TY - JOUR
AB - For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant depends at most on d, ε, and N.
AU - Timothy Browning
AU - Heath-Brown, Roger
AU - Salberger, Per
ID - 216
IS - 3
JF - Duke Mathematical Journal
TI - Counting rational points on algebraic varieties
VL - 132
ER -
TY - JOUR
AB - This paper is concerned with the average order of certain arithmetic functions, as they range over the values taken by binary forms.
AU - de la Bretèche, Régis
AU - Timothy Browning
ID - 218
IS - 3
JF - Acta Arithmetica
TI - Sums of arithmetic functions over values of binary forms
VL - 125
ER -
TY - CONF
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2333
TI - Ground-state energy of a dilute Fermi gas
VL - 412
ER -
TY - CONF
AU - Robert Seiringer
AU - Lieb, Élliott H
AU - Yngvason, Jakob
ED - Zambrini, Jean-Claude
ID - 2334
TI - One-dimensional behavior of dilute, trapped Bose gases in traps
ER -
TY - GEN
AB - We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2363
IS - 2
T2 - Communications in Mathematical Physics
TI - Derivation of the Gross-Pitaevskii equation for rotating Bose gases
VL - 264
ER -
TY - JOUR
AB - We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation.
AU - Robert Seiringer
ID - 2364
IS - 3
JF - Reviews in Mathematical Physics
TI - A correlation estimate for quantum many-body systems at positive temperature
VL - 18
ER -
TY - JOUR
AB - We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.
AU - Robert Seiringer
ID - 2365
IS - 3
JF - Communications in Mathematical Physics
TI - The thermodynamic pressure of a dilute fermi gas
VL - 261
ER -
TY - JOUR
AB - Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.
AU - Frank, Rupert L
AU - Laptev, Ari
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2366
IS - 3
JF - Letters in Mathematical Physics
TI - Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
VL - 77
ER -
TY - CHAP
AB - The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases.
AU - Robert Seiringer
ED - Dereziński, Jan
ED - Siedentop, Heinz
ID - 2368
T2 - Large Coulomb Systems
TI - Dilute, trapped Bose gases and Bose-Einstein condensation
VL - 695
ER -
TY - CHAP
AB - One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.
AU - Aizenman, Michael
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ED - Asch, Joachim
ED - Joye, Alain
ID - 2369
T2 - Mathematical Physics of Quantum Mechanics
TI - Bose-Einstein condensation as a quantum phase transition in an optical lattice
VL - 690
ER -
TY - CHAP
AU - Bang-Jensen, Jørgen
AU - Reed, Bruce
AU - Schacht, Bruce
AU - Šámal, Robert
AU - Toft, Bjarne
AU - Uli Wagner
ID - 2416
T2 - Topics in Discrete Mathematics
TI - On six problems posed by Jarik Nešetřil
VL - 26
ER -
TY - JOUR
AB - We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.
AU - Matoušek, Jiří
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
AU - Uli Wagner
ID - 2429
IS - 2
JF - Discrete & Computational Geometry
TI - K-sets in four dimensions
VL - 35
ER -
TY - JOUR
AB - We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω(√̃) colors in the worst case. We then derive two efficient variants of this simple algorithm. The first is deterministic and uses O(log 2 n) colors, and the second is randomized and uses O(log n) colors with high probability. We also show that the O(log 2 n) bound on the number of colors used by our deterministic algorithm is tight on the worst case. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case.
