Relationship between cooling rate and microsegregation in bottom-chilled directionally solidified ductile irons

This study explores the relationship between cooling rate and microsegregation of directionally solidified ductile iron. The unidirectional heat transfer system used in this research is made up of a copper mold kept chilled by circulating water and embedded in the bottom of Furan sand mold. Thermocouples are connected to the computer measuring system to record the cooling curves of the castings at a distance of 0, 30, 60 and 90 mm from the chilled copper mold surface. Alloys including Mn, Cr, Cu, Ni and Ti were added to the specimens. Electron microprobe analysis (EPMA) was employed to examine distribution of elements between the dendrite arms and nodular graphite. Results show that unidirectional heat transfer affects directly the solidification mode and microstructure of the casting. The cooling curves reveal that local solidification time increases with increasing distance from the chilled copper mold surface. Different solidification rates with corresponding microstructure and element segregation were observed in the same unidirectionally solidified casting. Local solidification time was closely related to element segregation. The effective segregation coefficient (Keff) calculated using the Scheil equation was found to vary, according to the stage of solidification. The actual segregation characteristics of complex alloys generally follow the Scheil equation

Non-perturbative calculations for the effective potential of the PTPT symmetric and non-Hermitian (−gϕ4)(-g\phi^{4}) field theoretic model

We investigate the effective potential of the $PT$ symmetric $(-g\phi^{4})$ field theory, perturbatively as well as non-perturbatively. For the perturbative calculations, we first use normal ordering to obtain the first order effective potential from which the predicted vacuum condensate vanishes exponentially as $G\to G^+$ in agreement with previous calculations. For the higher orders, we employed the invariance of the bare parameters under the change of the mass scale $t$ to fix the transformed form totally equivalent to the original theory. The form so obtained up to $G^3$ is new and shows that all the 1PI amplitudes are perurbative for both $G\ll 1$ and $G\gg 1$ regions. For the intermediate region, we modified the fractal self-similar resummation method to have a unique resummation formula for all $G$ values. This unique formula is necessary because the effective potential is the generating functional for all the 1PI amplitudes which can be obtained via $\partial^n E/\partial b^n$ and thus we can obtain an analytic calculation for the 1PI amplitudes. Again, the resummed from of the effective potential is new and interpolates the effective potential between the perturbative regions. Moreover, the resummed effective potential agrees in spirit of previous calculation concerning bound states.Comment: 20 page

Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

Null-plane Quantum Universal RR-matrix

A non-linear map is applied onto the (non-standard) null-plane deformation of (3+1) Poincar\'e algebra giving rise to a simpler form of this triangular quantization. A universal $R$-matrix for the null plane quantum algebra is then obtained from a universal $T$-matrix corresponding to a Hopf subalgebra. Finally, the associated Poincar\'e Poisson--Lie group is quantized by using the FRT approach.Comment: 8 pages, LaTe

Ordering effect of Coulomb interaction in ballistic double-ring systems

We study a model of two concentric onedimensional rings with incommensurate areas $A_1$ and $A_2$, in a constant magnetic field. The two rings are coupled by a nonhomogeneous inter-ring tunneling amplitude, which makes the one-particle spectrum chaotic. For noninteracting particles the energy of the many-body ground state and the first excited state exhibit random fluctuations characterized by the Wigner-Dyson statistics. In contrast, we show that the electron-electron interaction orders the magnetic field dependence of these quantities, forcing them to become periodic functions, with period $\propto 1/(A_1 + A_2)$. In such a strongly correlated system the only possible source of disorder comes from charge fluctuations, which can be controlled by a tunable inter-ring gate voltage.Comment: 4 pages, 4 eps figures, revised text and new figures (as published

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Reorientation of magnetic anisotropy in epitaxial cobalt ferrite thin films

Spin reorientation has been observed in CoFe2O4 thin single crystalline films epitaxially grown on (100) MgO substrate upon varying the film thickness. The critical thickness for such a spin-reorientation transition was estimated to be 300 nm. The reorientation is driven by a structural transition in the film from a tetragonal to cubic symmetry. At low thickness, the in-plane tensile stress induces a tetragonal distortion of the lattice that generates a perpendicular anisotropy, large enough to overcome the shape anisotropy and to stabilize the magnetization easy axis out of plane. However, in thicker films, the lattice relaxation toward the cubic structure of the bulk allows the shape anisotropy to force the magnetization to be in plane aligned

Effects of carbohydrate, branched-chain amino acids, and arginine in recovery period on the subsequent performance in wrestlers

Many athletes need to participate in multiple events in a single day. The efficient post-exercise glycogen recovery may be critical for the performance in subsequent exercise. This study examined whether post-exercise carbohydrate supplementation could restore the performance in the subsequent simulated wrestling match. The effect of branched-chain amino acids and arginine on glucose disposal and performance was also investigated. Nine well-trained male wrestlers participated in 3 trials in a random order. Each trial contained 3 matches with a 1-hr rest between match 1 and 2, and a 2-hr rest between match 2 and 3. Each match contained 3 exercise periods interspersed with 1-min rests. The subjects alternated 10-s all-out sprints and 20-s rests in each exercise period. At the end of match 2, 3 different supplementations were consumed: 1.2 g/kg glucose (CHO trial), 1 g/kg glucose + 0.1 g/kg Arg + 0.1 g/kg BCAA (CHO+AA trial), or water (placebo trial). The peak and average power in the 3 matches was similar in the 3 trials. After the supplementation, CHO and CHO+AA trial showed significantly higher glucose and insulin, and lower glycerol and non-esterified fatty acid concentrations than the placebo trial. There was no significant difference in these biochemical parameters between the CHO and CHO+AA trials. Supplementation of carbohydrate with or without BCAA and arginine during the post-match period had no effect on the performance in the following simulated match in wrestlers. In addition, BCAA and arginine did not provide additional insulinemic effect

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape

We report experimental evidence that chaotic and non-chaotic scattering through ballistic cavities display distinct signatures in quantum transport. In the case of non-chaotic cavities, we observe a linear decrease in the average resistance with magnetic field which contrasts markedly with a Lorentzian behavior for a chaotic cavity. This difference in line-shape of the weak-localization peak is related to the differing distribution of areas enclosed by electron trajectories. In addition, periodic oscillations are observed which are probably associated with the Aharonov-Bohm effect through a periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.