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Havriliak–Negami Relaxation
The Havriliak–Negami relaxation is an empirical modification of the Debye relaxation model in electromagnetism. Unlike the Debye model, the Havriliak–Negami relaxation accounts for the asymmetry and broadness of the dielectric dispersion curve. The model was first used to describe the dielectric relaxation of some polymers, by adding two exponential parameters to the Debye equation: : \hat(\omega) = \varepsilon_ + \frac, where \varepsilon_ is the permittivity at the high frequency limit, \Delta\varepsilon = \varepsilon_-\varepsilon_ where \varepsilon_ is the static, low frequency permittivity, and \tau is the characteristic relaxation time of the medium. The exponents \alpha and \beta describe the asymmetry and broadness of the corresponding spectra. Depending on application, the Fourier transform of the stretched exponential function can be a viable alternative that has one parameter less. For \beta = 1 the Havriliak–Negami equation reduces to the Cole–Cole equation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debye Relaxation
In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation. Because of dielectric polarisation, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field (for example, if the field is moving parallel to the positive ''x'' axis, the negative charges will shift in the negative ''x'' direction). This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Polymer Science Part B
''Journal of Polymer Science'' is a peer-reviewed journal of polymer science currently published in multiple parts by John Wiley & Sons. It was originally established as the ''Journal of Polymer Science'' in 1946 by Interscience Publishers and the founding editor Herman F. Mark, but it was split in various parts in 1962. The journal has undergone re-organization several times since. In 2020, the journal will consolidate in one single publication. The editor-in-chief is Ying Jia. History ;Establishment *''Journal of Polymer Science'' (1946–1962), ;First re-organization *''Journal of Polymer Science Part A: General Papers'' (1963–1965), **''Journal of Polymer Science Part A-1: Polymer Chemistry'' (1966–September 1972), **''Journal of Polymer Science Part A-2: Polymer Physics'' (1966–September 1972), *''Journal of Polymer Science Part B: Polymer Letters'' (1963–September 1972), *''Journal of Polymer Science Part C: Polymer Symposia'' (1963–1972), The coverage of bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dielectric Spectroscopy
Dielectric spectroscopy (which falls in a subcategory of impedance spectroscopy) measures the dielectric properties of a medium as a function of frequency.Kremer F., Schonhals A., Luck W. Broadband Dielectric Spectroscopy. – Springer-Verlag, 2002. It is based on the interaction of an external field with the electric dipole moment of the sample, often expressed by permittivity. It is also an experimental method of characterizing electrochemical systems. This technique measures the impedance of a system over a range of frequencies, and therefore the frequency response of the system, including the energy storage and dissipation properties, is revealed. Often, data obtained by electrochemical impedance spectroscopy (EIS) is expressed graphically in a Bode plot or a Nyquist plot. Impedance is the opposition to the flow of alternating current (AC) in a complex system. A passive complex electrical system comprises both energy dissipater (resistor) and energy storage (capacitor) eleme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mittag-Leffler Function
In mathematics, the Mittag-Leffler function E_ is a special function, a complex function which depends on two complex parameters \alpha and \beta. It may be defined by the following series when the real part of \alpha is strictly positive: :E_ (z) = \sum_^\infty \frac, where \Gamma(x) is the gamma function. When \beta=1, it is abbreviated as E_\alpha(z) = E_(z). For \alpha=0, the series above equals the Taylor expansion of the geometric series and consequently E_(z)=\frac\frac. In the case \alpha and \beta are real and positive, the series converges for all values of the argument z, so the Mittag-Leffler function is an entire function. This function is named after Gösta Mittag-Leffler. This class of functions are important in the theory of the fractional calculus. For \alpha >0 , the Mittag-Leffler function E_(z) is an entire function of order 1/\alpha, and is in some sense the simplest entire function of its order. The Mittag-Leffler function satisfies the recurrence prope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review
''Physical Review'' is a peer-reviewed scientific journal established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical Society (APS). The journal is in its third series, and is split in several sub-journals each covering a particular field of physics. It has a sister journal, ''Physical Review Letters'', which publishes shorter articles of broader interest. History ''Physical Review'' commenced publication in July 1893, organized by Cornell University professor Edward Nichols and helped by the new president of Cornell, J. Gould Schurman. The journal was managed and edited at Cornell in upstate New York from 1893 to 1913 by Nichols, Ernest Merritt, and Frederick Bedell. The 33 volumes published during this time constitute ''Physical Review Series I''. The American Physical Society (APS), founded in 1899, took over its publication in 1913 and star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fox–Wright Function
