@inproceedings{2331, abstract = {We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of Ref. 9 as well our recent joint work with Hamza and Solovej and with Frank and Naboko, respectively. In addition, we mention some related new results.}, author = {Hainzl, Christian and Robert Seiringer}, pages = {117 -- 136}, publisher = {World Scientific Publishing}, title = {{ Spectral properties of the BCS gap equation of superfluidity}}, doi = {10.1142/9789812832382_0009}, year = {2008}, } @inproceedings{2332, abstract = {We present a rigorous proof of the appearance of quantized vortices in dilute trapped Bose gases with repulsive two-body interactions subject to rotation, which was obtained recently in joint work with Elliott Lieb.14 Starting from the many-body Schrödinger equation, we show that the ground state of such gases is, in a suitable limit, well described by the nonlinear Gross-Pitaevskii equation. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.}, author = {Robert Seiringer}, pages = {241 -- 254}, publisher = {World Scientific Publishing}, title = {{Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases}}, doi = {10.1142/9789812832382_0017}, year = {2008}, } @article{2374, abstract = {A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.}, author = {Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {595 -- 636}, publisher = {Springer}, title = {{Free energy of a dilute Bose gas: Lower bound}}, doi = {10.1007/s00220-008-0428-2}, volume = {279}, year = {2008}, } @article{2376, abstract = {We derive upper and lower bounds on the critical temperature Tc and the energy gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions interacting via a local two-body interaction potential λV(x). At weak coupling λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ) and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a universal constant, independent of both V(x) and μ. Our analysis is valid for any μ; for small μ, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x).}, author = {Hainzl, Christian and Robert Seiringer}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {18}, publisher = {American Physical Society}, title = {{Critical temperature and energy gap for the BCS equation}}, doi = {10.1103/PhysRevB.77.184517}, volume = {77}, year = {2008}, } @article{2377, abstract = {We prove that the critical temperature for the BCS gap equation is given by T c = μ ( 8\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting Euler's constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.}, author = {Hainzl, Christian and Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {2-3}, pages = {99 -- 107}, publisher = {Springer}, title = {{The BCS critical temperature for potentials with negative scattering length}}, doi = {10.1007/s11005-008-0242-y}, volume = {84}, year = {2008}, } @article{2378, abstract = {We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.}, author = {Robert Seiringer and Yin, Jun}, journal = {Journal of Statistical Physics}, number = {6}, pages = {1139 -- 1154}, publisher = {Springer}, title = {{Ground state energy of the low density hubbard model}}, doi = {10.1007/s10955-008-9527-x}, volume = {131}, year = {2008}, } @article{2379, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Journal of the American Mathematical Society}, number = {4}, pages = {925 -- 950}, publisher = {American Mathematical Society}, title = {{Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators}}, doi = {10.1090/S0894-0347-07-00582-6}, volume = {21}, year = {2008}, } @article{2380, abstract = {The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.}, author = {Hainzl, Christian and Hamza, Eman and Robert Seiringer and Solovej, Jan P}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {349 -- 367}, publisher = {Springer}, title = {{The BCS functional for general pair interactions}}, doi = {10.1007/s00220-008-0489-2}, volume = {281}, year = {2008}, } @article{2381, abstract = {We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.}, author = {Frank, Rupert L and Robert Seiringer}, journal = {Journal of Functional Analysis}, number = {12}, pages = {3407 -- 3430}, publisher = {Academic Press}, title = {{Non-linear ground state representations and sharp Hardy inequalities}}, doi = {10.1016/j.jfa.2008.05.015}, volume = {255}, year = {2008}, } @article{2382, abstract = {We show that the Lieb-Liniger model for one-dimensional bosons with repulsive δ-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived. Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼ r -2 above the ground state energy.}, author = {Robert Seiringer and Yin, Jun}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {459 -- 479}, publisher = {Springer}, title = {{The Lieb-Liniger model as a limit of dilute bosons in three dimensions}}, doi = {10.1007/s00220-008-0521-6}, volume = {284}, year = {2008}, } @article{2383, abstract = {We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.