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Register a new userOn systematic effects in the numerical solutions of the JIMWLK equation
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In the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation. In this paper, we present a comprehensive study of systematic effects associated with the numerical framework, in particular the ones related to the inclusion of the running coupling. We consider three proposed ways in which the running of the coupling constant can be included: square root and noise prescriptions and the recent proposal by Hatta and Iancu. We implement them both in position and momentum spaces and we investigate and quantify the differences in the resulting evolved gluon distributions. We find that the systematic differences associated with the implementation technicalities can be of a similar magnitude as differences in running coupling prescriptions in some cases, or much smaller in other cases.
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Precise and detailed knowledge of the internal structure of hadrons is one of the most actual problems in elementary particle physics. In view of the planned high energy physics facilities, in particular, the Electron-Ion Collider constructed in Brookhaven National Laboratory, the Chinese Electron-Ion Collider of China, or upgrad
In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order to prevent wave breaking. Convergence is obtained when the time step is proportional to the square root of the spatial step size, which is a milder restriction than the common CFL condition for conservation laws.
The tt* equation that we will study here is classed as case 4a by Guest et al. in their series of papers Isomomodromy aspects of the tt* equations of Cecotti and Vafa. In their comprehensive works, Guest et al. give a lot of beautiful formulas on and finally achieve a complete picture of asymptotic data, Stokes data and holomorphic data. But, some of their formulas are complicated, lacking of intuitional explanation or other relevant results that could directly support them. In this paper, we will first verify numerically their formulas among the asymptotic data and Stokes data. Then, we will enlarge the solution class assumed by Guest et al. from the Stoke data side. Based on the numerical results, we put forward a conjecture on the enlarged class of solutions. At last, some trial to enlarge the solution class from the asymptotic data are done. It is the truncation structure of the tt* equation that enables us to do those numerical studies with a satisfactory high precision.
Giovanninis parton branching equation is integrated numerically using the 4th-order Runge-Kutta method. Using a simple hadronisation model, a charged-hadron multiplicity distribution is obtained. This model is then fitted to various experimental data up to the TeV scale to study how the Giovannini parameters vary with collision energy and type. The model is able to describe hadronic collisions up to the TeV scale and reveals the emergence of gluonic activity as the centre-of-mass energy increases. A prediction is made for $sqrt{s}$ = 14 TeV.
This paper presents two approaches to mathematical modelling of a synthetic seismic pulse, and a comparison between them. First, a new analytical model is developed in two-dimensional Cartesian coordinates. Combined with an initial condition of sufficient symmetry, this provides a valuable check for the validity of the numerical method that follows. A particular initial condition is found which allows for a new closed-form solution. A numerical scheme is then presented which combines a spectral (Fourier) representation for displacement components and wave-speed parameters, a fourth order Runge-Kutta integration method, and an absorbing boundary layer. The resulting large system of differential equations is solved in parallel on suitable enhanced performance desktop hardware in a new software implementation. This provides an alternative approach to forward modelling of waves within isotropic media which is efficient, and tailored to rapid and flexible developments in modelling seismic structure, for example, shallow depth environmental applications. Visual comparisons of the analytic solution and the numerical scheme are presented.
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