Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d, II: Special kinematics

Based on the method developed in [K.~H.~Phan and T.~Riemann, Phys.\ Lett.\ B {\bf 791} (2019) 257], detailed analytic results for scalar one-loop two-, three-, four-point integrals in general $d$-dimension are presented in this paper. The calculations are considered all external kinematic configurations and internal mass assignments. Analytic formulas are expressed in terms of generalized hypergeometric series such as Gauss $_2F_1$, Appell $F_1$ and Lauricella $F_S$ functions.Comment: 31 pages, references are added, typos are correcte

Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d

The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003 the solution of difference equations in the space-time dimension allowed to determine the necessary classes of special functions: self-energies need ordinary logarithms and Gauss hypergeometric functions $_2F_1$, vertices need additionally Kamp\'{e} de F\'{e}riet-Appell functions $F_1$, and box integrals also Lauricella-Saran functions $F_S$. In this study, alternative recursive Mellin-Barnes representations are used for the representation of $n$-point functions in terms of $(n-1)$-point functions. The approach enabled the first derivation of explicit solutions for the Feynman integrals at arbitrary kinematics. In this article, we scetch our new representations for the general massive vertex and box Feynman integrals and derive a numerical approach for the necessary Appell functions $F_1$ and Saran functions $F_S$ at arbitrary kinematical arguments.Comment: 9 pages, 3 table

Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$. Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at $d=4+2n$, $n$ non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.Comment: 9 pages, talk presented by TR at workshop "Matter To The Deepest", XLI International Conference on Recent Developments in Physics of Fundamental Interactions (MTTD 2017), September 3-8, 2017, Podlesice, Poland, to appear in the proceeding

POPULATION PRESSURE, MARKET ACCESS AND FOOD SECURITY IN THE UPLANDS OF NORTHERN VIETNAM: A MICRO-ECONOMIC ANALYSIS

Upland areas in Vietnam account for two-thirds of its natural area and one-third of its population. These uplands are characterized by heterogeneous and fragile ecosystems, a high incidence of poverty, severe deforestation and soil degradation. Rice is an important staple which is grown in the upland fields using shifting cultivation and in intensive lowland fields. The predominantly subsistence-oriented agricultural production system of these upland areas is undergoing intensification due to rapidly increasing population pressure. Changes in government policies regarding uplands and improvements in access to markets have led to the evolution of market-oriented production systems in some areas. In addition, rapid improvement in the productivity of lowland rice following decollectivization has also affected the use of upland areas. The paper examines the effect of population pressure and market access on cropping patterns, cropping intensity, the extent of commercialization of production systems, land and labor productivity, household food supply and the overall level of poverty. The analysis is based on a cross-sectional survey of 980 farm households from 33 communes of six provinces during the crop year 1997-98. It is hypothesized that (a) the cropping intensity is positively related to the population density and is negatively related to market access, (b) labor productivity in agriculture is higher in areas with better access to market, (c) upland rice occupies proportionately smaller area of upland as the size of the lowland holding increases, and (d) the extent of food shortage depends on land and labor endowments as well as the access to markets. Reduced-form models were used to investigate these hypotheses. Cropping intensity was found to be higher in communes with a higher population density supporting the Boserupian hypothesis. Market access, which was specified as a dummy variable (low access and high access), affected labor productivity and cash income positively. Despite these positive effects, the agricultural production system was found to be predominantly subsistence-oriented with farmers striving to achieve food self-sufficiency even in areas where a lot of cash crop is grown. The proportionate area under upland rice was found to be related negatively with the size of the lowland holding indicating that an improvement in lowland productivity can help reduce the intensification pressure in the upland. Farmers with better access to market and with larger farms were found to have a lower incidence of food shortage than farmers with limited access to markets and with smaller farms. A simulation model was developed to project the likely effect of continued increase in population pressure on food production, labor absorption in agriculture, calorie consumption per capita and the extent of poverty. A simple life table was used to project the population by sex and age group for the next 20 years. The effect of rising population pressure on food production was simulated assuming that the current agricultural productivity of different land/labor quartiles applies to the households as they move across the quartile groups. The static projection indicated that while the labor force will increase by 75% in 20 years, labor use in crop production will increase by only 9%, thus showing the need to expand labor absorption in the non-crop sector. With the existing technology, crop production will increase by only 5% of its current value leading to a dramatic decline in per capita food supply. The growth in rice yield (both upland and lowland) of at least 2% per annum is needed to maintain the current per capita calorie intake. An improvement in the upland rice yield was found to be an important strategy in reducing the poverty of the low-income quartile group that depends mostly on upland rice. Given the size of the population growth, the overall reduction in poverty will require an expansion of employment in the non-crop and non-farm sectors. The paper concludes with recommendations that include (a) further expansion of market access and development of more effective marketing institutions, (b) a regionally differentiated approach to agricultural diversification that recognizes the environmental diversity, (c) improvements in food production technology, (d) expansion of income-generating activities such as agro-processing and (e) more effective population control programs.Food Security and Poverty,

