Influence of structure disorders and temperaturesof systems on the bio-energy transport in proteinmolecules (Ⅱ)

The influence of molecular structure disorders and physiological temperature on the states and properties of solitons as transporters of bio-energy are numerically studied through the fourth-order Runge-Kutta method and a new theory based on my paper [Front. Phys. China, 2007, 2(4): 469]. The structure disorders include fluctuations in the characteristic parameters of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the chain-chain interaction coefficient among the three channels and ground state energy resulting from the disorder distributions of masses of amino acid residues and impurities. In this paper, we investigate the behaviors and states of solitons in a single protein molecular chain, and in α-Helix protein molecules with three channels. In the former we prove first that the new solitons can move without dispersion, retaining its shape, velocity and energy in a uniform and periodic protein molecule. In this case of structure disorder, the fluctuations of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the ground state energy and the disorder distributions of masses of amino acid residues of the proteins influence the states and properties of motion of solitons. However, they are still quite stable and are very robust against these structure disorders, even in the presence of larger disorders in the sequence of masses, spring constants and coupling constants. Still, the solitons may disperse or be destroyed when the disorder distribution of the masses and fluctuations of structure parameters are quite great. If the effect of thermal perturbation of the environment on the soliton in nonuniform proteins is considered again, it is still thermally stable at the biological temperature of 300 K, and at the longer time period of 300 ps and larger spacing of 400 amino acids. The new soliton is also thermally stable in the case of motion over a long time period of 300 ps in the region of 300–320 K under the influence of the above structure disorders. However, the soliton disperses in the case of a higher temperature of 325 K and in larger structure disorders. Thus, we determine that the soliton’s lifetime and critical temperature are 300 ps and 300–320 K, respectively. These results are also consistent with analytical data obtained via quantum perturbed theory. In α-Helix protein molecules with three channels, results obtained show that these structure disorders and quantum fluctuations can change the states and features of solitons, decrease their amplitudes, energies and velocities, but they still cannot destroy the solitons, which can still transport steadily along the molecular chains while retaining energy and momentum when the quantum fluctuations are small, such as in structure disorders and quantum fluctuations of and and . Therefore, the solitons in the improved model are quite robust against these disorder effects. However, the solitons may be dispersed or disrupted in cases of very large structure disorders. When the influence of temperature on solitons is considered, we find that the new solitons can transport steadily over 333 amino acid residues in the case of motion over a long time period of 120 ps, and can retain their shapes and energies to travel forward along protein molecules after mutual collision of the solitons at the biological temperature of 300 K. Therefore, the soliton is also very robust against thermal perturbation of the α-helix protein molecules at 300 K. However, the soliton disperses in cases of higher temperatures at 325 K and in larger structure disorders. Thus, their critical temperature is about 320 K. When the effects of structure disorder and temperature are considered simultaneously, the soliton has high thermal stability and can transport for a long time along the protein molecular chains while retaining its amplitude, energy and velocity, even though the fluctuations of the structure parameters and temperature of the medium increase continually. However, the soliton disperses in the larger fluctuations of and at T=300 K, and at temperatures higher than 315 K when the fluctuations are and . This means that the critical temperature of the soliton is only 315 K in this condition. In a word, we can conclude from the above investigations that the soliton in the improved model is very robust against the structure disorders and thermal perturbation of proteins at the biological temperature of 300 K in α-helix protein molecules, and is a possible bio-energy transport carrier; the improved model is a possible candidate for the mechanism of this transport.      

Alternative technique for Standard Model estimation of the rare kaon decay branchings \left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM}

We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ _t≡V _tdV _ts ^* of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? _K|, the CP-violating parameter describing K mixing, and a _ψ,K , the CP-violating asymmetry in B _d ⁰ → J/ψK ⁰ decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V _cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ _t with additional data from $\Delta m_{B_d } $ and |V _ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ .     

