Generalised CP and Trimaximal TM1_1 Lepton Mixing in S4S_4 Family Symmetry

We construct two flavor models based on $S_4$ family symmetry and generalised CP symmetry. In both models, the $S_4$ family symmetry is broken down to the $Z^{SU}_2$ subgroup in the neutrino sector, as a consequence, the trimaximal $\text{TM}_1$ lepton mixing is produced. Depending on the free parameters in the flavon potential, the Dirac CP is predicted to be either conserved or maximally broken, and the Majorana CP phases are trivial. The two models differ in the neutrino sector. The flavon fields are involved in the Dirac mass terms at leading order in the first model, and the neutrino mass matrix contains three real parameters such that the absolute neutrino masses are fixed. Nevertheless, the flavon fields enter into the Majorana mass terms at leading order in the second model. The leading order lepton mixing is of the tri-bimaximal form which is broken down to $\text{TM}_1$ by the next to leading order contributions.Comment: 28 page

Deviation from Bimaximal Mixing and Leptonic CP Phases in S4S_4 Family Symmetry and Generalized CP

The lepton flavor mixing matrix having one row or one column in common with the bimaximal mixing up to permutations is still compatible with the present neutrino oscillation data. We provide a thorough exploration of generating such a mixing matrix from $S_4$ family symmetry and generalized CP symmetry $H_{CP}$. Supposing that $S_4\rtimes H_{CP}$ is broken down to $Z^{ST^2SU}_2\times H^{\nu}_{CP}$ in the neutrino sector and $Z^{TST^{2}U}_4\rtimes H^{l}_{CP}$ in the charged lepton sector, one column of the PMNS matrix would be of the form $\left(1/2, 1/\sqrt{2}, 1/2\right)^{T}$ up to permutations, both Dirac CP phase and Majorana CP phases are trivial in order to accommodate the observed lepton mixing angles. The phenomenological implications of the remnant symmetry $K^{(TST^2, T^2U)}_4\rtimes H^{\nu}_{CP}$ in the neutrino sector and $Z^{SU}_{2}\times H^{l}_{CP}$ in the charged lepton sector are studied. One row of PMNS matrix is determined to be $\left(1/2, 1/2, -i/\sqrt{2}\right)$, and all the three leptonic CP phases can only be trivial to fit the measured values of the mixing angles. Two models based on $S_4$ family symmetry and generalized CP are constructed to implement these model independent predictions enforced by remnant symmetry. The correct mass hierarchy among the charged leptons is achieved. The vacuum alignment and higher order corrections are discussed.Comment: 44 pages, 7 figure

A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows IV: full Boltzmann and Model Equations

Fluid dynamic equations are valid in their respective modeling scales. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the flow study in this regime. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well

Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries

We discussed the scenario that a discrete flavor group combined with CP symmetry is broken to $Z_2\times CP$ in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free parameters $\theta_{l}$ and $\theta_{\nu}$ varying in the range of $[0, \pi)$. As an example, we comprehensively study the lepton mixing patterns which can be derived from the flavor group $\Delta(6n^2)$ and CP symmetry. Three kinds of phenomenologically viable lepton mixing matrices are obtained up to row and column permutations. We further extend this approach to the quark sector. The precisely measured quark mixing angles and CP invariant can be accommodated for certain values of the free parameters $\theta_{u}$ and $\theta_{d}$. A simultaneous description of quark and lepton flavor mixing structures can be achieved from a common flavor group $\Delta(6n^2)$ and CP, and accordingly the smallest value of the group index $n$ is $n=7$.Comment: 40 pages, 8 figure

