Investigation of two resonances in the18O(p,n)18F reaction

Excitation functions for the¹⁸O(p,n)¹⁸F reaction were measured at bombarding energiesE _p=4.6 to 6.6 MeV. In and near two resonances of the yield curves atE _p=5.622 and 6.061 MeV, angular distributions were measured with neutron time-of-flight techniques. The strong neutron decay to theT=1 state in¹⁸F and the similarity of the¹⁸O(p,n) and¹⁸O(n,n) yield curves give good evidence that the structures in the¹⁸O(p,n) yield curve arise from the formation ofT=3/2 states in¹⁹F. A two-level-analysis does not give satisfactory fits to the strongly asymmetric angular distributions.     

The Markov branching random walk and systems of reaction-diffusion (Kolmogorov-Petrovskii-Piskunov) equations

A general model of a branching random walk inR ¹ is considered, with several types of particles, where the branching occurs with probabilities determined by the type of a parent particle. Each new particle starts moving from the place where it was born, independently of other particles. The distribution of the displacement of a particle, before it splits, depends on its type. A necessary and sufficient condition is given for the random variable $$X^0 = \mathop {\sup max}\limits_{ n \geqq 0 1 \leqq k \leqq N_n } X_{n,k} $$ to be finite. Here,X _{n, k} is the position of thek ^th particle in then ^th generation,N _n is the number of particles in then ^th generation (regardless of their type). It turns out that the distribution ofX ⁰ gives a minimal solution to a natural system of stochastic equations which has a linearly ordered continuum of other solutions. The last fact is used for proving the existence of a monotone travelling-wave solution to systems of coupled non-linear parabolic PDE's.     

Scaling of the “superstable” fraction of the 2D period-doubling interval

The scaling properties of a “superstable” parameter interval, $\text{C}$, where the eigenvalues about a period-2n orbit are complex, are derived for 2D period-doubling maps. The ratio of $\text{C}$ to the whole parameter interval, between the nth and the (n+1)st bifurcation, is shown to be a universal function of the effective jacobian, B_e, only (B_e≡B²ⁿ, B is thejacobian of th e map). Unlike the whole period-2ⁿ interval, $\text{C}$ has a convergence rate that behaves as $\text{4.6692016×B}{}^{\mathrm{<mtext>-1</mtext><mtext>4</mtext>}}{}_{\mathrm{e}}$ as B_e↓), wh ile its complement has a convergence rate 8.7210972/4 as B_e↑1.     

The study of the (n, α) and (n, γ α) reactions on143Nd

Partial cross sections have been measured for the¹⁴³Nd(n _th,α)¹⁴⁰Ce reaction and also for the two-step process¹⁴³Nd(n _th,γα)¹⁴⁰Ce. The results of the present work confirm previous data, but due to lower background, better statistics and resolution improved precision has been obtained. The double-humped structure in the observed (n, γ α) spectrum can still be explained through the Porter-Thomas fluctuations of the reduced partialγ andα widths.     

The spectral class of the quantum-mechanical harmonic oscillator

The purpose of this paper is to study the so-calledspectral class Q of anharmonic oscillatorsQ=?D ²+q having the same spectrum λ _n =2n (n≧0) as the harmonic oscillatorQ ⁰=?D ²+x ²?1. Thenorming constants \(t_n = \mathop {\lim }\limits_{x \uparrow \infty } \ell g[( - 1)^n {{e_n (x)} \mathord{\left/ {\vphantom {{e_n (x)} {e_n }}} \right. \kern-0em} {e_n }}( - x)]\) of the eigenfunctions ofQ form a complete set of coordinates inQ in terms of which the potential may be expressed asq=x ²?1?2D ² ?g? with $$\theta = \det \left[ {\delta _{ij} + (e^{ti} - 1)\int\limits_x^\infty {e_i^0 e_j^0 :0 \leqq i,j,< \infty } } \right],$$ e _n ⁰ being then ^th eigenfunctionQ ⁰. The spectrum and norming constants are canonically conjugate relative to the bracket [F, G]=∫ΔFDΔGdx,to wit: [λ _i , λj=0, [t _i, 2λ _j ]=1 or 0 according to whetheri=j or not, and [t _i,t _j]=0. This prompts an investigation of the symplectic geometry ofQ. The function ? is related to the theta function of a singular algebraic curve. Numerical results are also presented.     

