A higher-order Skyrme model

We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed by Marleau has an instability in the form of a baby-Skyrmion string, while the static energies of our construction are positive definite, implying stability against time-independent perturbations. However, we also find that the Hamiltonians of our construction possess two kinds of dynamical instabilities, which may indicate the instability with respect to time-dependent perturbations. Different from the well-known Ostrogradsky instability, the instabilities that we find are intrinsically of nonlinear nature and also due to the fact that even powers of the inverse metric gives a ghost-like higher-order kinetic-like term. The vacuum state is, however, stable. Finally, we show that at sufficiently low energies, our Hamiltonians in the simplest cases, are stable against time-dependent perturbations.Comment: LaTeX: 42 pages, 3 figures; V2: simplifications implemented in Secs. 5 and 6, and references adde

Towards Vacuum Superstring Field Theory: The Supersliver

We extend some aspects of vacuum string field theory to superstring field theory in Berkovits' formulation, and we study the star algebra in the fermionic matter sector. After clarifying the structure of the interaction vertex in the operator formalism of Gross and Jevicki, we provide an algebraic construction of the supersliver state in terms of infinite-dimensional matrices. This state is an idempotent string field and solves the matter part of the equation of motion of superstring field theory with a pure ghost BRST operator. We determine the spectrum of eigenvalues and eigenvectors of the infinite-dimensional matrices of Neumann coefficients in the fermionic matter sector. We then analyze coherent states based on the supersliver and use them in order to construct higher-rank projector solutions, as well as to construct closed subalgebras of the star algebra in the fermionic matter sector. Finally, we show that the geometric supersliver is a solution to the superstring field theory equations of motion, including the (super)ghost sector, with the canonical choice of vacuum BRST operator recently proposed by Gaiotto, Rastelli, Sen and Zwiebach.Comment: 45 pages, JHEP styl

Renormalizable 1/N_f Expansion for Field Theories in Extra Dimensions

We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories. It is based on $1/N_f$-expansion and results in a logarithmically divergent perturbation theory in arbitrary high space-time dimension. First, we consider a simple example of $N$-component scalar filed theory and then extend this approach to Abelian and non-Abelian gauge theories with $N_f$ fermions. In the latter case, due to self-interaction of non-Abelian fields the proposed recipe requires some modification which, however, does not change the main results. The resulting effective coupling is dimensionless and is running in accordance with the usual RG equations. The corresponding beta function is calculated in the leading order and is nonpolynomial in effective coupling. It exhibits either UV asymptotically free or IR free behaviour depending on the dimension of space-time. The original dimensionful coupling plays a role of a mass and is also logarithmically renormalized. We analyze also the analytical properties of a resulting theory and demonstrate that in general it acquires several ghost states with negative and/or complex masses. In the former case, the ghost state can be removed by a proper choice of the coupling. As for the states with complex conjugated masses, their contribution to physical amplitudes cancels so that the theory appears to be unitary.Comment: 32 pages, 20 figure

Nernst effect as a probe of superconducting fluctuations in disordered thin films

In amorphous superconducting thin films of $Nb_{0.15}Si_{0.85}$ and $InO_x$, a finite Nernst coefficient can be detected in a wide range of temperature and magnetic field. Due to the negligible contribution of normal quasi-particles, superconducting fluctuations easily dominate the Nernst response in the entire range of study. In the vicinity of the critical temperature and in the zero-field limit, the magnitude of the signal is in quantitative agreement with what is theoretically expected for the Gaussian fluctuations of the superconducting order parameter. Even at higher temperatures and finite magnetic field, the Nernst coefficient is set by the size of superconducting fluctuations. The Nernst coefficient emerges as a direct probe of the ghost critical field, the normal-state mirror of the upper critical field. Moreover, upon leaving the normal state with fluctuating Cooper pairs, we show that the temperature evolution of the Nernst coefficient is different whether the system enters a vortex solid, a vortex liquid or a phase-fluctuating superconducting regime.Comment: Submitted to New. J. Phys. for a focus issue on "Superconductors with Exotic Symmetries

Investment potentials in shellfish culture in Nigeria

Shellfish are a major but cheap protein source for human consumption as well as source of income for coastal towns and villages of the Niger Delta in Rivers State, Cross River, and Lagos States. A research into the nutritive value of some of these marine shellfish viz: bivalves (oyster - Crassostrea gasar and cockle - Anadara senilis); gastropods (periwinkle - Tympanotonus fuscatus, obtuse periwinkle - Semifusus morio and the giant whelk - Thais callifera) and mangrove crabs (green crab - Goniopsis pelli, ghost crab - Cardisoma ormatum, and common blue crab - Callinectes latimanus) was carried out to compare their quality and cost with beef, chicken meat, pork and egg in order to identify those most suitable for commercial culture. Results show that all shellfish had at least 16% crude protein except blue crab (13.38%). All shellfish had higher protein content than egg (13.36%). Cockle with protein content 25.47% compared favourably with beef, (29.60%). Beef, chicken meat and pork cost 11.50, 9.00 and 8.00 per kilo respectively while oyster, periwinkle and the common blue crab cost 3.50, 3.00, and 1.50 per kilo respectively. Oysters and Cockles are recommended for commercial culture based on the findings of this researc