Hadronic corrections to QCD sum rules and light quark masses

A parametrization of theJ ^p =0^? hadronic continuum, in the framework of Extended PCAC, is discussed with emphasis on finite-width effects and on the constraints imposed by the correct threshold behavior of the pion spectral function. As an application light quark masses are calculated using both Hilbert and Laplace transform QCD sum rules. The results for the runing quark masses are: \((\bar m_u + \bar m_d )|_{1 Gev} = 16 \pm 2 MeV,(\bar m_u + \bar m_s )|_{1 Gev} = 199 \pm 27 MeV\) , and a ratio \(R \equiv 2(\bar m_u + \bar m_s )/(\bar m_u + \bar m_d )_{1 Gev} = 25 \pm 4\) .     

Dispersionskorrektur Δf′ für Nickel nahe derK-absorptionskante

Employing an X-ray interferometer the dispersion correction Δf′ of the forward atomic scattering amplitude \(f = z + \Delta f' + \Delta f''\) of Nickel is measured using CuK \(\bar \alpha \) -radiation. Since \(\lambda _{CuK\bar \alpha } /\lambda _{K - edge Ni} = 1.037 \approx 1\) a value of Δf′ close to theK-absorption edge is obtained. The result $$\Delta f\prime = - 1.45 \pm 7.6\% $$ is compared with experimental values by Doan, Kiessing and Lameris and Prins and also theoretical values by Hönl, Dauben and Templeton and Cromer. The present value is considerably smaller than all theoretical estimates. It is the most accurate value measured so far and-except for the value measured by Kiessing-aggrees with the other experimental values within their (comparatively large) error limits.     

Charged particle induced ternary fission

Ternary fission has been investigated by irradiating a natural uranium target with 13.5 MeV deuterons. The energy and angular distributions of ternary alpha particles do not differ from those observed in spontaneous or thermal neutron induced fission. The angle between alpha particles and light fragments has a most probable value of \(\bar \vartheta _{\ell f - \alpha } = 82.1 \circ \pm 0.6 \circ \) with a dispersion (FWHM) of \(\Delta \vartheta = 18.4 \circ \pm 1.2 \circ \) . The corresponding values of the energy distribution are \(\bar E\alpha \) =(14.8 ±0.5)MeV and ΔE(FWHM)= (9.1±1.1)MeV. The peak-to-valley ratio of the ternary fission fragment mass distribution is found to increase with increasing alpha energy. For near-symmetric mass division a strong broadening of the angular distribution is observed.     

Absence of classical lumps

Solutions of the equations of classical Yang-Mills theory in four dimensional Minkowski space are studied. It is proved (Theorem 1) that there is no finite energy (nonsingular) solution of the Yang-Mills equations having the property that there exists ?,R,t ₀>0 such that $$E_R (t) = \int\limits_{|\bar x| \leqq R} {\theta _{00} (t,\bar x)d^3 \bar x \geqq \varepsilon foreveryt > t_0 ,} $$ \(\theta _{00} (\bar x,t)\) being the energy density. Previously known theorems on the absence of finite energy nonsingular solutions that radiate no energy out to spatial infinity are particular cases of Theorem 1. The result stated in Theorem 1 is not restricted to the Yang-Mills equations. In fact, it extends to a large class of relativistic equations (Theorem 2).     

Peculiarities of the electronic structure of Yb, In, Ag, and Cu in the heavy-fermion system YbIn1−x AgxCu4

The method of x-ray spectral line displacement is used for studying the electronic structure, i.e., the population of the 4f shell of Yb, 5s shells of In and Ag, and 4s shell of Cu, in the YbIn_1?x Ag_xCu₄ heavy-fermion system (0≤x≤1, T=300 K; T=77, 300, and 1000 K for YbIn_0.7Ag_0.3Cu₄). It is shown that Yb is in a state with fractional valence whose value is independent of x (or on the type of the partner, i.e., In and Ag) in the entire range of compositions and is equal to $\bar m = 2.91 \pm 0.01$ at T=300 K. An increase in the population of the In s states of In, Ag, and Cu (as compared to metals) is observed: $\overline {\Delta n_s } (In) = 0.65 \pm 0.05 el/at$ , $\overline {\Delta n_s } (Ag) = 0.71 \pm 0.09 el/at$ , and $\overline {\Delta n_s } (Cu) = 0.08 \pm 0.02 el/at$ . A practically linear decrease in the valence of Yb to the value m(T=1000 K)=2.81±0.02 is observed in YbIn_0.7Ag_0.3Cu₄ upon an increase in temperature from T=77 to 1000 K.     