Period doubling in maps with a maximum of order z

We consider the scaling behaviour in period-doubling systems, exemplified by the one-dimensional map χ_n+1 = 1 − λ|χ_n|^z, which has a maximum of order z (z > 1). The Feigenbaum scaling factors α and δ are studied as functions of z, and more generally the scaling functions 1/σ and ƒ(a). In particular, using the universal functions g(x) and h(x) we establish the inequality δ < α^z, which implies that δ remains finite (≲ 30) in the limit z → ∞.     

一维单峰映象的拓扑熵

在对Logistic映象数值计算的基础上,我们分析了一维单峰映象的逆轨道结构,证明了不同参数处逆轨道总数N(n)随求逆次数n而变化的递推公式。借此解析地求得了在倍周期区中h(f)≡0;在U序列RLR²¹的m=3+2l周期点上h(f)=logα_mp,其中α_mp为方程α^m-2α^m-2-1=0的最大实根;在2^j-1常和2j带交界处h_j(f)=(1/2)^jlog2,由此可得聚点μ_∞处拓扑熵的标度指数t=0.449806…。在此基础上,我们还求得了混沌区的周期窗口,U序列RL^aR^b所对应的各点处的拓扑熵,以及h_R*Q(f)=(1/2)h_Q(f)的关系。证明是在M.S.S.规则和“*”乘法则的基础上进行的。所以本文的结果对一维单峰映象是普适的。 关键词：     

Multiple Devil's staircase in a discontinuous circle map

The multiple Devil's staircase, which describes phase-locking behavior, is observed in a discontinuous nonlinear circle map. Phase-locked steps form many towers with similar structure in winding number(W)-parameter(k) space. Each step belongs to a certain period-adding sequence that exists in a smooth curve. The Collision modes that determine steps and the sequence of mode transformations create a variety of tower structures and their particular characteristics. Numerical results suggest a scaling law for the width of phase-locked steps in the period-adding (W=n/(n+i), n,i∈int) sequences, that is, Δk(n)∝n^-τ (τ>0). And the study indicates that the multiple Devil's staircase may be common in a class of discontinuous circle maps.     

The transition from simple to fractal basin boundary structure displayed by unimodal maps

One-dimensional unimodal maps of the form X_{n + 1} = F (r, x_n) exhibit periodic orbits, or p-cycles, confined within specific values of the control parameter r. For any p-cycle almost all initial conditions x_O will iterate to one of attracting fixed points of the map under iteration of the pth iterate of the map F^(p). The basin boundaries which confine points attracted to the fixed points are simple or fractal depending upon whether the cycle is a member of the period doubling cascade or is a cycle in the aperiodic region beyond the period doubling accumulation point. The topology of these basin structures and the transition from simple to fractal behaviour is analyzed as a function of control parameter in terms of a scenario which parallels that of the progression from period doubling to the aperiodic regime.     

Fractal basin boundary in dynamical systems and the Weierstrass-Takagi functions

It is shown that the basin boundary of the complex maps Z_n+1 = Z^q_n + C (q⩾2 is an integer and |C| ⪡ 1) is expressible with the Weierstrass function which is continuous but nowhere differentiable. The relation between the Weierstrass function and the Takagi function is discussed, and these functions are extended in a general situation. The fractal basin boundaries expressed by the generalized Weierstrass-Takagi functions are investigated.     