AU - Chent, Ke
AU - Fiat, Amos
AU - Kaplan, Haim
AU - Levy, Meital B
AU - Matoušek, Jiří
AU - Mossel, Elchanan
AU - Pach, János
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
AU - Uli Wagner
AU - Welzl, Emo
ID - 2430
IS - 5
JF - SIAM Journal on Computing
TI - Online conflict-free coloring for intervals
VL - 36
ER -
TY - CONF
AB - We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most t in an arrangement of n halfspaces in R , for arbitrary n and d (in particular, the dimension d is not considered constant). This partially settles a conjecture of Eckhoff, Linhart, and Welzl. Up to the factor of 2, the result generalizes McMullen's Upper Bound Theorem for convex polytopes (the case ℓ = O) and extends a theorem of Linhart for the case d ≤ 4. Moreover, the bound sharpens asymptotic estimates obtained by Clarkson and Shor. The proof is based on the h-matrix of the arrangement (a generalization, introduced by Mulmuley, of the h-vector of a convex polytope). We show that bounding appropriate sums of entries of this matrix reduces to a lemma about quadrupels of sets with certain intersection properties, and we prove this lemma, up to a factor of 2, using tools from multilinear algebra. This extends an approach of Alon and Kalai, who used linear algebra methods for an alternative proof of the classical Upper Bound Theorem. The bounds for the entries of the h-matrix also imply bounds for the number of i-dimensional faces, i > 0, at level at most ℓ. Furthermore, we discuss a connection with crossing numbers of graphs that was one of the main motivations for investigating exact bounds that are valid for arbitrary dimensions.
AU - Uli Wagner
ID - 2431
TI - On a geometric generalization of the Upper Bound Theorem
ER -
TY - CONF
AB - Often the properties of a single cell are considered as representative for a complete polymer electrolyte fuel cell stack or even a fuel cell system. In some cases this comes close, however, in many real cases differences on several scales become important. Cell interaction phenomena in fuel cell stacks that arise from inequalities between adjacent cells are investigated in detail experimentally. For that, a specialized 2-cell stack with advanced localized diagnostics was developed. The results show that inequalities propagate by electrical coupling, inhomogeneous cell polarization and inducing in-plane current in the common bipolar plate. The effects of the different loss-mechanisms are analyzed and quantified.
AU - Büchi, Felix N.
AU - Freunberger, Stefan Alexander
AU - Santis, Marco
ID - 7326
IS - 1
T2 - ECS Transactions
TI - What is learned beyond the scale of single cells?
VL - 3
ER -
TY - JOUR
AB - Propagation of performance changes to adjacent cells in polymer electrolyte fuel cell stacks is studied by means of voltage monitoring and local current density measurements in peripheral cells of the stack. A technical fuel cell stack has been modified by implementing two independent reactant and coolant supplies in order to deliberately change the performance of one cell (anomalous cell) and study the coupling phenomena to adjacent cells (coupling cells), while keeping the working conditions of the later cell-group unaltered.
Two anomalies are studied: (i) air starvation and (ii) thermal anomaly, in a single anomalous cell in the stack and their coupling to adjacent cells. The results have shown that anomalies inducing considerable changes in the local current density of the anomalous cell (such as air starvation) propagate to adjacent cells affecting their performance. The propagation of local current density changes takes place via the common bipolar plate due to its finite thickness and in-plane conductivity. Consequently, anomalies which do not strongly influence the local current density distribution (such as a thermal anomaly under the studied working conditions) do not propagate to adjacent cells.
AU - Santis, Marco
AU - Freunberger, Stefan Alexander
AU - Papra, Matthias
AU - Wokaun, Alexander
AU - Büchi, Felix N.
ID - 7327
IS - 2
JF - Journal of Power Sources
SN - 0378-7753
TI - Experimental investigation of coupling phenomena in polymer electrolyte fuel cell stacks
VL - 161
ER -
TY - JOUR
AB - An experimental technique for measuring the current density distribution with a resolution smaller than the channel/rib scale of the flow field in polymer electrolyte fuel cells (PEFCs) is presented. The electron conductors in a plane perpendicular to the channel direction are considered as two-dimensional resistors. Hence, the current density is obtained from the solution of Laplace's equation with the potentials at current collector and reaction layer as boundary conditions. Using ohmic drop for calculating the local current, detailed knowledge of all resistances involved is of prime importance. In particular, the contact resistance between the gas diffusion layer (GDL) and flow field rib, as well as GDL bulk conductivity, are strongly dependent on clamping pressure. They represent a substantial amount of the total ohmic drop and therefore require careful consideration. The detailed experimental setup as well as the concise procedure for quantitative data evaluation is described. Finally, the method is applied successfully to a cell operated on pure oxygen and air up to high current densities. The results show that electrical and ionic resistances seem to govern the current distribution at low current regimes, whereas mass transport limitations locally hamper the current production at high loads.