Non-renewable resources and recycling: experimental evidence

Nicht-erneuerbare oder erschöpfbare Ressourcen beziehen sich auf die Ressourcen, deren Gesamtbestand in der Erde über den für die menschliche Planung relevanten Zeitraum konstant ist. Aufgrund ihrer begrenzten Verfügbarkeit und wichtigen Anwendungen in der Entwicklung der menschlichen Gesellschaft ist ihrer Versorgungssicherheit immer mehr Aufmerksamkeit geschenkt worden. Darüber hinaus sind schlimme Umweltauswirkungen und riesige Mengen an Abfällen während der Produktions- und Verbrauchsprozesse nicht-erneuerbarer Ressourcen und Materialien entstanden. Recycling ist ein wirksamer Weg gegen diese Probleme. Ein Recyclingprozess setzt sich normalerweise aus zwei Teilen zusammen: zuerst werden die verwertbaren Materialien am Ende der Produktlebensdauer wiederverarbeiet und dann in die Lieferkette zurückgeschickt. Diese Arbeit befasst sich überwiegend mit dem Gleichgewicht eines erschöpfbaren Ressourcenmarktes mit Recyclingaktivitäten. Boyce (2012) baut ein solches Modell, das auf der berühmten Hotelling-Regel basiert. Diese Regel besagt, dass der Nettopreis, auch als Knappheitsprämie bezeichnet, einer erschöpfbaren Ressource im Laufe der Zeit mit der Zinsrate in einem wettbewerblichen Marktgleichgewicht anwachsen sollte. Seiner Ansicht nach sind Sammlungsaktivitäten nur dann wirtschaftlich, wenn der aktuelle Wert der erschöpfbaren Ressourceneinheiten die Sammlungskosten übersteigt. Die externe Validität dieses Modells wird dann durch ökonomische Laborexperimente verifiziert. In jeder Session des Basis-Treatments werden zwei exakt identische Runden (oder Märkte) zum Testen der Lerneffekte durchgeführt. In den Perioden, in denen Sammlung theoretisch wirtschaftlich ist, erscheint in den beiden Märkten die Recyclingperformance mit der Standardentwicklung übereinzustimmen. In den Perioden, in denen sich Sammlung theoretisch nicht lohnt, ist jedoch die Recyclingperformance der zweiten Märkte schlechter als die der ersten Märkte. Darüber hinaus spiegelt sich die Knappheit der erschöpfbaren Ressource in den frühen Perioden der beiden Märkte nicht wider. Die unbefriedigenden experimentellen Ergebnisse lassen sich durch „rolling planning horizons“ erklären. Jeder Agent machte einen Plan für eine begrenzte Anzahl von Perioden und aktualisierte ihn regelmäßig. Nur die erste Periode wurde durchgeführt und dann ein neuer Plan für eine ebenso lange Zukunft gemacht. Da der verbleibende Ressourcenbestand in den frühen Perioden hoch war und seine Handelsentscheidungen für den Planungshorizont immer erfüllt werden konnten, war in den frühen Perioden die Ressourcenbeschränkung nicht bindend und es bestand kein Zusammenhang zwischen der Preisentwicklung und dem Zinssatz. Mit weiteren Transaktionen wurde der Ressourcenbestand jedoch schließlich so klein, dass er innerhalb des Planungshorizonts erschöpft sein könnte. Die neuen Pläne mussten die bindende Ressourcenbeschränkung berücksichtigen und die Knappheit der erschöpfbaren Ressource wurde schließlich Teil ihres Preises. Obwohl die Probanden die Knappheit ihrer Ressourceneinheiten seit der letzten Phase der ersten Märkte bemerkt und berücksichtigt haben könnten, trafen sie in den fühen Perioden der zweiten Märkte sogar höhere Recyclingentscheidungen. Das Sammlungskriterium von Boyce (2012) erhielt in den beiden Märkten keine Unterstützung. Das komplexe Design des Basis-Treatments könnte die dynamische Optimierung erschweren, da die Probanden in einem intertemporalen Kontext Preis-, Handels- und Recyclingentscheidungen treffen mussten. In einem neuen Treatment, nämlich dem Recycling-Treatment, wird mehr Aufmerksamkeit auf Recyclingentscheidungen gelenkt werden. In diesem Treatment sollten Sammlungsaktivitäten nur dann stattfinden, wenn der Transaktionspreis einer recycelten erschöpfbaren Ressourceneinheit die durch Recycling- und Produktionsaktivitäten entstehenden Gesamtkosten übersteigt. Damit der Einfluss sozialer und ökologischer Präferenzen auf Recyclingentscheidungen untersucht werden kann, müssen die Probanden ihr eigenes Umweltbewusstsein im Fragebogen nach dem Experiment bewerten. Die Experimente des Recycling-Treatments zeigten bessere Recyclingperformance, aber nur in den profitablen Perioden für Recycling hatten soziale und ökologische Präferenzen einen klaren positiven Effekt auf Recyclingentscheidungen. Die stark umweltbewussten Probanden wagten sich in den beiden Märkten daran, mit den steigenden vorgegebenen Transaktionspreisen ihre Recyclingmengen stark zu erhöhen. Im Gegensatz dazu könnten die Probanden mit geringerem Umweltbewusstsein mehr auf ihre Payments achten und daher konservative Recyclingstrategien durchgeführt haben. Sie trafen relativ niedrigere Recyclingentscheidungen, um große Verluste zu vermeiden, und