On p-Adic Sector of Adelic String

We consider construction of Lagrangians which are candidates for p-adic sector of an adelic open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and contain the Riemann zeta function with the d'Alembertian in its argument. In particular, we present a new Lagrangian obtained by an additive approach which takes into account all p-adic Lagrangians. The very attractive feature of this new Lagrangian is that it is an analytic function of the d'Alembertian. Investigation of the field theory with Riemann zeta function is interesting in itself as well.Comment: 10 pages. Presented at the 2nd Conf. on SFT and Related Topics, Moscow, April 2009. Submitted to Theor. Math. Phy

Nonlocal Dynamics of p-Adic Strings

We consider the construction of Lagrangians that might be suitable for describing the entire $p$-adic sector of an adelic open scalar string. These Lagrangians are constructed using the Lagrangian for $p$-adic strings with an arbitrary prime number $p$. They contain space-time nonlocality because of the d'Alembertian in argument of the Riemann zeta function. We present a brief review and some new results.Comment: 8 page

Petrology and Structure of the Cascade River Schist, in the Sibley Creek Area, Northern Cascades, Washington

The focus of this study is on the protolith types, metamorphism and structure of the Cascade River Schist in the Sibley Creek area of the North Cascades, Washington. The two general lithologic packages are an arc and ocean floor unit termed the Cascade River and Napeequa units, respectively, by Tabor and others (in press). The Cascade River unit has a recognizable stratigraphy which is inverted and repeated across strike from the southwestern to northeastern sides of the field area, apparently as a result of macroscopic synclinal folding. The Napeequa unit lies on top of the Cascade River unit, in the center of the sync line, probably as a result of thrust faulting. Metamorphic zones and facies in the field area increase from the biotite zone of the greenschist facies, west of the Le Conte fault, to the garnet and staurolite-kyanite zones of the epidote amphibolite facies east of the fault. The greenschist facies is estimated to be metamorphosed at pressures of 3-5 Kb, and temperatures of 450-500 C and the amphibolite facies at 8-10 kb and 600-700 C. Structural control of the greenschist-anphibolite facies transition by the Le Conte fault is suggested by the first appearance of the garnet and oligoclase with the fault, as well as a P-T differential across the fault, which suggests considerable dip-slip displacement across the fault. The metamorphic structures in the field area consist of: 1) a synmetamorphic first deformation characterized by steeply dipping S-tectonites containing weakly defined down-dip mineral lineations and flattened conglomerate clasts, and 2) a late-metamorphic and commonly retrogressive second deformation characterized by steeply dipping L-Stectonites containing a sub-horizontal stretching lineation, prolate spheroidal conglomerate clasts, and dextral kinematic indicators. Later post-metamorphic structures are folds and faults related to forceful enplacement of the 73 Ma Hidden Lake pluton and Eocene strike-slip offset along the Le Conte fault

p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency

The classical and quantum formalism for a p-adic and adelic harmonic oscillator with time-dependent frequency is developed, and general formulae for main theoretical quantities are obtained. In particular, the p-adic propagator is calculated, and the existence of a simple vacuum state as well as adelic quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical phase are noted.Comment: 10 page

Zeta Nonlocal Scalar Fields

We consider some nonlocal and nonpolynomial scalar field models originated from p-adic string theory. Infinite number of spacetime derivatives is determined by the operator valued Riemann zeta function through d'Alembertian $\Box$ in its argument. Construction of the corresponding Lagrangians L starts with the exact Lagrangian $\mathcal{L}_p$ for effective field of p-adic tachyon string, which is generalized replacing p by arbitrary natural number n and then taken a sum of $\mathcal{L}_n$ over all n. The corresponding new objects we call zeta scalar strings. Some basic classical field properties of these fields are obtained and presented in this paper. In particular, some solutions of the equations of motion and their tachyon spectra are studied. Field theory with Riemann zeta function dynamics is interesting in its own right as well.Comment: 13 pages, submitted to Theoretical and Mathematical Physic

A p-Adic Model of DNA Sequence and Genetic Code

Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are nucleotides, codons and genes. We show that a 5-adic model is appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance, is also suitable for genetic code and for a more advanced employment in genomics. We find that genetic code degeneracy is related to the p-adic distance between codons.Comment: 13 pages, 2 table

Deep Structure of Siletzia in the Puget Lowland: Imaging an Obducted Plateau and Accretionary Thrust Belt With Potential Fields

Detailed understanding of crustal components and tectonic history of forearcs is important due to their geological complexity and high seismic hazard. The principal component of the Cascadia forearc is Siletzia, a composite basaltic terrane of oceanic origin. Much is known about the lithology and age of the province. However, glacial sediments blanketing the Puget Lowland obscure its lateral extent and internal structure, hindering our ability to fully understand its tectonic history and its influence on modern deformation. In this study, we apply map-view interpretation and two-dimensional modeling of aeromagnetic and gravity data to the magnetically stratified Siletzia terrane revealing its internal structure and characterizing its eastern boundary. These analyses suggest the contact between Siletzia (Crescent Formation) and the Eocene accretionary prism trends northward under Lake Washington. North of Seattle, this boundary dips east where it crosses the Kingston arch, whereas south of Seattle the contact dips west where it crosses the Seattle uplift (SU). This westward dip is opposite the dip of the Eocene subduction interface, implying obduction of Siletzia upper crust at this southern location. Elongate pairs of high and low magnetic anomalies over the SU suggest imbrication of steeply-dipping, deeply rooted slices of Crescent Formation within Siletzia. We hypothesize these features result from duplication of Crescent Formation in an accretionary fold-thrust belt during the Eocene. The active Seattle fault divides this Eocene fold-thrust belt into two zones with different structural trends and opposite frontal ramp dips, suggesting the Seattle fault may have originated as a tear fault during accretion

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page