Definition and statistical distributions of a topological number in the lattice O(3) σ-model

We define a topological number Q for spin fields on a two-dimensional lattice. Q assumes integer values only and reduces to the well-known winding number in the classical continuum limit. A Monte Carlo measurement of the topological susceptibility χ_t = 〈Q²〉 / volume on a 100 × 100 lattice reveals that it decreases exponentially with increasing β( = inverse bare coupling constant). The corresponding prediction of the perturbative renormalization group is not matched, however.     

Zeroes of chromatic polynomials: A new approach to Beraha conjecture using quantum groups

The number of colourings of a graphG withQ or fewer colors is a polynomial inQ known as the chromatic polynomialP _G (Q). It coïncides with the partition functionF _G of theQ state Potts model onG at zero temperature and in the antiferromagnetic regimee ^K =0. In the planar case, the Beraha conjecture particularizes the numbers \(B_n = 4\cos ^2 \frac{\pi }{n}\) as possible accumulation points of real zeroes ofP _G in the infinite graph limit. We suggest in this work an approach based on recent developments of quantum groups to handle this conjecture. For the square, triangular and honeycomb lattices and systems wrapped on a cylinderl×t, we first exhibit in the (Q, e ^K ) Potts parameter space a critical line, whereF _G(Q,e ^K) has real zeroes converging to and only to theB _n 's asl, t→∞. The analysis is based on the vertex representation of theQ state Potts model, quantum algebraU _qSl (2) properties forq a root of unity, and conformal invariance.U _qSl (2) symmetry is present for anye ^K , including the chromatic polynomial casee ^K =0. Using an additional hypothesis on the eigenvalues structure and knowledge of the Potts parameter space, we then argue that forP _G (Q), real zeros occur and converge toB _n 's, 2≦n≦n ₀ only, wheren ₀ depends on the lattice. Extensions to other kinds of graphs and size dependence of the zeros are discussed. Finally physical applications are also mentioned.     

A radiochemical study on the existence of dineutron

A radiochemical study has been made to search for dineutron² n produced in the simultaneous two-neutron emission of the excited⁶He nuclei,⁶He^*, induced in the reaction of⁹Be+n→-⁶He^*+α with fast neutrons in a reactor. It was attempted to detect the radio-activity of²⁸Mg as a product of the reaction² n+²⁷Al→²⁸Mg+p. The²⁸Mg radioactivity observed in heterogeneous samples composed of the² n-producing target Be and the² n-detecting target Al separately was not found to be more than that of a side reaction,²⁷Al{(n, p)(n _th, γ)+(n _th, γ)(n, p)}²⁸Mg, whereas it clearly exceeded that of the side reaction in alloy samples made of Be and Al metals. The former experiment gives an upper limit of the production rate of the dineutron in the bound state 1×10^?7 per event of the simultaneous two-neutron emission. A tentative explanation for the excessive²⁸Mg radioactivity observed in the latter experiment is the following two-step process,⁹Be+n→⁶He+α and²⁷Al+⁶He→+²⁸Mg+α+p, rather than the process induced by the dineutron in a virtual state.     

Study of neutron induced charged particle reactions on 40K: (I). Thermal neutrons

The (n_th, α) (n_th, p) and (n_th, γα) reactions spectroscopical data are reported on ⁴⁰K and ¹⁴³Nd. For ⁴⁰K, values of σ_α = 0.39 ± 0.08 b, σ_p = 4.4 ± 0.9 b, σ_γα = 26 ± 4 mb are obtained and accurate measurements of E_α0 = 3491.7 ± 7 keV and E_po = 2232.9 ± 3 keV have been performed, α₁, and p₁ transitions and the ⁴⁰K(n_th, γp) reaction have not been observed. The ⁴⁰K(n_th, γα)³⁷Cl and ¹⁴³Nd(n_th, γα)¹⁴⁰Ce spectra are presented. The multipolarity of the primary low energy γ-rays is deduced from the γ-α spectra.     

