Scaling assumption for lattice animals in percolation theory

A scaling assumption for the numberg _ns of different cluster configurations with perimeters and sizen leads to the desired cluster numbers near the percolation threshold. The perimeter distribution function has a mean square width proportional ton for largen. The relation between the average perimeter and the cluster sizen for percolation has three different forms atp _c, belowp _c, and abovep _c and is closely related to the shape of the cluster size distribution.     

Continuity of percolation probability on hyperbolic graphs

LetT _k be a forwarding tree of degreek where each vertex other than the origin hask children and one parent and the origin hask children but no parent (k2). DefineG to be the graph obtained by adding toT _k nearest neighbor bonds connecting the vertices which are in the same generation.G is regarded as a discretization of the hyperbolic planeH ² in the same sense thatZ ^d is a discretization ofR ^d . Independent percolation onG has been proved to have multiple phase transitions. We prove that the percolation probabilityO(p) is continuous on [0,1] as a function ofp.     

Rich-club and page-club coefficients for directed graphs

Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed real-world networks: Arxiv High Energy Physics paper citation network, Web network (released from Google), Citation network among US Patents, and email network from a EU research institution. The results show a high correlation between rich-club and page-club ordering. For journal paper citation network, we identify both rich-club and page-club ordering, showing that “elite” papers are cited by other “elite” papers. Google web network shows partial rich-club and page-club ordering up to some point and then a narrow declining of the corresponding normalized coefficients, indicating the lack of rich-club ordering and the lack of page-club ordering, i.e. high in-degree (PageRank) pages purposely avoid sharing links with other high in-degree (PageRank) pages. For UC patents citation network, we identify page-club and rich-club ordering providing a conclusion that “elite” patents are cited by other “elite” patents. Finally, for email communication network we show lack of both rich-club and page-club ordering. We construct an example of synthetic network showing page-club ordering and the lack of rich-club ordering.     

The statistics of random directed graphs

The analysis of random graphs developed by the author, principally as a model for polymerization processes, is extended to the case of directed random graphs, with models of neural nets in mind. The principal novelty of the directed case is the representation of the partition function by a complex rather than a real integral, and the replacement of simple maxima in asymptotic evaluations by an interesting form of saddle point.     

A remark on diffusion of directed polymers in random environments

We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. Under minimal assumptions on the distribution of the environment, we prove that this system has diffusive behavior with probability one ifd>2 and <₀, where ₀ is defined in terms of the probability that the symmetric nearest neighbor random walk on thed-dimensional integer lattice ever returns to its starting point. We also obtain a precise estimate for the mean square displacement of this system.     

On the Bethe ansatz for random directed polymers

We show that the inclusion of the (gapless) center-of-mass motion together with a functional integral representation of the Bethe wave function allows one to predict exactly the critical exponents for random directed polymers in (1+1) dimensions. The corresponding amplitudes are computed; they compare satisfactorily with existing numerical data. Within a replica-symmetric theory, we find that the Green function of the polymer has the form recently proposed by Parisi.     

阀门气动噪声的振声转化计算方法

采用振动与噪声转化的方法计算气体流经阀门产生的管内气动噪声。通过推导管壁振动与管内噪声的计算公式,建立了管壁振动加速度级与管内噪声级之间的转换损失数理模型,并在低频区域,通过修正的频率因子,扩展了转换损失适用的频率范围,实现了通过阀门管内气动噪声的无损伤预测。利用实验对计算模型和方法进行了验证,结果表明,预测总声级的最大误差为0.98%,在整个频域内大约有69.3%⁷8.3%的数据预测误差在±5 dB以内,因而具有较高的精度,为阀门气动噪声的计算和分析提供了新的方法。     

基于混合映射模型的语音转换算法研究

分析了语音转换研究中使用高斯混合模型映射算法时转换特征出现过平滑的问题,认为协方差矩阵估计不准确导致的转换特征细节信息的丢失是产生过平滑问题的主要原因,提出了使用码本映射和高斯混合模型共同转换声学特征细节的混合映射算法。此外提出了利用音素信息进行快速高斯混合模型训练的训练方法。客观评价表明使用音素信息的训练方法比常规方法性能指标平均提高了12.87%,而混合映射算法在使用音素信息的训练方法基础上比传统高斯混合模型转换算法性能指标提高了27.13%     

Diffusion of directed polymers in a random environment

We consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time. In spatial dimensionsd>2, we establish that the behavior is diffusive with probability one. The diffusion constant is not renormalized by the interaction.     

Novel scaling behavior of directed polymers: Disorder distribution with long tails

We study the problem of directed polymers (DP) on a square lattice. The distribution of disorder is assumed to be independent but non-Gaussian. We show that for distributions with a power-law tailP() 1/||¹⁺ , where>2, so that the mean and variance are well defined, the scaling exponentv of the DP model depends on in a continuous fashion.     

Diffusion of directed polymers in a strong random environment

We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. It was shown by Imbrie and Spencer that in spatial dimensions three or above the behavior is diffusive if the directed polymer interacts weakly with the environment and if the random environment follows the Bernoulli distribution. Under the same assumption on the random environment as that of Imbrie and Spencer, we establish that in spatial dimensions four or above the behavior is still diffusive even when the directed polymer interacts strongly with the environment. More generally, we can prove that, if the random environment is bounded and if the supremum of the support of the distribution has a positive mass, then there is an integerd ₀ such that in dimensions higher thand ₀ the behavior of the random polymer is always diffusive.     

Nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices

We prove the moments of the directed polymer partition function GZ, using an exact position space renormalization group scheme on a hierarchical lattice. After sufficient iteration the characteristic functionf(n)=lnGZⁿ of the probability (Z) converges to a stable limitf ^*(n). For smalln the limiting behavior is independent of the initial distribution, while for largen,f ^*(n) is completely determined by it and is thus nonuniversal. There is a smooth crossover between the two regimes for small effective dimensions, and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution. For large effective dimensions there is a sharp transition between the two regimes, and analytical continuation from integer moments ton0 is not possible. Replica arguments can account for most features of the observed results.     

A model for anomalous directed percolation

We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for long-range infections which decays in d spatial dimensions as . Extensive numerical simulations are performed in order to determine the density exponent and the correlation length exponents and for various values of . We observe that these exponents vary continuously with , in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions. Received: 4 September 1998 / Accepted: 22 September 1998     

在医学物理教学中引入约化质量的一种方法

根据医学专业物理教学的特点,给出一种用形象的物理情景引入约化质量的方法．     

Sum of characteristic polynomial coefficients of cycloparaphenylene graphs as topological index

ABSTRACT

Algorithm for obtaining characteristic polynomial (CP) coefficients of an alternant edge-weighted cycle is used to arrive at the algorithm for that of the cycloparaphenylene (CPP) graphs in matrix product form. The algorithm gives a recursive relation in expressing the sum of the CP coefficients of a CPP in terms of that of its two immediately preceding analogues which ultimately ends up with the use of transfer matrix in an analytical form. The sum of CP coefficients, being combinatorial in nature, is found to be used as a topological index showing much similarity with Hosoya index (sum all matching polynomial coefficients), cardinality and number of Kekulé valence structures of CPP graphs compared to the Wiener index which is the distance sum of all pairs of vertices in the graph. The sum of CP coefficients has been found to model the physical properties like strain energy and diameter of CPPs that are verified by the respective excellent correlations.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

A new method of waveform digitization based on time-interleaved A/D conversion

Time interleaved analog-to-digital conversion （TIADC） based on parallelism is an effective way to meet the requirement of the ultra-fast waveform digitizer beyond Gsps. Different methods to correct the mismatch errors among different analog-to-digital conversion channels have been developed previously. To overcome the speed limi- tation in hardware design and to implement the mismatch correction algorithm in real time, this paper proposes a fully parallel correction algorithm. A 12-bit l-Gsps waveform digitizer with ENOB around 10.5 bit from 5 MHz to 200 MHz is implemented based on the real-time correction algorithm.     

高温高压下CeTbO3合成过程中电阻的动态测试研究

 在0.5 GPa、4.0 GPa的压力下，从室温到800 ℃的温度范围内测量了氧化物CeTbO₃、单稀土氧化物Tb₄O₇、CeO₂和摩尔比维4∶1配比的混合物CeO₂+Tb₄O₇等的电阻随温度变化关系。对这四种物质均反映出电阻随温度增加而减小的半导体特征。在压力维0.5 GPa，温度高于600 ℃时发现了混合物CeO₂+Tb₄O₇、氧化物Tb₄O₇中电阻变化的起伏。X射线衍射谱表明，对应这一电阻变化，在结构上出现了变化。结果分析表明，这一变化与Tb⁴⁺→Tb³⁺的价态变化密切相联。     

A fluorescence study on the critical exponents for the linear polymerization of butyl-methacrylate

The steady-state fluorescence (SSF) technique was used to study the sol-gel transition for the linear bulk polymerization of butyl methacrylate (BMA), carried out above the glass transition temperature of polybutylmethacrylate (PBMA) (T _g?=?20°C). Pyrene (P_y) was used as the fluorescence probe. The increase in P_y intensity was monitored during free radical polymerization of BMA by using SSF technique. Changes in the viscosity of the pregel solutions due to gel formation dramatically enhance the fluorescent yield of aromatic molecules. This effect is used to monitor the sol-gel transition of BMA, as a function of time, at various temperatures. The results are interpreted in the view of percolation theory. The gel fraction exponent β?=?0.39?±?0.02 agreed the best with the static percolation values for the linear bulk BMA polymerization carried out above T _g but weight average degree of polymerization exponent,?γ?deviated from the percolation results.     

A new method of waveform digitization based on time-interleaved A/D conversion

Time interleaved analog-to-digital conversion (TIADC) based on parallelism is an effective way to meet the requirement of the ultra-fast waveform digitizer beyond Gsps. Different methods to correct the mismatch errors among different analog-to-digital conversion channels have been developed previously. To overcome the speed limitation in hardware design and to implement the mismatch correction algorithm in real time,this paper proposes a fully parallel correction algorithm. A 12-bit 1-Gsps waveform digitizer with ENOB around 10.5 bit from 5 MHz to 200 MHz is implemented based on the real-time correction algorithm.