Partonske raspodjele u nukleonu na osnovi relativističkog modela neovisnih kvarkova

At a low resolution scale with Q2 = µ2 corresponding to the nucleon bound state, deep inelastic unpolarized structure functions F1(x, µ2) and F2(x, µ2) are derived, with correct support using the symmetric part of the hadronic tensor under some simplifying assumptions in the Bjorken limit. For doing this, the nucleon in its ground state has been represented by a suitably constructed momentum wave packet of its valence quarks in their appropriate SU(6) spin flavour configuration, with the momentum probability amplitude taken phenomenologically in reference to the independent quark model of scalar-vector harmonic potential. The valence quark distribution functions uv(x, µ2) and dv(x, µ2), extracted from the structure function F1(x, µ2) in a parton model interpretation, satisfy normalization constraints as well as the momentum sum-rule requirements at a bound state scale of µ2 = 0.1 GeV2. QCD evolution of these distribution functions taken as the inputs, yields at Q2 0 = 15 GeV2, xuv(x, Q2 0) and xdv(x, Q2 0) in good qualitative agreement with the experimental data. The gluon distribution G(x, Q2 0) and the sea-quark distribution qs(x, Q2 0), which are dynamically generated using the leading order renormalization group equation, also match reasonably well with the available experimental data.Upotrebom simetričnog dijela hadronskog tenzora, uz pojednostavljenje u Bjorkenovoj granici, izveli smo duboko-neelastične strukturne funkcije bez polarizacije F1(x, µ2) i F2(x, µ2) za slabo razlučivanje sa Q2 = µ2, što odgovara vezanom nukleonskom stanju. Nukleon se u svom osnovnom stanju predstavlja pogodno odabranim impulsnim valnim paketom svojih valentnih kvarkova u prikladnom SU(6) spinskom okusnom sklopu, a impulsne amplitude vjerojatnosti uzimaju se fenomenološki prema modelu neovisnih kvarkova skalarno-vektorskog harmoničkog potencijala. Iz strukturne funkcije F1(x, µ2) izvode se funkcije raspodjele valentnih kvarkova uv(x, µ2) i dv(x, µ2) u partonskom modelu, i one zadovoljavaju uvjete normalizacije i impulsnog zbrojnog pravila na ljestvici vezanja µ2 = 0.1 GeV2. Polazeći od tih funkcija za Q2 0 = 15 GeV2, QCD razvoj daje xuv(x, Q2 0) i xdv(x, Q2 0), u dobrom skladu s mjernim podacima. Gluonska G(x, Q2 0) i kvarkovska qs(x, Q2 0) raspodjela tvore se dinamički upotrebom jednadžbe renormalizacijske grupe u prvom redu i također se dobro slažu s mjernim podacima

Partonske raspodjele u nukleonu na osnovi relativističkog modela neovisnih kvarkova

At a low resolution scale with Q2 = µ2 corresponding to the nucleon bound state, deep inelastic unpolarized structure functions F1(x, µ2) and F2(x, µ2) are derived, with correct support using the symmetric part of the hadronic tensor under some simplifying assumptions in the Bjorken limit. For doing this, the nucleon in its ground state has been represented by a suitably constructed momentum wave packet of its valence quarks in their appropriate SU(6) spin flavour configuration, with the momentum probability amplitude taken phenomenologically in reference to the independent quark model of scalar-vector harmonic potential. The valence quark distribution functions uv(x, µ2) and dv(x, µ2), extracted from the structure function F1(x, µ2) in a parton model interpretation, satisfy normalization constraints as well as the momentum sum-rule requirements at a bound state scale of µ2 = 0.1 GeV2. QCD evolution of these distribution functions taken as the inputs, yields at Q2 0 = 15 GeV2, xuv(x, Q2 0) and xdv(x, Q2 0) in good qualitative agreement with the experimental data. The gluon distribution G(x, Q2 0) and the sea-quark distribution qs(x, Q2 0), which are dynamically generated using the leading order renormalization group equation, also match reasonably well with the available experimental data.Upotrebom simetričnog dijela hadronskog tenzora, uz pojednostavljenje u Bjorkenovoj granici, izveli smo duboko-neelastične strukturne funkcije bez polarizacije F1(x, µ2) i F2(x, µ2) za slabo razlučivanje sa Q2 = µ2, što odgovara vezanom nukleonskom stanju. Nukleon se u svom osnovnom stanju predstavlja pogodno odabranim impulsnim valnim paketom svojih valentnih kvarkova u prikladnom SU(6) spinskom okusnom sklopu, a impulsne amplitude vjerojatnosti uzimaju se fenomenološki prema modelu neovisnih kvarkova skalarno-vektorskog harmoničkog potencijala. Iz strukturne funkcije F1(x, µ2) izvode se funkcije raspodjele valentnih kvarkova uv(x, µ2) i dv(x, µ2) u partonskom modelu, i one zadovoljavaju uvjete normalizacije i impulsnog zbrojnog pravila na ljestvici vezanja µ2 = 0.1 GeV2. Polazeći od tih funkcija za Q2 0 = 15 GeV2, QCD razvoj daje xuv(x, Q2 0) i xdv(x, Q2 0), u dobrom skladu s mjernim podacima. Gluonska G(x, Q2 0) i kvarkovska qs(x, Q2 0) raspodjela tvore se dinamički upotrebom jednadžbe renormalizacijske grupe u prvom redu i također se dobro slažu s mjernim podacima

Heat and mass transfer on MHD flow through a porous medium over a stretching surface with heat source

An attempt has been made to study the heat and mass transfer effect on the flow over a stretching sheet in the presence of a heat source. The novelty of the present study is to consider the span wise variation of magnetic field strength, heat source and heat flux. It is also considered the effect of viscous dissipation. The method of solution involves similarity transformation which leads to an exact solution of velocity field. The coupled non-linear and non homogeneous heat equation has been solved by applying Kummer’s function. The non-homogeneity of the heat equation is contributed by the consideration of viscous dissipative energy. KYEWORDS: Heat source, Viscous dissipation, Porous medium, Kummer’s function

Brackish Water Aquaculture

About 75 per cent of the world production of farmed shrimp comes from Asian countrie

Langevin dynamics with dichotomous noise; direct simulation and applications

We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on Fokker-Planck description. We present a method for direct numerical simulation of dichotomous noise to solve the Langevin equation. The method is applied to calculate nonequilibrium fluctuation induced current in a symmetric periodic potential using asymmetric dichotomous noise and compared to Fokker-Planck-Master equation based algorithm for a range of parameter values. Our second application concerns the study of resonant activation over a fluctuating barrier.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen

Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero

We find necessary conditions for every solution of the neutral delay difference equation Δ(rnΔ(yn−pnyn−m))+qnG(yn−k)=fn to oscillate or to tend to zero as n→∞, where Δ is the forward difference operator Δxn=xn+1−xn, and pn, qn, rn are sequences of real numbers with qn≥0, rn>0. Different ranges of {pn}, including pn=±1, are considered in this paper. We do not assume that G is Lipschitzian nor nondecreasing with xG(x)>0 for x≠0. In this way, the results of this paper improve, generalize, and extend recent results. Also, we provide illustrative examples for our results