}, author = {Hainzl, Christian and Lewin, Mathieu and Robert Seiringer}, journal = {Reviews in Mathematical Physics}, number = {10}, pages = {1283 -- 1307}, publisher = {World Scientific Publishing}, title = {{A nonlinear model for relativistic electrons at positive temperature}}, doi = {10.1142/S0129055X08003547}, volume = {20}, year = {2008}, } @inbook{2415, author = {Uli Wagner}, booktitle = {Surveys on Discrete and Computational Geometry: Twenty Years Later}, editor = {Goodman, Jacob E and Pach, János and Pollack, Richard}, pages = {443 -- 514}, publisher = {American Mathematical Society}, title = {{k-Sets and k-facets}}, doi = {10.1090/conm/453}, volume = {453}, year = {2008}, } @inproceedings{2432, abstract = {We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.}, author = {Smorodinsky, Shakhar and Sulovský, Marek and Uli Wagner}, pages = {363 -- 373}, publisher = {Springer}, title = {{On center regions and balls containing many points}}, doi = {10.1007/978-3-540-69733-6_36}, volume = {5092}, year = {2008}, } @article{7320, abstract = {A comparative, experimental diffusivity study of gas diffusion layer (GDL) materials for polymer electrolyte fuel cells (PEFC) is presented for the first time. The GDL plays an important role for electrochemical losses due to gas transport limitations at high current densities. Characterization and optimization of these layers is therefore essential to improve power density. A recently developed method which allows for fast diffusimetry is applied and data compared to the literature values. Measurements are made as a function of direction and compression and the effect of different binder structures and hydrophobic treatments on effective diffusivities are discussed. A better understanding of the results is gained by including novel GDL cross-section images and a meaningful unit cell model for the interpretation of the data. The diffusivity data is valuable for GDL manufacturers and future PEFC models. The study reveals that a binder–fiber ratio larger than 50% has a negative impact on the effective diffusion properties. The hydrophobic treatment which is necessary to improve the water management can impede diffusion and thus reduce the power density. Furthermore binder has an isotropic effect while compression pronounces the in-plane orientation of the fibers.}, author = {Flückiger, Reto and Freunberger, Stefan Alexander and Kramer, Denis and Wokaun, Alexander and Scherer, Günther G. and Büchi, Felix N.}, issn = {0013-4686}, journal = {Electrochimica Acta}, number = {2}, pages = {551--559}, publisher = {Elsevier}, title = {{Anisotropic, effective diffusivity of porous gas diffusion layer materials for PEFC}}, doi = {10.1016/j.electacta.2008.07.034}, volume = {54}, year = {2008}, } @article{7321, abstract = {Cell interaction phenomena in polymer electrolyte fuel cell stacks that arise from imbalance between adjacent cells are investigated in detail experimentally and theoretically. A specialized two-cell stack with advanced localized diagnostics was developed and used to analyze the mechanism and effect of cell-to-cell coupling as a result of operationally relevant variations in reactant feed flow. Contributions to overall and local voltage changes with respect to uniformly operated cells are scrutinized. Unequal operation of the cells causes in-plane current in the bipolar plate to redistribute current and result in inhomogeneous polarization. Both increasing and decreasing polarization along the air-flow path reduces cell power as compared to isopotential operation. A two-dimensional model based on a commercial computational fluid dynamics code is used to back and extend the experimental results to more general cases. Furthermore, the experimental setup presented allowed for the first time to perform simultaneous localized electrochemical impedance spectroscopy beyond the single-cell level. The mechanism of mutual cell interaction on local and integral spectra is revealed. Results show that virtually identical operation of the cells is essential to obtain meaningful integral spectra.}, author = {Freunberger, Stefan Alexander and Schneider, Ingo A. and Sui, Pang-Chieh and Wokaun, Alexander and Djilali, Nedjib and Büchi, Felix N.}, issn = {0013-4651}, journal = {Journal of The Electrochemical Society}, number = {7}, publisher = {The Electrochemical Society}, title = {{Cell interaction phenomena in polymer electrolyte fuel cell stacks}}, doi = {10.1149/1.2913095}, volume = {155}, year = {2008}, } @article{7322, abstract = {The gas diffusion layers (GDLs) of a membrane electrode assembly (MEA) serve as link between flow field and porous electrode within a polymer electrolyte fuel cell. Beside ensuring sufficient electrical and thermal contact between the whole electrode area and the flow field, these typically 200–400 μm thick porous structures enable the access of educts to the electrode area which would be occluded by the flow field lands if the flow field is directly attached to the electrode. Hence, the characterisation of properties pertaining to mass transport of educts and