General ε\varepsilon-representation for scalar one-loop Feynman integrals

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms of higher transcendental functions. The integrals play a role as building blocks in general higher-loop or multi-leg processes. We also perform numerical checks of the calculations using AMBRE/MB and LoopTools/FF.Comment: 5 pages Latex,Contribution to the Proceedings of QCD 15, Montpellier, July 201

A Dual Resonant Transformer and a Dielectric Antenna for Picosecond Pulse Radiation

This thesis discusses the development of a pulsed power system for high power picosecond pulse radiation. In the system, a charging transformer, which generates a high voltage pulse of ~100 kV, can be used for charging a transmission line in less than 100 ns. Such a short pulse could cause a peak gap switch to break down and generate a picosecond pulse transient for radiation. A dielectric antenna, if fed with the high voltage picosecond pulses, can radiate them to targets made of high dielectric materials. Biological tissues, for instance, can be targeted for electrostimulation. The transformer was designed considering the needs to deliver a high gain and fast output. We showed that a transformer in the dual resonant mode, in which the resonance of the primary and the second is equal, can produce a voltage gain of approximately 6. The output voltage of the transformer is more than 100kV with an input of 15kV. This shows the average gain of the transformer is 7. The fast output requires the voltage at the secondary winding needs to be less than 100 ns in order for achieving a picosecond transient in the oil peak switch. This was done by low-inductance windings with an air core. Two winding configurations were explored: a cylindrical winding and a toroidal winding. The cylindrical winding appears to be a better option in terms of the gain. Experimental results show that for a capacitive load (30pF), the voltage can be charged up to 33 kV in 20 ns. A conical dielectric antenna was investigated through simulation and experiments. The antenna is made of a V-shape transmission line on a ceramic conical body with dielectric constant of 28. This antenna was immersed in transformer oil for high voltage insulation, which allowed for the feed voltage to be as high as 50 kV. The antenna was characterized by an electric field sensor immersed in water. We found that the emitted field increases as the voltage increases, but it reaches a saturation for 40 kV. The highest electric field is 1.5 kV/cm even for the input voltage 50 kV. This is 6 times less than simulation. We speculate that the discrepancy is caused by the dielectric tangent loss, which was not taken into account in the simulation. Future work towards a complete system includes a choice of a linear dielectric material which is capable of sustaining its dielectric constant for a high electric field and the study of an oil peak switch, which is a critical component between the transformer and the antenna

Framework for optimizing intelligence collection requirements

In the military, typical mission execution goes through cycles of intelligence collection and action planning phases. For complex operations where many parameters affect the outcomes of the mission, several steps may be taken for intelligence collection before the optimal Course of Action is actually carried out. Human analytics suggests the steps of: (1) anticipating plausible futures, (2) determining information requirements, and (3) optimize the choice of feasible and cost-effective intelligence requirements. This work formalizes this process by developing a decision support tool to determine information requirements needed to differentiate critical plausible futures, and formulating a mixed integer programming problem to trade-off the feasibility and benefits of intelligence collection requirements. Course of Action planning has been widely studied in the military domain, but mostly in an abstract fashion. Intelligence collection, while intuitively aiming at reducing uncertainties, should ultimately produce optimal outcomes for mission success. Building on previous efforts, this work studies the effect of plausible futures estimated based on current adversary activities. A set of differentiating event attributes are derived for each set of high impact futures, forming a candidate collection requirement action. The candidate collection requirement actions are then used as inputs to a Mixed Integer Programming formulation, which optimizes the plausible future mission state subject to timing and cost constraints. The plausible future mission state is estimated by assuming that the Collection Requirement Actions can potentially avert the damages adversary future activities might cause. A case study was performed to demonstrate several use cases for the overall framework