erst spät in den zweiten Märkten erhöhten sie ihr Recycling deutlich.Non-renewable or exhaustible resources refer to the resources whose total stocks provided by the earth are constant over the period relevant to human planning. Due to their limited availability and important applications in human society development, their supply security has been widely concerned by the public. Moreover, severe environmental impacts and huge amounts of waste have been generated during the extraction, processing and use of these resources and materials. Recycling, a process of reprocessing recoverable materials at the end of product life and sending them back into the supply chain, seems to be an effective way to alleviate the above problems. Although there are technical, economical and practical obstacles to recycling, efforts have been made in the product design stage, the separate collection systems, the cooperation between developing countries and industrialized countries and the effective application of political instruments. The economic models of most interest in this work are those that focus on the competitive equilibrium of an exhaustible resource market with recycling activities. Based on the famous Hotelling rule which argues that the net price (also called the scarcity rent) of a non-renewable resource should rise over time at the rate of interest in a competitive market equilibrium, Boyce (2012) provides a typical model of this kind. In his view, sorting activities are economic only when the current value of the non-renewable resource units exceeds the sorting cost. The external validity of this model is then verified by economics laboratory experiments. Two same rounds (or markets) are conducted in each session of the basic treatment to see whether learning happens. The experimental results, however, “polarize”. The recycling performance shown in the periods when sorting is theoretically worthwhile seems to be in line with the standard development in both markets, while the recycling performance of the second markets is even worse than that of the first markets in the periods when sorting is theoretically not economic. Moreover, the scarcity of the non-renewable resource is not reflected in the early periods in both markets. The unsatisfactory experimental results can largely be explained by rolling planning horizons. Each agent made a plan for a finite number of periods and updated it regularly. Only the first period was carried out and a new plan was then made for an equally long future. Since the remaining resource stock was high in the early periods and his trading decisions for the planning horizon could always be met, the resource constraint was not binding and there was no connection between the price development and the interest rate in the early periods. When the resource stock finally became so small that it could be exhausted within the planning horizon, the new plans had to take the binding resource constraint into account and the scarcity of the exhaustible resource finally became a component of its price. However, even though the subjects may have realized and taken the resource scarcity into account since the latter phase of the first markets, they still made even higher recycling decisions in the early periods of the second markets. The subjects did not realize the sorting criterion proposed by Boyce (2012) in both markets. The complex design of the basic treatment makes it difficult for the subjects to do dynamic optimization, since they had to make pricing, trading and recycling decisions in an intertemporal context. A much simplified treatment which focuses on recycling decisions is then proposed. In this new treatment, sorting activities should occur only when the transaction price of a recycled non-renewable resource unit exceeds the total costs incurred by recycling and production activities. In addition, to verify whether and to what extent social and environmental preferences can affect recycling decisions, the subjects are required to evaluate their environmental awareness in the post-experiment questionnaire. Better recycling performance was shown in the experiments of the new treatment. However, environmental awareness had a clear positive impact on recycling decisions only in the periods when recycling is theoretically profitable. The highly environmentally conscious subjects dared to greatly increase their recycling quantities with the increasing predetermined transaction prices in both markets. The subjects with lower environmental awareness might value their payments more and thus haven taken conservative recycling measures. They maintained a relatively low recycling level to avoid big losses and only dared to greatly increase their recycling in the later periods of the second markets