Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e., time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different system. First, we discuss the linear stability of homogeneous steady states, i.e., flat films; and second the systematics of non-trivial steady states, i.e., drop/hole states for dewetting films and quantum dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing to the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly not related physical systems mathematically, but does as well allow to discuss model extensions in a more unified way

MUNICIPAL CORPORATIONS-ZONING-RIGHT OF MUNICIPALITY AND PROPERTY OWNERS THEREIN TO OBJECT TO AMENDMENT OF ZONING ORDINANCE OF ADJACENT MUNICIPALITY

The borough of Dumont in New Jersey amended its zoning ordinance to change one city block from a residential area to a district in which business user would be permissible. The amendment occasioned objections By certain boroughs which were adjacent to the reclassified block, property owners in the adjacent boroughs, property owners in Dumont, and property owners in the block itself. On suit in lieu of prerogative writ by these parties, held, ordinance set aside. Where several boroughs are adjacent to the block of the defendant borough, and in reliance on the residential character of the whole area single family dwellings are erected in all the boroughs, property owners in adjacent boroughs have vested rights to benefits from the zoning restrictions of defendant borough, subject only to a proper exercise by defendant of its police power. The adjacent boroughs are proper parties to contest the validity of the amendment. Borough of Cresskill v. Borough of Dumont, (N. J. Super. Ct. 1953) 100 A. (2d) 182

Corporations - Officers and Directors - Liability for Realizing Less than Full Value from Sale of Corporate Assets on Dissolution

The defendants were directors, officers, and sole stockholders of a corporation engaged in the business of wholesaling electrical supplies. The business gradually declined until the corporation was no longer able to meet maturing obligations, even though expenses had been cut to a minimum. After trying unsuccessfully to borrow more money the defendants decided to wind up the business. Faced with several possible methods of liquidation, they chose to sell the assets at an open auction sale. The net proceeds of the sale were about $20,000, while the cost of the inventory had been at least$60,000. The creditors, through the trustee in bankruptcy, sued the directors for waste of the assets under the New York statute. The appellate division decided that there had been waste, for the directors had not given the required notice to the creditors of the sale and bad not realized full value for the assets. On appeal, held, affirmed, two judges dissenting. While notice to the creditors is not required, directors must respond in damages for the amount, if any, by which less than full value is realized from the liquidation sale of a corporation\u27s assets. New York Credit Men\u27s Adjustment Bureau., Inc. v. Weiss, 305 N.Y. 1, 110 N.E. (2d) 397 (1953)

CONSTITUTIONAL LAW-DUE PROCESS-SEARCH AND SEIZURE-USE IN STATE COURTS OF EVIDENCE OBTAINED ILLEGALLY

Petitioner was convicted of bookmaking under the anti-gambling laws of California by the use of evidence obtained through unreasonable search and seizure and through disclosures petitioner made when purchasing a federal wagering tax stamp. While petitioner and his wife were away, police concealed a microphone in the hall of his home, later moving it to the bedroom and finally to a bedroom closet. The instrument was connected to a receiver in a neighboring garage where other officers monitored all conversations for more than a month. Petitioner exhausted all state remedies in his attempt to have the evidence so obtained declared inadmissible. On certiorari the United States Supreme Court held, affirmed, four justices dissenting. The Fourteenth Amendment does not prevent the use in a state court of evidence acquired illegally. Irvine v. People of State of California, 347 U.S. 128, 74 S.Ct. 381 (1954)

Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder

We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects of gravity, viscosity, rotation, surface tension and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids the behavior \bfuwe{only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes changes with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers

Negligence - Causation - Liability Under Statute for Injury Resulting from Fire Started by Railroad Locomotive

Sparks from defendant\u27s train started a fire on defendant\u27s right of way which spread toward plaintiff\u27s farm. Plaintiff, in an attempt to contain the fire, plowed a fire guard along the edge of his property. While driving his tractor to a safe place after completing the last furrow, he ran over a root or limb which flew up and struck him in the eye, causing blindness. In the trial court plaintiff recovered from the railroad under an Oklahoma statute which specified that Any railroad company operating any line in this state shall be liable for all damages sustained by fire originating from operating its road. On appeal, held, affirmed, three judges dissenting. The fire was the proximate cause of the injury. St. Louis-San Francisco R. Co. v. Ginn, (Okla. 1953) 264 P. (2d) 351

Real Property - Compensation for Abrogation of a Restrictive Covenant by Public Authority

It is the purpose of this comment to examine the legal consequences produced when the tranquility of the residential district is disturbed by governmental action

Replacement of hematopoietic system by allogeneic stem cell transplantation in myelofibrosis patients induces rapid regression of bone marrow fibrosis

Bone marrow fibrosis is a hallmark of primary and post ET/PV myelofibrosis. To investigated the impact of replacement of the hematopoietic system in myelofibrosis patients by allogeneic stem cell transplantation on bone marrow fibrosis, we studied bone marrow fibrosis on bone marrow samples from 24 patients with myelofibrosis before and after dose-reduced conditioning followed by allogeneic stem cell transplantation from related or unrelated donor. Using the European Consensus on Grading Bone Marrow Fibrosis, before allografting all patients had advanced fibrosis MF-2 (n = 13) or MF-3 (n = 11). After transplantation, a complete (MF-0) or nearly complete (MF-1) regression of bone marrow fibrosis was seen in 59 % at day +100, in 90 % at day +180, and in 100 % at day +360. No correlation between occurrence of acute graft-versus-host disease, and fibrosis regression on day +180 was seen. We conclude that dose-reduced conditioning, followed by allogeneic stem cell transplantation, resulted in a rapid resolution of bone-marrow fibrosis suggesting the bone marrow fibrogenesis is a highly dynamic rather than static process in patients with myelofibrosis