The virial relation for the Q-balls in the thermal logarithmic potential revisited analytically

We study the properties of Q-balls dominated by the thermal logarithmic potential analytically instead of estimating the characters with only some specific values of model variables numerically. In particular the analytical expressions for radius and energy of this kind of Q-ball are obtained. According to these explicit expressions we demonstrate strictly that the large Q-balls enlarge and the small ones become smaller in the background with lower temperature. The energy per unit charge will not be divergent if the charge is enormous. We find that the lower temperature will lead the energy per unit charge of Q-ball smaller. We also prove rigorously the necessary conditions that the model parameters should satisfy to keep the stability of the Q-balls. When one of model parameters of Q-balls $K$ is positive, the Q-balls will not form or survive unless the temperature is high enough. In the case of negative $K$, the Q-balls are stable no matter the temperature is high or low.Comment: 12 pages, 2 figure

Pollutant Emissions from Biodiesels in Diesel Engine Tests and On-road Tests

Interest in biodiesel use is increasing due to concerns over the availability and environmental impact of petroleum fuels. In this study, we analyzed biodiesels prepared from seven different feedstocks: waste cooking oil, rapeseed oil, olive oil, palm oil, coconut oil, canola oil, and soybean oil. Exhaust emissions of gas-phase compounds (CO2, CO, NO2, NO, THC) and particulate matter were measured for each biodiesel and Ultra Low Sulfur Diesel (ULSD) during combustion in a diesel generator operating under different engine loads (0, 25, 50, 75, 100%). The composition of each biodiesel was also analyzed using a variety of chemical and physical tests to investigate the relationship between fuel properties and pollutant emissions. The results showed that both engine performance and biodiesel composition affected emissions levels. All brake-specific emissions decreased with increased of engine load because of high fuel efficiency at high loads. All of the biodiesels except coconut oil produced less THC emissions than ULSD, and soybean oil, palm oil, olive oil produced less CO than ULSD. Particulate matter emissions were reduced for all biodiesel fuels compared to ULSD. However, CO2 emissions from biodiesels were higher than ULSD. NO emissions from biodiesels were higher than ULSD at low load, but some of them started (ex. Palm oil) to perform better with increased load, and finally produced less NO than ULSD. All biodiesel produced less NO2 than ULSD. Considering NOx emissions in unit of g/kg fuel, NO increased and NO2 decreased with increased engine loads, resulting in highest total NOx emissions at 50% to 75% load, depending on the fuel. NO was the majority of total NOx emission. Biodiesel oxygen content was strongly correlated to PM and HC emissions. The H: C ratio, ratio of saturated fatty acids and degree of unsaturation of biodiesels all had a substantial effect on NO emissions. Density measurement was an easy way to predict total NOx from biodiesels. Methods of running on-road biodiesel truck tests and data analysis were developed. Both road condition and engine performance affected the formation of emissions. Vehicle specific power (VSP) was calculated to present real power required in on-road tests. Tests data of highways showed that CO and HC emissions (g/kg/fuel) decreased with the increase of VSP

Energy transport faster than light in good conductors and superconductors

People need a model to study tachyons whose prediction can be tested easily. The dispersion relation w^2=k^2C^2-a^2C^2 of a low-frequency electromagnetic field in good conductors is equivalent to the energy-momentum equation E^2=p^2C^2-m^2C^4 of a tachyon where the proportionality coefficient is h^2. An experiment in 1980s to measure the phase velocity Vp [1] can be regarded as an indirect evidence of the superluminal velocity V>>c of those photons just equals the rate of energy flow S/w of the field.Instability of the tachyonic field corresponds to the Joule heat. To detect the speed of energy is difficult and we plan to modulate signals to observe the information velocity (speed of points of non-analyticity)[2].Comment: 16 page

Dynamics of non-autonomous reaction-diffusion equations in locally uniform spaces

In this paper, we first prove the well-posedness for thenon-autonomous reaction-diffusion equations on the entire space $\R^N$ in thesetting of locally uniform spaces with singular initial data. Thenwe study the asymptotic behavior of solutions of such equation andshow the existence of$(H^1,q_U(\R^N),H^1,q_\phi(\R^N))$-uniform(w.r.t.g\in\mcH_L^q_U(\R^N)(g_0)) attractor\mcA_\mcH_L^q_U(\R^N)(g_0) with locally uniform externalforces being translation uniform bounded but not translation compactin $L_b^p(\R;L^q_U(\R^N))$. We also obtain the uniform attracting propertyin the stronger topology

The fate of the Q-balls with one-loop motivated effective potential revisited analytically

The analytical description on the Friedberg-Lee-Sirlin typed Q-balls is performed. The two-field Q-balls are also discussed under the one-loop motivated effective potential subject to the temperature. We prove strictly to confirm that the parameters from the potential can be regulated to lead the energy per unit charge of Q-balls to be lower to keep the model stable. If the energy density is low enough, the Q-balls can become candidates of dark matter. It is also shown rigorously that the two-field Q-balls can generate in the first-order phase transition and survive while they are affected by the expansion of the universe. The analytical investigations show that the Q-balls with one-loop motivated effective potential can exist with the adjustment of coefficients of terms. We cancel the infinity in the energy to obtain the necessary conditions consist with those imposed in the previous work. According to the explicit expressions, the lower temperature will reduce the energy density, so there probably have been more and more stable Friedberg-Lee-Sirlin typed Q-balls to become the dark matter in the expansion of the universe.Comment: 15 page