QCD calculation ofB \to \pi l\bar v_l and the matrix element |V bu|

Using QCD sum rules for a two-point function involving beauty vector currents, together with current algebra-PCAC sum rules, we estimate the hadronic matrix element in \(B \to \pi l\bar v_l \) . We find \(\Gamma \left( {\bar {\rm B}^0 \to \pi ^ + l\bar v_l } \right) = \left( {1.45 \pm 0.59} \right) \times 10^{13} \left| {V_{bu} } \right|^2 s^{ - 1} \) . As a byproduct, the vector current contribution to the decay \(B \to \rho l\bar v_l \) is also estimated.     

CPT Violation in Atmospheric Neutrino Oscillation: A Two Flavour Matter Effects

We have studied CPT Violation in atmospheric neutrino oscillation considering two flavour framework with matter effects. We analyze the atmospheric neutrino data within the simplest scheme of two neutrino oscillation. We consider as special case of matter density profile, which are relevant for neutrino oscillations. In particular, we compute to constrain a specific from of CPT violation in matter by upper bound, \(|\Delta _{31}^{m}-\overline {\Delta _{31}^{m}}<<4.80\times 10^{-3}eV^{2}\) and \(|sin2\theta _{13}^{m}-sin2\bar {\theta _{13}^{m}}|<0.685.\) The dispersion relation for the CPT violation in neutrino oscillation in matter are discussed     

Remeasurement of the magnetic moment of the antiproton

A high-precision measurement of the finestructure splitting in the circular 11→10 X-ray transition of \(\bar p^{208} Pb\) was performed. The experimental value of 1199(5) eV is in agreement with QED calculations. From that value the magnetic moment of the antiproton was deduced to be ?2.8005(90)μ _nucl. With this result the uncertainty of the previous world average value was reduced by a factor of ≈2. A comparison with the corresponding quantity of the proton now yields: \({{\left( {\mu _p - \left| {\left\langle {\mu _{\bar p} } \right\rangle } \right|} \right)} \mathord{\left/ {\vphantom {{\left( {\mu _p - \left| {\left\langle {\mu _{\bar p} } \right\rangle } \right|} \right)} {\mu _p }}} \right. \kern-0em} {\mu _p }} = \left( { - 2.4 \pm 2.9} \right) \times 10^{ - 3} \) .     

Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations

The asymptotic behavior of solutions to the Cauchy problem for the equation $$i\psi _\imath = \frac{1}{2}\Delta \psi - \upsilon (\psi )\psi , \upsilon = r^{ - 1} *|\psi |^2 ,$$ and for systems of similar form, is studied. It is shown that the norms $$\parallel \psi (t)\parallel _{L_2 (|x| \leqq R)}^2 + \parallel \nabla \psi (t)\parallel _{L_2 (|x| \leqq R)}^2 $$ are integrable in time for any fixedR>0, from which it follows that $$\mathop {\lim }\limits_{t \to \infty } \parallel \psi (t)\parallel _{L_2 (|x| \leqq R)} = 0.$$ \] Nevertheless, it is established that anL ₂-scattering theory is impossible.     

Analyticity properties of the weakly coupled double-well model

In this note we study lattice Φ⁴-models with Hamiltonian $$H = \tfrac{1}{2}(\varphi , - \Delta \varphi ) + \lambda \Sigma \left( {\varphi _i^2 - \frac{{m^2 }}{{8\lambda }}} \right)^2$$ and Gaussian boundary conditions. Using the polymer expansion we obtain analyticity of the pressure and the correlation functions in the infinite volume limit in a region $$\left\{ {\left. \lambda \right| \left| \lambda \right|< \varepsilon ,\left| {arg } \right.\left. \lambda \right|< \frac{\pi }{2} - \delta } \right\}$$ for every δ>0.     