products through these structures is indispensable whilst examining the contribution of the GDLs to the overall electrochemical characteristics of a MEA. A fast and cost effective method to measure the effective diffusivity of a GDL is presented. Electrochemical impedance spectroscopy is applied to measure the effective ionic conductivity of an electrolyte-soaked GDL. Taking advantage of the analogy between Ficks and Ohms law, this provides a measure for the effective diffusivity. The method is described in detail, including experimental as well as theoretical aspects, and selected results, highlighting the anisotropy and dependence on the degree of compression, are shown. Moreover, a two-dimensional model consisting of regularly spaced ellipses is developed to represent the porous structure of the GDL, and by using conformal maps, the agreement between this model and experiment with respect to the sensitivity of the effective diffusivity towards compression is shown.}, author = {Kramer, Denis and Freunberger, Stefan Alexander and Flückiger, Reto and Schneider, Ingo A. and Wokaun, Alexander and Büchi, Felix N. and Scherer, Günther G.}, issn = {1572-6657}, journal = {Journal of Electroanalytical Chemistry}, number = {1}, pages = {63--77}, publisher = {Elsevier}, title = {{Electrochemical diffusimetry of fuel cell gas diffusion layers}}, doi = {10.1016/j.jelechem.2007.09.014}, volume = {612}, year = {2008}, } @inproceedings{7425, abstract = {The propagation of single cell performance losses to adjacent cells in a polymer electrolyte fuel cell stack is studied by means of local current density measurements in a two cell stack. In this stack, the working conditions of adjacent cells can be controlled independently in order to deliberately change the performance of one cell (inducing cell) and study the coupling effects to the adjacent cell (response cell), while keeping the working conditions of the later one unchanged. The experiments have shown that changes in the current density distribution caused by lowering of the air stoichiometry in the inducing cell cause changes in the current density distribution of the response cell in the order of 60% of the change of the inducing cell, even when the air stoichiometry of the response cell is kept constant. The losses in cell voltage of the inducing cell cause losses in cell voltage of the response cell in a magnitude between 30 and 50%.}, author = {Santis, Marco and Freunberger, Stefan Alexander and Papra, Matthias and Büchi, Felix N.}, booktitle = {3rd International Conference on Fuel Cell Science, Engineering and Technology}, isbn = {0791837645}, location = {Ypsilanti, MI, United States}, pages = {763--765}, publisher = {ASMEDC}, title = {{Experimental investigation of the propagation of local current density variations to adjacent cells in PEFC stacks}}, doi = {10.1115/fuelcell2005-74116}, year = {2008}, } @inproceedings{753, abstract = {This paper addresses the following question: what is the minimum-sized synchronous window needed to solve consensus in an otherwise asynchronous system? In answer to this question, we present the first optimally-resilient algorithm ASAP that solves consensus as soon as possible in an eventually synchronous system, i.e., a system that from some time GST onwards, delivers messages in a timely fashion. ASAP guarantees that, in an execution with at most f failures, every process decides no later than round GST + f + 2, which is optimal.}, author = {Alistarh, Dan-Adrian and Gilbert, Seth and Guerraoui, Rachid and Travers, Corentin}, pages = {32 -- 46}, publisher = {Springer}, title = {{How to solve consensus in the smallest window of synchrony}}, doi = {10.1007/978-3-540-87779-0_3}, volume = {5218 LNCS}, year = {2008}, } @article{7752, author = {Robinson, Matthew Richard and Pilkington, Jill G. and Clutton-Brock, Tim H. and Pemberton, Josephine M. and Kruuk, Loeske. E.B.}, issn = {0960-9822}, journal = {Current Biology}, number = {10}, pages = {751--757}, publisher = {Elsevier}, title = {{Environmental heterogeneity generates fluctuating selection on a secondary sexual trait}}, doi = {10.1016/j.cub.2008.04.059}, volume = {18}, year = {2008}, } @inproceedings{4568, abstract = {We present and evaluate a framework and tool for combining multiple program analyses which allows the dynamic (on-line) adjustment of the precision of each analysis depending on the accumulated results. For example, the explicit tracking of the values of a variable may be switched off in favor of a predicate abstraction when and where the number of different variable values that have been encountered has exceeded a specified threshold. The method is evaluated on verifying the SSH client/server software and shows significant gains compared with predicate abstraction-based model checking.}, author = {Beyer, Dirk and Thomas Henzinger and Théoduloz, Grégory}, pages = {29 -- 38}, publisher = {ACM}, title = {{Program analysis with dynamic change of precision}}, doi = {10.1109/ASE.2008.13}, year = {2008}, }