Finding critical points using improved scaling Ansaetze

Analyzing in detail the first corrections to the scaling hypothesis, we develop accelerated methods for the determination of critical points from finite size data. The output of these procedures are sequences of pseudo-critical points which rapidly converge towards the true critical points. In fact more rapidly than previously existing methods like the Phenomenological Renormalization Group approach. Our methods are valid in any spatial dimensionality and both for quantum or classical statistical systems. Having at disposal fast converging sequences, allows to draw conclusions on the basis of shorter system sizes, and can be extremely important in particularly hard cases like two-dimensional quantum systems with frustrations or when the sign problem occurs. We test the effectiveness of our methods both analytically on the basis of the one-dimensional XY model, and numerically at phase transitions occurring in non integrable spin models. In particular, we show how a new Homogeneity Condition Method is able to locate the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state quantities on relatively small systems.Comment: 16 pages, 4 figures. New version including more general Ansaetze basically applicable to all case

Injector fouling and its impact on engine emissions and spray characteristics in gasoline direct injection engines

In Gasoline Direct Injection engines, direct exposure of the injector to the flame can cause combustion products to accumulate on the nozzle, which can result in increased particulate emissions. This research observes the impact of injector fouling on particulate emissions and the associated injector spray pattern and shows how both can be reversed by utilising fuel detergency. For this purpose multi-hole injectors were deliberately fouled in a four-cylinder test engine with two different base fuels. During a four hour injector fouling cycle particulate numbers (PN) increased by up to two orders of magnitude. The drift could be reversed by switching to a fuel blend that contained a detergent additive. In addition, it was possible to completely avoid any PN increase, when the detergent containing fuel was used from the beginning of the test. Microscopy showed that increased injector fouling coincided with increased particulate emissions. Based on these results a selection of the injectors was installed in a laboratory injection chamber and the spray patterns were investigated with a high speed camera. Injectors corresponding to the largest PN drift produced the thinnest spray jets with the deepest penetration. These factors amplify the risk of wall wetting and provide an explanation for the increase of PN. The positive effect of the detergent was also reflected in the spray pattern analysis, which illustrates the potential benefits of such fuel additives

Quenched bond dilution in two-dimensional Potts models

We report a numerical study of the bond-diluted 2-dimensional Potts model using transfer matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one observed in the random bond case, confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder: dilution, self-dual binary random-bond, self-dual continuous random bond.Comment: LaTeX file with IOP macros, 29 pages, 14 eps figure

Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets

Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width $N$ sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the ``analytical'' correction terms, $N^{-2}$, are identically zero for triangular-- and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.Comment: 11 pages, LaTeX with Institute of Physics macros, 2 EPS figures; to appear in Journal of Physics

SU(2)/Z2SU(2)/Z_2 symmetry of the BKT transition and twisted boundary conditio n

Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the 2D sine-Gordon model, plays an important role in the low dimensional physics. We relate the operator content of the BKT transition to that of the SU(2) Wess-Zumino-Witten model, using twisted boundary conditions. With this method, in order to determine the BKT critical point, we can use the level crossing of the lower excitations than the periodic boundary case, thus the convergence to the transition point is highly improved. Then we verify the efficiency of this method by applying to the S=1,2 spin chains.Comment: LaTex2e,, 33 pages, 14 figures in eps file

The critical Ising model on a torus with a defect line

The critical Ising model in two dimensions with a defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically the partition function and the asymptotic expansions of the free energy and inverse correlation lengths for an infinitely long cylinder of circumference $L_x$. We find that finite-size corrections to scaling are of the form $a_k/L^{2k-1}_x$ for the free energy $f$ and $b_k(p)/L_x^{2k-1}$ and $c_k(p)/L_x^{2k-1}$ for inverse correlation lengths $\xi^{-1}_p$ and $\xi^{-1}_{L-p}$, respectively, with integer values of $k$. By exact evaluation we find that the amplitude ratios $b_k(p)/a_k$ and $c_k(p)/a_k$ are universal and verify this universal behavior using a perturbative conformal approach.Comment: 5 pages, 5 figures, added Acknowledgment

Recycling bins, garbage cans or think tanks? Three myths regarding policy analysis institutes

The phrase 'think tank' has become ubiquitous – overworked and underspecified – in the political lexicon. It is entrenched in scholarly discussions of public policy as well as in the 'policy wonk' of journalists, lobbyists and spin-doctors. This does not mean that there is an agreed definition of think tank or consensual understanding of their roles and functions. Nevertheless, the majority of organizations with this label undertake policy research of some kind. The idea of think tanks as a research communication 'bridge' presupposes that there are discernible boundaries between (social) science and policy. This paper will investigate some of these boundaries. The frontiers are not only organizational and legal; they also exist in how the 'public interest' is conceived by these bodies and their financiers. Moreover, the social interactions and exchanges involved in 'bridging', themselves muddy the conception of 'boundary', allowing for analysis to go beyond the dualism imposed in seeing science on one side of the bridge, and the state on the other, to address the complex relations between experts and public policy

Genetic diversity in nutritional parameters in response to drought of Coffea canephora cultivated in Rondonia state, Brazil.

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Renormalization group analysis of the spin-gap phase in the one-dimensional t-J model

We study the spin-gap phase in the one-dimensional t-J model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also check that the universality class of the transition belongs to the $k=1$ SU(2) Wess-Zumino-Witten model.Comment: 4 pages(RevTeX), 5 figures(EPS), TITCMT-97-10, to appear in Phys. Rev. Let