In mathematics, the Fox–Wright function (also known as Fox–Wright Psi function, not to be confused with Wright Omega function) is a generalisation of the generalised hypergeometric function ''p''''F''''q''(''z'') based on ideas of and : _p\Psi_q \left begin ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end ; z \right= \sum_^\infty \frac \, \frac . Upon changing the normalisation _p\Psi^*_q \left begin ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end ; z \right= \frac \sum_^\infty \frac \, \frac it becomes ''p''''F''''q''(''z'') for ''A''1...''p'' = B1...''q'' = 1. The Fox–Wright function is a special case of the Fox H-function : _p\Psi_q \left begin ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end ; z \right= H^_ \left \begin ( 1-a_1 , A_1 ) & ( 1-a_2 , A_2 ) & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Polymerica
Acta or ACTA may refer to: Institutions * Anti-Counterfeiting Trade Agreement, an intellectual property trade agreement * Administrative Council for Terminal Attachments, a standards organization for terminal equipment such as registered jacks * Alameda Corridor Transportation Authority, in southern California * American Council of Trustees and Alumni, an education organization * Atlantic County Transportation Authority, a transportation agency in Atlantic County, New Jersey * Australian Community Television Alliance, an industry association representing community television licensees in Australia Science and technology * Acta, the transactions (proceedings) of an academic field, a learned society, or an academic conference * Acta (software), early outliner software * Activin A, mammalian protein * ACTA1, actin alpha 1 (skeletal muscle), human protein * ACTA2, actin alpha 2 (smooth muscle), human protein * Actin assembly-inducing protein, motility protein in the bacterium ''Listeri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Chemical Physics
''The Journal of Chemical Physics'' is a scientific journal published by the American Institute of Physics that carries research papers on chemical physics."About the Journal" from the ''Journal of Chemical Physics'' website. Two volumes, each of 24 issues, are published annually. It was established in 1933 when '''' editors refused to publish theoretical works. The editors have been: *2019-present: Tim Lian *2008–2018: *2007–2008: [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Constant
Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (). It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by \log: :\begin \gamma &= \lim_\left(-\log n + \sum_^n \frac1\right)\\ px&=\int_1^\infty\left(-\frac1x+\frac1\right)\,dx. \end Here, \lfloor x\rfloor represents the floor function. The numerical value of Euler's constant, to 50 decimal places, is: : History The constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled ''De Progressionibus harmonicis observationes'' (Eneström Index 43). Euler used the notations and for the constant. In 1790, Italian mathematician Lorenzo Mascheroni used the notations and for the constant. The notation appears nowhere in the writings of either Euler or Mascheroni, and was chosen at a later time perhaps because of the constant's connection ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digamma Function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: :\psi(x)=\frac\ln\big(\Gamma(x)\big)=\frac\sim\ln-\frac. It is the first of the polygamma functions. It is strictly increasing and strictly concave on (0,\infty). The digamma function is often denoted as \psi_0(x), \psi^(x) or (the uppercase form of the archaic Greek consonant digamma meaning double-gamma). Relation to harmonic numbers The gamma function obeys the equation :\Gamma(z+1)=z\Gamma(z). \, Taking the derivative with respect to gives: :\Gamma'(z+1)=z\Gamma'(z)+\Gamma(z) \, Dividing by or the equivalent gives: :\frac=\frac+\frac or: :\psi(z+1)=\psi(z)+\frac Since the harmonic numbers are defined for positive integers as :H_n=\sum_^n \frac 1 k, the digamma function is related to them by :\psi(n)=H_-\gamma, where and is the Euler–Mascheroni constant. For half-integer arguments the digamma function takes the values : \psi \left(n+\tfrac12\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cole–Davidson Equation
The Cole-Davidson equation is a model used to describe dielectric relaxation in glass-forming liquids. The equation for the complex permittivity is : \hat(\omega) = \varepsilon_ + \frac, where \varepsilon_ is the permittivity at the high frequency limit, \Delta\varepsilon = \varepsilon_-\varepsilon_ where \varepsilon_ is the static, low frequency permittivity, and \tau is the characteristic relaxation time of the medium. The exponent \beta represents the exponent of the decay of the high frequency wing of the imaginary part, \varepsilon''(\omega) \sim \omega^. The Cole–Davidson equation is a generalization of the Debye relaxation keeping the initial increase of the low frequency wing of the imaginary part, \varepsilon''(\omega) \sim \omega. Because this is also a characteristic feature of the Fourier transform of the stretched exponential function The stretched exponential function f_\beta (t) = e^ is obtained by inserting a fractional power law into the exponential function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymmetry
Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms. The absence of or violation of symmetry that are either expected or desired can have important consequences for a system. In organisms Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension. Louis Pasteur proposed that biological molecules are asymmetric because the cosmic .e. physicalforces that preside over their formation are themselves asymmetric. While at his time, and even now, the symmetry of physical processes are highlighted, it is known that there are fundamental physical asymmetries, starting with time. Asymmetry in biology Asymmetry is an important and widespread ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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