Search for scalar bottom quark pair production with the ATLAS detector in pp collisions at sqrt[s]=7 TeV

The results of a search for pair production of the scalar partners of bottom quarks in 2.05 fb(-1) of pp collisions at sqrt[s]=7 TeV using the ATLAS experiment are reported. Scalar bottom quarks are searched for in events with large missing transverse momentum and two jets in the final state, where both jets are identified as originating from a bottom quark. In an R-parity conserving minimal supersymmetric scenario, assuming that the scalar bottom quark decays exclusively into a bottom quark and a neutralino, 95% confidence-level upper limits are obtained in the b(1) - χ(1)(0) mass plane such that for neutralino masses below 60 GeV scalar bottom masses up to 390 GeV are excluded.     

Fly Cheaply: On the Minimum Fuel Consumption Problem

In planning a flight, stops at intermediate airports are sometimes necessary to minimize fuel consumption, even if a direct flight is available. We investigate the problem of finding the cheapest path from one airport to another, given a set of n airports in ² and a function l: ² × ² → ⁺ representing the cost of a direct flight between any pair. Given a source airport s, the cheapest-path map is a subdivision of ² where two points lie in the same region iff their cheapest paths from s use the same sequence of intermediate airports. We show a quadratic lower bound on the combinatorial complexity of this map for a class of cost functions. Nevertheless, we are able to obtain subquadratic algorithms to find the cheapest path from s to all other airports for any well-behaved cost function l: our general algorithm runs in O(n^{4/3 +} ) time, and a simpler, more practical variant runs in O(n^{3/2 +} ) time, while a special class of cost functions requires just O(n log n) time.     

Large Eddy Simulation and Thermodynamic Design of the Organic Rankine Cycle Based on Butane Working Fluid and the High-Boiling-Point Phenyl Naphthalene Liquid Heating System

Large Eddy Simulation (LES) and Thermodynamic study have been performed on Organic Rankine Cycle (ORC) components (boiler, evaporator, turbine, pump, and condenser). The petroleum Coke burner provided the heat flux needed for the butane evaporator. High boiling point fluid (called phenyl-naphthalene) has been applied in the ORC. The high boiling liquid is safer (steam explosion hazard may be prevented) for heating the butane stream. It has best exergy efficiency. It is non-corrosive, highly stable, and flammable. Fire Dynamics Simulator software (FDS) has been applied in order to simulate the pet-coke combustion and calculate the Heat Release Rate (HRR). The maximal temperature of the 2-Phenylnaphthalene flowing in the boiler is much less than its boiling temperature (600 K). Enthalpy, entropy and specific volume required for evaluating the heat rates and the power have been computed by employing the THERMOPTIM thermodynamic code. The proposed design ORC is safer. This is because the flammable butane is separated from the flame produced in the petroleum coke burner. The proposed ORC obeys the two fundamental laws of thermodynamics. The calculated net power is 3260 kW. It is in good agreement with net power is reported in the literature. The thermal efficiency of the ORC is 18.0%.     

An extremal problem for sets with applications to graph theory

Let X₁, …, X_n be n disjoint sets. For 1 ? i ? n and 1 ? j ? h let A_ij and B_ij be subsets of X_i that satisfy |A_ij| ? r_i and |B_ij| ? s_i for 1 ? i ? n, 1 ? j ? h, $\text{(∪}{}_{\mathrm{i}}\text{A}{}_{\mathrm{ij}}\text{) ∩ (∪}{}_{\mathrm{i}}\text{B}{}_{\mathrm{ij}}\text{) = ?}$ for 1 ? j ? h, $\text{(∪}{}_{\mathrm{i}}\text{A}{}_{\mathrm{ij}}\text{) ∩ (∪}{}_{\mathrm{i}}\text{B}{}_{\mathrm{il}}\text{) ≠ ?}$ for 1 ? j < l ? h. We prove that $\text{h?}\text{Π}\text{i=1}\text{n}\text{r}{}_{\mathrm{i}}\text{+s}{}_{\mathrm{i}}\text{r}{}_{\mathrm{i}}$. This result is best possible and has some interesting consequences. Its proof uses multilinear techniques (exterior algebra).     