AU - Freunberger, Stefan Alexander
AU - Reum, Mathias
AU - Evertz, Jörg
AU - Wokaun, Alexander
AU - Büchi, Felix N.
ID - 7328
IS - 11
JF - Journal of The Electrochemical Society
SN - 0013-4651
TI - Measuring the current distribution in PEFCs with sub-millimeter resolution
VL - 153
ER -
TY - JOUR
AB - A novel measurement principle for measuring the current distribution in polymer electrolyte fuel cells (PEFCs) is introduced. It allows, in contrast to all other known techniques, for the first time for a resolution smaller than the channel/rib scale of the flow field in PEFCs. The current density is obtained by considering the electron conductors in the cell as a two-dimensional resistor with the voltage drop caused by the current. The method was applied to a cell operated on oxygen up to high current densities. The results show that the ohmic resistances govern the current distribution in the low current regime, whereas mass transport limitations hamper the current production under the land at high loads.
AU - Freunberger, Stefan Alexander
AU - Reum, Mathias
AU - Wokaun, Alexander
AU - Büchi, Felix N.
ID - 7329
IS - 9
JF - Electrochemistry Communications
SN - 1388-2481
TI - Expanding current distribution measurement in PEFCs to sub-millimeter resolution
VL - 8
ER -
TY - JOUR
AB - Polymer electrolyte fuel cells (PE fuel cells) working with air at low stoichiometries (<2.0) and standard electrochemical components show a high degree of inhomogeneity in the current density distribution over the active area. An inhomogeneous current density distribution leads to a non-uniform utilization of the active area, which could negatively affect the time of life of the cells. Furthermore, it is also believed to lower cell performance. In this work, the homogenization of the current density, realized by means of tailored cathodes with along-the-air-channel redistributed catalyst loadings, is investigated. The air stoichiometry range for which a homogenization of the current density is achieved depends upon the gradient with which the catalyst is redistributed along the air channel. A gentle increasing catalyst loading profile homogenizes the current density at relatively higher air stoichiometries, while a steeper profile is suited better for lower air stoichiometries. The results show that a homogenization of the current density by means of redistributed catalyst loading has negative effects on cell performance. Model calculations corroborate the experimental findings on homogenization of the current density and deliver an explanation for the decrease in cell performance.
AU - Santis, M.
AU - Freunberger, Stefan Alexander
AU - Reiner, A.
AU - Büchi, F.N.
ID - 7330
IS - 25
JF - Electrochimica Acta
SN - 0013-4686
TI - Homogenization of the current density in polymer electrolyte fuel cells by in-plane cathode catalyst gradients
VL - 51
ER -
TY - JOUR
AB - A previously developed mathematical model for water management and current density distribution in a polymer electrolyte fuel cell (PEFCs) is employed to investigate the effects of cooling strategies on cell performance. The model describes a two-dimensional slice through the cell along the channels and through the entire cell sandwich including the coolant channels and the bipolar plate. Arbitrary flow arrangements of fuel, oxidant, and coolant stream directions can be described. Due to the serious impact of temperature on all processes in the PEFC, both the relative direction of the coolant stream to the gas streams and its mass flow turns out to significantly affect the cell performance. Besides influencing the electrochemical reaction and all kinds of mass transfer temperature, variations predominantly alter the local membrane hydration distribution and subseqently its conductivity.
AU - Freunberger, Stefan Alexander
AU - Wokaun, Alexander
AU - Büchi, Felix N.
ID - 7331
IS - 5
JF - Journal of The Electrochemical Society
SN - 0013-4651
TI - In-plane effects in large-scale PEFCs: II. The influence of cooling strategy on cell performance
VL - 153
ER -