Density matrix of a quantum field in a particle-creating background

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark–gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.     

Dynamics and nonlinearities of the BOLD response at very short stimulus durations

In designing a functional imaging experiment or analyzing data, it is typically assumed that task duration and hemodynamic response are linearly related to each other. However, numerous human and animal studies have previously reported a deviation from linearity for short stimulus durations (<4 s). Here, we investigated nonlinearities of blood-oxygenation-level-dependent (BOLD) signals following visual stimulation of 5 to 1000 ms duration at two different luminance levels in human subjects. It was found that (a) a BOLD response to stimulus durations as short as 5 ms can be reliably detected; this stimulus duration is shorter than employed in any previous study investigating BOLD signal time courses; (b) the responses are more nonlinear than in any other previous study: the BOLD response to 1000 ms stimulation is only twice as large as the BOLD response to 5 ms stimulation although 200 times more photons were projected onto the retina; (c) the degree of nonlinearity depends on stimulus intensity; that is, nonlinearities have to be characterized not only by stimulus duration but also by stimulus features like luminance. These findings are especially of most practical importance in rapid event-related functional magnetic resonance imaging (fMRI) experimental designs. In addition, an 'initial dip' response--thought to be generated by a rapid increase in cerebral metabolic rate of oxygen metabolism (CMRO2) relative to cerebral blood flow--was observed and shown to colocalize well with the positive BOLD response. Highly intense stimulation, better tolerated by human subjects for short stimulus durations, causes early CMRO2 increase, and thus, the experimental design utilized in this study is better for detecting the initial dip than standard fMRI designs. These results and those from other groups suggest that short stimulation combined with appropriate experimental designs allows neuronal events and interactions to be examined by BOLD signal analysis, despite its slow evolution.     

Experimental and numerical simulation of effects of CO2/N2 concentration and initial temperature on combustion characteristics of biomass syngas

Biomass syngas is a form of renewable energy with very broad application prospects, and it has different combustion characteristics according to the fuel composition and processing technology of biomass syngas. The influence of combustion composition, diluent and temperature variation on combustion characteristics were studied in this paper. The FFCM-1 mechanism was used to investigate the combustion characteristics of CO/CH₄/H₂ under varied diluents CO₂/N₂ and temperature by using spherical expansion flame method and ANSYS CHEMKIN-PRO. The experimental laminar burning velocity was compared with the simulation results of FFCM-1 mechanism. The results reveal that the experimental data are in good agreement with the simulation results, which are somewhat different under the condition of rich fuel. The laminar burning velocity decreases significantly with the increase of diluent CO₂/N₂, with the effect of diluent CO₂ being more significant. The laminar burning velocity increase dramatically with the increase of initial temperature, and the adiabatic flame temperature also decreases with the increase of diluent. The reduction caused by diluent CO₂ is much larger than that caused by diluent N₂. The change of initial temperature also affects the adiabatic flame temperature, but the range of variation is not as pronounced as that of diluent. Not only was the interaction between the combustion characteristics of CO/CH₄/H₂ under different diluents and temperature changes explored in this paper, but the influence mechanism was also revealed in depth.     

Exploring mathematical connections of pre-university students through tasks involving rates of change

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration.     

On the Cauchy problem for higher-order nonlinear dispersive equations

We study the higher-order nonlinear dispersive equation

     

pH-sensing properties of PbO<Subscript>2</Subscript> thin film electrodeposited on carbon ceramic electrode

In this paper, a new highly sensitive potentiometric pH electrode is proposed based on the solid-state PbO₂ film electrodeposited on carbon ceramic electrode (CCE). Two different crystal structures of PbO₂, α and β were examined and the similar results were obtained. Moreover, the experimental results obtained for the proposed pH sensor and a conventional glass pH electrode were in good agreement. The electromotive force (emf) signal between the pH-sensitive PbO₂-coated CCE and SCE reference electrode was linear over the pH range of 1.5–12.5. Near-Nernstian slopes of −64.82 and −57.85 mV/pH unit were obtained for α- and β-PbO₂ electrodes, respectively. The interferences of some mono-valence and multi-valence ions on potentiometric response of the sensor were studied. The proposed pH sensor displayed high ion selectivity with respect to K⁺, Na⁺, Ca²⁺, and Li⁺, with log values around −12 and has a working lifetime of about 30 days. Key parameters important for the pH sensor performance, including kind of PbO₂ film, selectivity, response time, stability, and reproducibility, have been characterized. The proposed electrode showed a good efficiency for direct pH-metry after calibration and pH-metric titrations without calibration step. The response time was about 1 s in acidic medium and less than 30 s in alkaline solutions. The pH values of complex matrix samples such as fruit juices measured by the proposed sensor and a conventional glass pH electrode were in good agreement.     

Kinetic spectrophotometric determination of submicromolar orthophosphate by molybdate reduction

A kinetic spectrophotometric procedure was developed for determination of submicromolar orthophosphate based on the reaction in which orthophosphate serves as a catalyst in the reduction of molybdenum, and the initial rate of molybdenum-blue formation (λ_max = 780 nm) is proportional to the concentration of orthophosphate in the samples. The detection limit (3 × standard deviation of blank, n = 8) was 6 nM and the linear calibration ranged from 10 to 100 nM (r² = 0.997). The precisions of this method were 3.3% at 10 nM and 5.4% at 50 nM (n = 8), respectively. Similar to other molybdate based methods, silica and arsenate in the samples can interfere with phosphate determination. The responses of silicate and arsenate were about 25% and 7% of that of orthophosphate, respectively, and their interferences were enhanced in the presence of phosphate in the samples due to the synergistic effect of phosphate with arsenate or silicate on the molybdate reagent.     

New figuring model based on surface slope profile for grazing‐incidence reflective optics

Surface slope profile is widely used in the metrology of grazing‐incidence reflective optics instead of surface height profile. Nevertheless, the theoretical and experimental model currently used in deterministic optical figuring processes is based on surface height, not on surface slope. This means that the raw slope profile data from metrology need to be converted to height profile to perform the current height‐based figuring processes. The inevitable measurement noise in the raw slope data will introduce significant cumulative error in the resultant height profiles. As a consequence, this conversion will degrade the determinism of the figuring processes, and will have an impact on the ultimate surface figuring results. To overcome this problem, an innovative figuring model is proposed, which directly uses the raw slope profile data instead of the usual height data as input for the deterministic process. In this paper, first the influence of the measurement noise on the resultant height profile is analyzed, and then a new model is presented; finally a demonstration experiment is carried out using a one‐dimensional ion beam figuring process to demonstrate the validity of our approach.     

Relationships between different types of initial conditions for simultaneous root finding methods

The construction of initial conditions of an iterative method is one of the most important problems in solving nonlinear equations. In this paper, we obtain relationships between different types of initial conditions that guarantee the convergence of iterative methods for simultaneously finding all zeros of a polynomial. In particular, we show that any local convergence theorem for a simultaneous method can be converted into a convergence theorem with computationally verifiable initial conditions which is of practical importance. Thus, we propose a new approach for obtaining semilocal convergence results for simultaneous methods via local convergence results.