viewed as the large N limit of the Matrix theory description of three supergraviton scattering at leading order. The result is consistent with the perturbative supergravity calculation., 10 pages, tex (harvmac)

Frames for glass doors and windows need to be designed to be both thermally insulating and structurally strong, and there are computer programs which accurately determine the required properties. However, these programs are complex and expensive to use and are not useful for initial design work. By identifying the structural and insulating roles of the various layers within the frames we obtain simple results for the thermal transmittance and structural properties of frames. These results can be used for design guidance. More accurate (but still simple) results were obtained and coded in Excel for easy processing. References R. J. Roark ``Formulas for stress and strain'' McGraw-Hill (1965), 4th ed. ``Thermal performance of windows, doors and sharing devices–-Detailed Calculations''. iso 15099:2003(E) ``Thermal performance of windows, doors and shutters–-Calculation of thermal transmittance–-Part 2 Numerical Method for Frames''. bs eniso 10077-2-2003 ``Thermal performance of windows, doors and sharing devices–-Part 1 General''. bs en 10077-1:2006

The level-set method of topology optimization is used to design isotropic two-phase periodic multifunctional composites in three dimensions. One phase is stiff and insulating whereas the other is conductive and mechanically compliant. The optimization objective is to maximize a linear combination of the effective bulk modulus and conductivity of the composite. Composites with the Schwartz primitive and diamond minimal surfaces as the phase interface have been shown to have maximal bulk modulus and conductivity. Since these composites are not elastically isotropic their stiffness under uniaxial loading varies with the direction of the load. An isotropic composite is presented with similar conductivity which is at least 23% stiffer under uniaxial loading than the Schwartz structures when loaded uniaxially along their weakest direction. Other new near-optimal isotropic composites are presented, proving the capablities of the level-set method for microstructure design., 25 pages, 11 figures, to be submitted to International Journal of Solids and Structures

Couplings between a closed string RR field and open strings are calculated in a system of coincident branes and antibranes of type II theory. The result can be written cleanly using the curvature of the superconnection., Comment: Latex, 9 pages. Ver2: exposition clarified

The first massive level of closed bosonic string theory is studied. Free-field equations are derived by imposing Weyl invariance on the world sheet. A two-parameter solution to the equation of motion and constraints is found in two dimensions with a flat linear-dilaton background. One-to-one tachyon scattering is studied in this background. The results support Dhar, Mandal and Wadia's proposal that 2D critical string theory corresponds to the c=1 matrix model in which both sides of the Fermi sea are excited., Comment: 17 pages, Latex. V2: One ref added, minor rephrasing of the first paragraph in Sec.3.1, typos in (56) and (57) corrected

We examine the claim that the effective action of four-dimensional SU(2)_L gauge theory at high and low temperature contains a three-dimensional Chern-Simons term with coefficient being the chemical potential for baryon number. We perform calculations in a two-dimensional toy model and find that the existence of the term is rather subtle., 12 pages, LaTeX