On the definition of a diffusion constant in a nonequilibrium system

A diffusion constant for electrons in a current-carrying semiconductor can be unambiguously defined in nearly uniform systems. For frequency-dependent density gradients it is $$D_{\alpha \beta } (\omega ) \equiv \int\limits_0^\infty {dt e^{i\omega t} \overline {\Delta \upsilon _\alpha (t)\Delta \upsilon _\beta (0),} } $$ where \(\overline {\Delta \upsilon _\alpha (t)\Delta \upsilon _\beta (0)} \) is the velocity correlation function with respect to the steady state in a bias field. This result has been elucidated in the relaxation approximation by different approaches to the diffusion problem. Essential for its derivation is a statistical independence assumption of space and velocities, and in order to get a classical diffusion law of Fick's type certain velocities have to be distributed according to the steady state in a bias field. Diffusion constant and noise temperature are discussed for a few band structures in the relaxation approximation.     

Universality of the Local Regime for the Block Band Matrices with a Finite Number of Blocks

We consider the block band matrices, i.e. the Hermitian matrices $H_N$ , $N=|\Lambda |W$ with elements $H_{jk,\alpha \beta }$ , where $j,k \in \Lambda =[1,m]^d\cap \mathbb {Z}^d$ (they parameterize the lattice sites) and $\alpha , \beta = 1,\ldots , W$ (they parameterize the orbitals on each site). The entries $H_{jk,\alpha \beta }$ are random Gaussian variables with mean zero such that $\langle H_{j_1k_1,\alpha _1\beta _1}H_{j_2k_2,\alpha _2\beta _2}\rangle =\delta _{j_1k_2}\delta _{j_2k_1} \delta _{\alpha _1\beta _2}\delta _{\beta _1\alpha _2} J_{j_1k_1},$ where $J=1/W+\alpha \Delta /W$ , $\alpha < 1/4d$ . This matrices are the special case of Wegner’s $W$ -orbital models. Assuming that the number of sites $|\Lambda |$ is finite, we prove universality of the local eigenvalue statistics of $H_N$ for the energies $|\lambda _0|< \sqrt{2}$ .     

The Higgs boson inclusive decay channels H \rightarrow b\bar{b} and H \rightarrow gg up to four-loop level

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, $H\rightarrow b\bar{b}$ and $H\rightarrow gg$ , up to four-loop and three-loop levels, respectively. After PMC scale setting, it is found that the conventional scale uncertainty for these two channels can be eliminated to a high degree. There is small residual initial scale dependence for the Higgs decay widths due to unknown higher-order $\{\beta _i\}$ terms. Up to four-loop level, we obtain $\Gamma (H\rightarrow b\bar{b}) = 2.389\pm 0.073 \pm 0.041$ MeV and up to three-loop level, we obtain $\Gamma (H\rightarrow gg) = 0.373\pm 0.030$ MeV, where the first error is caused by varying $M_H=126\pm 4$ GeV and the second error for $H\rightarrow b\bar{b}$ is caused by varying the $\overline{\mathrm{MS}}$ -running mass $m_b(m_b)=4.18\pm 0.03$ GeV. Taking $H\rightarrow b\bar{b}$ as an example, we present a comparison of three BLM-based scale-setting approaches, e.g. the PMC-I approach based on the PMC–BLM correspondence, the $R_\delta $ -scheme and the seBLM approach, all of which are designed to provide effective ways to identify non-conformal $\{\beta _i\}$ -series at each perturbative order. At four-loop level, all those approaches lead to good pQCD convergence, they have almost the same pQCD series, and their predictions are almost independent on the initial renormalization scale. In this sense, those approaches are equivalent to each other.     

