Comparison of KP and BBM-KP models

In this dissertation we show that the solution of the pure initial-value problems for the KP and regularize KP equations are the same, to within the order of accuracy attributable to either, on the time scale from zero to epsilon to negative three halves power, during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles

Comparison of KP and BBM-KP Models

It is shown that the solutions of the pure initial-value problem for the KP and regularized KP equations are the same, within the order of accuracy attributable to either, on the time scale 0≤t≤ε−3/2, during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles

Analysis of Nonlinear Dispersive Model Equations

In this work we begin with a brief survey of the classical fluid dynamics problem of water waves, and then proceed to derive well known evolution equations via a Hamiltonian Variational approach. This method was first introduced in the seminal work of Walter Craig, et al. \cite{CG}. The distinguishing feature of this scheme is that the Dirichlet-Neumann operator of the fluid domain appears explicitly in the Hamiltonian. In the second and third chapters, we utilize the Hamiltonian perturbation theory introduced in \cite{CG} to derive the Benjamin-Bona-Mahony (BBM) and Benjamin-Bona-Mahony-Kadomtsev-Petviashvili (BBM-KP)equations. Finally, we briefly review the existence theory for their corresponding Cauchy problems. In the fourth chapter, I motivate and present my first result and demonstrate how it ties in with the literature and previous chapters. In particular, we show that the solution of the Cauchy problem for the BBM-KP equation converges to the solution of the Cauchy problem for the BBM equation in a suitable function space whenever the initial data for both equations are close as the transverse variable $y \rightarrow \pm \infty$. \\ \indent In the final chapter we introduce and analyze a new modified Kadomstev-Petviashvili equation. This model was introduced in an effort to remedy the odd behavior of the mass of a given solution to the Kadomstev-Petviashvili model. This results in a model which does not impose specified restrictions upon the initial data. After motivating and deriving the model we prove various linear estimates for the operator equation arising from the Duhamel formulation of system. To this end I discuss my future work

Traveling waves and homogeneous fragmentation

We formulate the notion of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process and study its traveling waves. Specifically, we establish existence, uniqueness and asymptotics. In the spirit of classical works such as McKean [Comm. Pure Appl. Math. 28 (1975) 323-331] and [Comm. Pure Appl. Math. 29 (1976) 553-554], Neveu [In Seminar on Stochastic Processes (1988) 223-242 Birkh\"{a}user] and Chauvin [Ann. Probab. 19 (1991) 1195-1205], our analysis exposes the relation between traveling waves and certain additive and multiplicative martingales via laws of large numbers which have been previously studied in the context of Crump-Mode-Jagers (CMJ) processes by Nerman [Z. Wahrsch. Verw. Gebiete 57 (1981) 365-395] and in the context of fragmentation processes by Bertoin and Martinez [Adv. in Appl. Probab. 37 (2005) 553-570] and Harris, Knobloch and Kyprianou [Ann. Inst. H. Poincar\'{e} Probab. Statist. 46 (2010) 119-134]. The conclusions and methodology presented here appeal to a number of concepts coming from the theory of branching random walks and branching Brownian motion (cf. Harris [Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 503-517] and Biggins and Kyprianou [Electr. J. Probab. 10 (2005) 609-631]) showing their mathematical robustness even within the context of fragmentation theory.Comment: Published in at http://dx.doi.org/10.1214/10-AAP733 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

PELUANG DAN TANTANGAN PENGEMBANGAN BISNIS INKLUSIF PERIKANAN TUNA SKALA KECIL DI PULAU MOROTAI

Potensi Kabupaten Pulau Morotai untuk mendukung produksi tuna sirip kuning provinsi maupun nasional sangat besar, namun tingkat pemanfaatannya rendah. Penelitian ini bertujuan untuk menganalisis: (1) kelayakan finansial usaha, (2) rantai pasok, (3) model bisnis eksisting, dan (4) strategi pengembangan bisnis. Penelitian dilaksanakan Maret hingga Juni 2021 di Kecamatan Morotai Selatan, Timur, dan Barat. Data primer dikumpulkan melalui wawancara dengan 60 nelayan dan pendalaman dengan pedagang besar, pengelola koperasi, unit pengolahan tuna. Analisis mencakup kelayakan usaha, rantai pasok, SWOT, dan deskriptif. Hasil menunjukkan bahwa penangkapan tuna di Morotai, yang dilakukan menggunakan alat pancing ulur dan tonda dan armada kapal motor dan kapal motor tempel memberikan penghasilan memadai bagi nelayan, namun sistem bisnis yang ada masih perlu ditingkatkan. Keuntungan yang diperoleh nelayan adalah Rp 153 juta untuk alat pancing ukur dengan kapal motor dan berturut-turut Rp 1,1 milyar dan Rp 134 juta untuk alat pancing ulur dan tonda dengan kapal motor tempel. Rantai pasok tuna di Morotai terdiri dari lima simpul, dengan share terbesar pada simpul koperasi, yaitu 45%. Hasil lain menunjukkan bahwa dalam sistem bisnis eksisting di Kepulauan Morotai terdapat kelompok nelayan yang belum inklusif dalam rantai pasok tuna, tidak bermitra dengan koperasi, tidak memiliki akses pasar, dan tidak terlibat dalam penentuan harga. Strategi pengembangan bisnis inklusif tuna di Morotai yang dapat direkomendasikan dari hasil penelitian ini adalah penerapan model pengelolaan perikanan terpadu yang didukung: (i) pasar yang mengakomodasikan investor rantai pasok, (ii) pembukaan akses permodalan bank, dan (iii) kemitraan nelayan dengan koperasi sebagai perantara dan unit pengolah ikan sebagai mitra bisnis. Title: Prospect and Challenges for the Development of Small Scale Tuna Fisheries Inclusive Business in Morotai IslandThe potential of the Morotai Island Regency to support the production of provincial and national yellowfin tuna is very large, but its utilization is low. The research aims to analyze: (1) the financial viability of the business, (2) the supply chain, (3) the existing business model, and (4) the business development strategy. The research was conducted from March to June 2021 in the South, East, and West Morotai Subdistrict. Primary data was collected through interviews with 60 fishers and deepening with wholesalers, cooperative managers, tuna processing units. The analysis includes business feasibility, supply chain, SWOT, and descriptive. The results showed that tuna fishing in Morotai, which was carried out using fishing rods and tonda and a fleet of motorboats and outboard motorboats, provided adequate income for fishers, but the existing business system still needed to be improved. The profit obtained byfishermen is IDR 153 million for measuring fishing rods with motorboats and IDR 1.1 billion and IDR 134 million for fishing rods and trolleys with outboard motorboats. The tuna supply chain in Morotai consists of five nodes, with the largest share in cooperative nodes, which is 45%. Other results show that in theexisting business system in the Morotai Islands, there are fishing groups that are not yet included in the tuna supply chain, do not partner with cooperatives, do not have market access, and are not involved in pricing. The tuna inclusive business development strategy in Morotai that can be recommended fromthe results of this study is the implementation of an integrated fisheries management model supported:(i) a market that accommodates supply chain investors, (ii) the opening of bank capital access, and (iii) fisher’s partnership with cooperatives as intermediaries and fish processing units as business partners