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The family of Fokker–Planck (FP) equations has been widely used in various physical applications, especially optical physics. It has proven effective in understanding numerous nonlinear phenomena observed in optical fiber. Accordingly, we analyze the time fractional FP (FFP) equations to understand the underlying mechanics of the phenomena described by the suggested models, control the generation and propagation of these phenomena, or prevent their occurrence altogether to achieve the desired applications. Thus, in this investigation, some techniques, such as a novel technique, which is called the “Tantawy technique” and the optimal auxiliary function method (OAFM) are implemented to analyze different types of FFP equations in the framework of the Caputo operator. Using fractional calculus, we develop a complete framework for effectively managing complex diffusion processes and their corresponding probability density functions. We apply the OAFM and the “Tantawy technique” to three different models of the FFP. Some highly accurate approximations for the two models are derived and discussed numerically. The accuracy of the obtained approximations is checked by analyzing these approximations numerically and graphically using some suitable values for the related parameters. In addition, the absolute error for the obtained approximations is estimated compared to the exact solutions for the integer cases to confirm the validity and accuracy of these approximations. Moreover, the novel “Tantawy technique,” developed for the first time, is highly accurate and efficient in analyzing the most complicated and nonlinear problems. It is also far more precise than the optimal auxiliary function method. Moreover, it is characterized by extreme simplicity, high accuracy, and stability throughout the study domain, which is not achieved in many other methods. The derived approximations using the “Tantawy technique” are compared to the Laplace homotopy perturbation method.

The GridPP Collaboration is building a UK computing Grid for particle physics, as part of the international effort towards computing for the Large Hadron Collider. The project, funded by the UK Particle Physics and Astronomy Research Council (PPARC), began in September 2001 and completed its first phase 3 years later. GridPP is a collaboration of approximately 100 researchers in 19 UK university particle physics groups, the Council for the Central Laboratory of the Research Councils and CERN, reflecting the strategic importance of the project. In collaboration with other European and US efforts, the first phase of the project demonstrated the feasibility of developing, deploying and operating a Grid-based computing system to meet the UK needs of the Large Hadron Collider experiments. This note describes the work undertaken to achieve this goal.

A 21-year-old man was referred to the ear, nose and throat outpatients with a 2-month history of sore throat and a right-sided neck lump, which had persisted despite antibiotics. On direct questioning, he was found to have a long history of right-sided nasal congestion and rhinorrhoea. He had previously had a nasal polyp removed from the right side 10 years before, but with no resolution in his nasal blockage. On examination there was a 1.5 cm soft, mobile, non-tender mass in the right anterior triangle. Direct inspection of the oral cavity and oropharynx was normal, while anterior rhinoscopy revealed a deviated nasal septum to the right. Blood tests were normal and an infectious mononucleosis screen was negative.Following a further course of antibiotics, he was reviewed in clinic showing some improvement in his throat symptoms while the neck mass remained unchanged. Flexible nasendoscopy was normal on the left side, but the scope could not be passed on the right. He was offered surgery for his nasal obstruction and under general anaesthesia, a rigid scope was introduced into the right nasal cavity and the diagnosis was made. A subsequent computed tomography (CT) scan confirmed right-sided choanal atresia (Figure 1).

A15-year-old girl presented with a 3-week history of sore throat, which had been unresponsive to penicillin. She had also recently developed a painful swelling in the left side of the neck. On examination she had tonsillitis and a large tender mass in the jugulodigastric region on the left side. This was hard and non-fluctuant with no overlying cellulitis or erythema. Ultrasound confirmed cervical lymphadenitis and she was commenced on intravenous antibiotics.Despite an initial improvement in her symptoms, on the third day after admission she remained pyrexial and developed a left spastic torticollis. A computed tomography (CT) scan was performed which showed a large parapharyngeal abscess (Figure 1). This was incised and drained immediately and she was discharged home 4 days later having made an excellent recovery.A week later, however, she was reviewed in clinic and was found to have an ipsilateral Horner's syndrome. After 6 months, this has yet to recover (Figure 2).