Cosmological data favor Galileon ghost condensate over Λ CDM

We place observational constraints on the Galileon ghost condensate model, a dark energy proposal in cubic-order Horndeski theories consistent with the gravitational-wave event GW170817. The model extends the covariant Galileon by taking an additional higher-order field derivative X2 into account. This allows for the dark energy equation of state wDE to access the region −2Theoretical Physic

A type-theory for higher-order amortized analysis

Die Verifikation von "Worst-Case" Schranken für Ressourcennutzung ist ein wichtiges Problem in der Informatik. Der Nutzen einer solchen Verifikation hängt von der Präzision der Analyse ab. Aus Gründen der Präzision ist es manchmal nützlich, die durchschnittlichen Kosten einer Folge von Operationen zu berücksichtigen, statt die Kosten jeder einzelnen Operation getrennt zu betrachten. Diese Art von Analyse wird oft als amortisierte Ressourcenanalyse bezeichnet. Typischerweise profitieren Programme, die ihren Zustand optimieren, um die Kosten zukünftiger Ausführungen zu reduzieren, von solchen Ansätzen. Die Analyse der Ressourcennutzung einer mit zwei (LIFO) Listen implementierten funktionalen (FIFO) Schlange ist ein klassisches Beispiel für eine amortisierte Analyse. In dieser Arbeit präsentieren wir λamor, eine Typentheorie für die amortisierte Analyse der Ressourcennutzung höherstufiger Programme. Eine typische amortisierte Analyse speichert einen "ghost state", der als Potenzial bezeichnet wird, zusammen mit den Datenstrukturen. Die Kernidee der amortisierten Analyse ist es, zu zeigen, dass das dem Programm zur Verfügung stehende Potenzial ausreicht, um die Ressourcennutzung des Programms zu erfassen. Die Verifikation in λamor basiert auf der Realisierung dieser Idee in einer Typentheorie. Wir erreichen dies indem wir ein allgemeines typentheoretisches Konstrukt zur Darstellung des Potenzials auf der Ebene von Typen definieren und anschließend eine affine Typentheorie aufbauen. Mit λamor zeigen wir, dass eine typentheoretische amortisierte Analyse mit gut verstandenen Konzepten aus substrukturellen und modalen Typentheorien durchgeführt werden kann. Trotzdem ergibt sich ein äußerst aussagekräftiges Framework, das für die Ressourcenanalyse von höherstufigen Programmen, sowohl ein einem "strikten", als auch in einem "lazy" Setting, verwendet werden kann. Wir präsentieren Einbettungen zweier stark verschiedener Arten von typentheoretischen Ressourcenanalyseframeworks (eines basiert auf Effekten, das andere auf Koeffekten) in λamor. Wir zeigen, dass λamor korrekt (sound) ist (mithilfe eines "Logical relations" Modells) und, dass es vollständig für PCF-Programme ist (unter Verwendung einer der Einbettungen). Als nächstes verwenden wir Ideen von λamor, um eine andere Typentheorie (genannt λcg) für einen ganz anderen Anwendungsfall - Informationsflusskontrolle (IFC) - zu entwickeln. λcg verwendet ähnliche typentheoretische Konstrukte wie λamor für das Potenzial verwendet, um die Vertraulichkeitsmarkierungen (den "ghost state" für IFC) darzustellen. Schließlich abstrahieren wir von den spezifischen "ghost states" (Potenzial und Vertraulichkeitsmarkierungen) und entwickeln eine Typentheorie für einen allgemeinen "ghost state" mit einer monoidalen Struktur.Verification of worst-case bounds (on the resource usage of programs) is an important problem in computer science. The usefulness of such verification depends on the precision of the underlying analysis. For precision, sometimes it is useful to consider the average cost over a sequence of operations, instead of separately considering the cost of each individual operation. This kind of an analysis is often referred to as amortized resource analysis. Typically, programs that optimize their internal state to reduce the cost of future executions benefit from such approaches. Analyzing resource usage of a standard functional (FIFO) queue implemented using two functional (LIFO) lists is a classic example of amortized analysis. In this thesis we present λamor, a type-theory for amortized resource analysis of higher-order functional programs. A typical amortized analysis works by storing a ghost state called the potential with data structures. The key idea underlying amortized analysis is to show that, the available potential with the program is sufficient to account for the resource usage of that program. Verification in λamor is based on internalizing this idea into a type theory. We achieve this by providing a general type-theoretic construct to represent potential at the level of types and then building an affine type-theory around it. With λamor we show that, type-theoretic amortized analysis can be performed using well understood concepts from sub-structural and modal type theories. Yet, it yields an extremely expressive framework which can be used for resource analysis of higher-order programs, both in a strict and lazy setting. We show embeddings of two very different styles (one based on effects and the other on coeffects) of type-theoretic resource analysis frameworks into λamor. We show that λamor is sound (using a logical relations model) and complete for cost analysis of PCF programs (using one of the embeddings). Next, we apply ideas from λamor to develop another type theory (called λcg) for a very different domain – Information Flow Control (IFC). λcg uses a similar typetheoretic construct (which λamor uses for the potential) to represent confidentiality label (the ghost state for IFC). Finally, we abstract away from the specific ghost states (potential and confidentiality label) and describe how to develop a type-theory for a general ghost state with a monoidal structure