键电导宽分布的等级网络

研究了等级模型分形网络在键电导指数型宽分布g=g₀e^Wx情形下的一些标度行为,分析了无序宽度w对总电阻和分布矩的影响,得到了相应的普适曲线.可以认为这是无序宽度和网络大小之间竞争效应的一个渡越行为.本文的结果和Tong等对Sierpinski蜂巢网络的数值模拟是一致的。     

Topological vacuum structure of a latticeCP 3-model onT 2 andS 2

The topological susceptibility 〈Q _t ² 〉/V is computed for theCP ³-model appropriately discretized on simplicial lattices onT ² andS ², respectively. We concentrate on volumes 1?V/ξ²?100, ξ being the correlation length measured onT ². Approximate scaling behaviour is found presumably not related to the continuum limit but rather to the occurence of dislocations. We observe finite-size effects which are fairly weak on the sphere, however.     

A study of QCD scaling violations by direct resolution of Altarelli-Parisi type equations

We present a detailed study of scaling violations for non-singlet, singlet and glue distribution functions in the framework of several approximation schemes of QCD. Our formalism consists of direct resolution of the Altarelli-Parisi type equations and leads to a simple exponential form for the function q(x, Q²). This form is very suitable for the analysis of experimental data and for the exploration of different evolution schemes. In particular, we examine the implications on the QCD scaling parameter Λ and the gluon parameter n_G.     

Microwave Fractal Bandpass Filters Based on Modified Hilbert Curves of the First and the Second Orders

The microwave fractal bandpass filters based on modified Hilbert shaped curves of the first and second fractal orders are experimentally and numerically analyzed. As a substrate Al₂O₃ ceramic covered by the thin silver layer with thickness of 50 μm was used. The laser patterning technique was used to design the structures of filters. The filter based on the Hilbert curve of the first order has resonance at ～4.01 GHz, while the filter based on the second order Hilbert curve has resonances at ～3.09 and ～6.34 GHz. The estimated loaded Q-factor of the filter based on the first order Hilbert curve was ～94. The electromagnetic field distribution of the filter was visualized by using the thermo-elastic optical indicator microscopy.     

On theg-value shift and intersystem crossing in photo-excited radical-triplet systems

The electron paramagnetic resonance (EPR) signals of photoexcited quartet (Q₁) states for zinc(II) tetra-tert-butyl-phthalocyanine (ZnPc) ligated by 3- and 4-(N-nitronyl-nitroxide) pyridine radicals (3-NOPy, 4-NOPy) were observed in toluene solution at room temperature by means of X-band (9.4 GHz) time-resolved EPR (TREPR) spectroscopy. Theg values of Q₁ in the ZnPc-3-NOPy and ZnPc-4-NOPy complexes were found to beg=2.0025 andg=2.0036, respectively. The obtainedg value (2.0036) for ZnPc-4-NOPy is in good agreement with the value (g=2.0037) of the Q₁ state calculated under the strong-exchange limit. Theg value (2.0025) is just an average of the Q₁ and D₁ (g=2.0013) states for ZnPc-3-NOPy. Theg value of Q₁ for zinc(II) meso-tetraphenylporphine (ZnTPP) ligated by 3-NOPy showed a slight shift (g=2.0027) at X-band and no shift (g=2.0031) at W-band from the calculatedg value (g=2.0031) (J. Fujisawa, Y. Iwasaki, Y. Ohba, S. Yamauchi, K. Koga, S. Karasawa, M. Fuhs, K. Möbius, S. Weber, Appl. Magn. Reson. 21, 483–493, 2001). These changes in theg value were found to originate from an averaging of the TREPR spectra over the Q₁ and photoexcited doublet (D₁) states via a fast intersystem crossing (ISC) process. The ISC rates between these two states were estimated by means of numerical calculations with the modified Bloch equations as 1.2·10⁸ and 6·10⁷ s^?1 for the ZnTPP-3-NOPy complex at the X- and W-bands, respectively. The lower limit of the ISC rate was obtained as 10⁹s^?1 for the ZnPc-3-NOPy complex and the higher limit was found to be 3.1·10⁸ s^?1 for the ZnPc-4-NOPy complex.