Independent sets in tensor graph powers

The tensor product of two graphs, G and H, has a vertex set V(G) × V(H) and an edge between (u,v) and (u′,v′) iff both u u′ ∈ E(G) and v v′ ∈ E(H). Let A(G) denote the limit of the independence ratios of tensor powers of G, lim, α(Gⁿ)/|V(Gⁿ)|. This parameter was introduced in [Brown, Nowakowski, Rall, SIAM J Discrete Math 9 ( 5 ), 290–300], where it was shown that A(G) is lower bounded by the vertex expansion ratio of independent sets of G. In this article we study the relation between these parameters further, and ask whether they are in fact equal. We present several families of graphs where equality holds, and discuss the effect the above question has on various open problems related to tensor graph products. © 2006 Wiley Periodicals, Inc. J Graph Theory     

Prediction of adsorption of xenon in zeolite NaA with molecular density functional theory

The Tarazona model of molecular density functional theory is used to determine the adsorption isotherm and the density distribution of xenon atoms in zeolite NaA. We consider the alpha cage of NaA to be fully three-dimensional and we introduce a basis set for the density distribution to make the solution computationally tractable. The results of this density functional theory model are compared to previous results of grand canonical Monte Carlo simulations for the same system.We dedicate this paper to Professor Herbert Wagner, whose excellent contributions to density functional theory typify his valuable role in the advancement of statistical physics     

Breaking the rhythm on graphs

We study graph colorings avoiding periodic sequences with large number of blocks on paths. The main problem is to decide, for a given class of graphs F, if there are absolute constants t,k such that any graph from the class has a t-coloring with no k identical blocks in a row appearing on a path. The minimum t for which there is some k with this property is called the rhythm threshold of F, denoted by t(F). For instance, we show that the rhythm threshold of graphs of maximum degree at most d is between (d+1)/2 and d+1. We give several general conditions for finiteness of t(F), as well as some connections to existing chromatic parameters. The question whether the rhythm threshold is finite for planar graphs remains open.     

Scheduling transmissions in a network

Consider k stations wishing to transmit messages over a network of channels to a common receiver. The capacity of a channel is the maximum amount of data which can be transmitted in a time unit. In addition to the transmission stations, the network contains switching nodes. Given that the jth station has σ_j messages (j = 1,…, k) to transmit, it is desired to find a schedule with minimum completion time T. The amount of data sent over a channel may vary in time. A schedule is stationary if the amount of data sent in a time unit is constant throughout the schedule. It is first shown that for every schedule there exists a stationary schedule with the same completion time. Thus, the search for an optimum schedule is confined to stationary schedules. The problem of finding an optimum stationary schedule is formulated as a multisource single-sink network flow problem, in which the net amount of outgoing flow from each source (transmission station) within one time unit is $\text{σ}{}_{\mathrm{j}}\text{T}$. An O(k|E||V|²) time algorithm to find the minimum T similar to Dinic's flow algorithm is suggested. Using Sleator and Tarjan's techniques an O(k²|E||V|log|V|) algorithm is derived. The running time of both algorithms is independent of the σ_j's and the capacities.     

Testing satisfiability

Let Φ be a set of general boolean functions on n variables, such that each function depends on exactly k variables, and each variable can take a value from [1,d]. We say that Φ is ε-far from satisfiable, if one must remove at least εn^k functions in order to make the set of remaining functions satisfiable. Our main result is that if Φ is ε-far from satisfiable, then most of the induced sets of functions, on sets of variables of size c(k,d)/ε², are not satisfiable, where c(k,d) depends only on k and d. Using the above claim, we obtain similar results for k-SAT and k-NAEQ-SAT.Assume we relax the decision problem of whether an instance of one of the above mentioned problems is satisfiable or not, to the problem of deciding whether an instance is satisfiable or ε-far from satisfiable. While the above decision problems are NP-hard, our result implies that we can solve their relaxed versions, that is, distinguishing between satisfiable and ε-far from satisfiable instances, in randomized constant time.From the above result we obtain as a special case, previous results of Alon and Krivelevich, and of Czumaj and Sohler, concerning testing of graphs and hypergraphs colorability. We also discuss the difference between testing with one-sided and two-sided error.     

On the Chaotic Behavior of a Third-Order Log-Domain Filter

Operation of log-domain filters revolves around the large-signal forward-active mode exponential current-voltage relationship of the bipolar junction transistor, which is used to map the input currents to the logarithmic domain, where the analog processing takes place, and to convert the filtered voltage waveforms back to the linear domain. Sometimes, the inherent internal nonlinearity of such circuits is the cause of unwanted externally-nonlinear effects. In this paper a differential third-order log-domain Chebyshev low-pass filter is designed by applying the method of operational simulation of doubly-terminated LC ladders. When the six grounded shunt capacitors of this filter are properly replaced with three half-sized floating capacitors, as is common practice in internally-linear fully-differential capacitively-loaded circuits, under particular conditions the resulting system exhibits limit-cycle oscillations, period-doubling bifurcations and chaotic behavior for zero-input. The presence of chaos is confirmed by extracting the spectrum of Lyapunov exponents of the system from the time series of the output voltage.