Limit behavior of saturated approximations of nonlinear Schrödinger equation

We consider the solutionu _?(t) of the saturated nonlinear Schrödinger equation (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} u + \varepsilon \left| u \right|^{q - 1} uandu(0,.) = \varphi (.)$$ where \(N \geqslant 2,\varepsilon > 0,1 + 4/N< q< (N + 2)/(N - 2),u:\mathbb{R} \times \mathbb{R}^N \to \mathbb{C},\varphi \) , ? is a radially symmetric function inH ¹(R ^N ). We assume that the solution of the limit equation is not globally defined in time. There is aT>0 such that \(\mathop {\lim }\limits_{t \to T} \left\| {u(t)} \right\|_{H^1 } = + \infty \) , whereu(t) is solution of (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} uandu(0,.) = \varphi (.)$$ For ?>0 fixed,u _?(t) is defined for all time. We are interested in the limit behavior as ?→0 ofu _?(t) fort≥T. In the case where there is no loss of mass inu _? at infinity in a sense to be made precise, we describe the behavior ofu _? as ? goes to zero and we derive an existence result for a solution of (1) after the blow-up timeT in a certain sense. Nonlinear Schrödinger equation with supercritical exponents are also considered.     

The vector coupling α V((r) and the scales r 0, r 1 in the background perturbation theory

We study the universal static potential V _st(r) and the force, which are fully determined by two fundamental parameters: the string tension σ = 0.18 ± 0.02 GeV² and the QCD constants \(\Lambda _{\overline {MS} } (n_f )\) , taken from pQCD, while the infrared (IR) regulator M _B is taken from the background perturbation theory and expressed via the string tension. The vector couplings α _V(r) in the static potential and α _F(r) in the static force, as well as the characteristic scales, r ₁(n _f = 3) and r ₀(n _f = 3), are calculated and compared to lattice data. The result \(r_0 \Lambda _{\overline {MS} } (n_f = 3) = 0.77 \pm 0.03\) , which agrees with the lattice data, is obtained for M _B = (1.15 ± 0.02) GeV. However, better agreement with the bottomonium spectrum is reached for a smaller \(\Lambda _{\overline {MS} } (n_f = 3) = (325 \pm 15)\) MeV and the frozen value of α _V = 0.57 ± 0.02. The mass splittings \(\bar M(1D) - \bar M(1P)\) and \(\bar M(2P) - \bar M(1P)\) are shown to be sensitive to the IR regulator used. The masses M(1 ³ D ₃) = 10169(2) MeV andM(1 ³ D ₁) = 10155(3) MeV are predicted.     

Time decay of solutions to the cauchy problem for time-dependent Schrödinger-Hartree equations

We consider the time-dependent Schrödinger-Hartree equation (1) $$iu_t + \Delta u = \left( {\frac{1}{r}*|u|^2 } \right)u + \lambda \frac{u}{r},(t, x) \in \mathbb{R} \times \mathbb{R}^3 ,$$ (2) $$u(0,x) = \phi (x) \in \Sigma ^{2,2} ,x \in \mathbb{R}^3 ,$$ where λ≧0 and \(\Sigma ^{2,2} = \{ g \in L^2 ;\parallel g\parallel _{\Sigma ^{2,2} }^2 = \sum\limits_{|a| \leqq 2} {\parallel D^a g\parallel _2^2 + \sum\limits_{|\beta | \leqq 2} {\parallel x^\beta g\parallel _2^2< \infty } } \} \) . We show that there exists a unique global solutionu of (1) and (2) such that $$u \in C(\mathbb{R};H^{1,2} ) \cap L^\infty (\mathbb{R};H^{2,2} ) \cap L_{loc}^\infty (\mathbb{R};\Sigma ^{2,2} )$$ with $$u \in L^\infty (\mathbb{R};L^2 ).$$ Furthermore, we show thatu has the following estimates: $$\parallel u(t)\parallel _{2,2} \leqq C,a.c. t \in \mathbb{R},$$ and $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$