Growth inside a corner: the limiting interface shape

Jason Olejarz1, P L Krapivsky, S Redner

  • 1Center for Polymer Studies, and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review Letters
|February 7, 2012
PubMed

Related Concept Videos

Optimization Problems01:26

Optimization Problems

Optimization problems often involve identifying maximum or minimum values under specific constraints. A well-known example is determining the longest horizontal pipe that can be moved around a right-angled corner, where a 3-meter-wide hallway meets a 2-meter-wide hallway. This scenario, common in architectural design and industrial transport, can be understood conceptually through geometric and trigonometric reasoning.To visualize the problem, consider the pipe as a straight line that touches...
Indeterminate Products01:29

Indeterminate Products

Indeterminate forms also arise in the evaluation of limits involving products, particularly when one factor approaches zero while the other tends to positive or negative infinity. This situation, commonly described as a zero-times-infinity form, does not have an immediately interpretable outcome. Depending on how the factors behave relative to one another, the limit of such a product may be zero, infinite, or a finite nonzero value.Product Limits and Algebraic RewritingTo analyze limits of this...
Limit Laws II01:26

Limit Laws II

In calculus, limit laws serve as foundational tools for evaluating the behavior of functions as inputs approach specific values. Among these, the laws concerning quotients, powers, and roots are particularly useful in breaking down complex expressions.The Quotient Law allows the limit of a division between two functions to be calculated by dividing their individual limits, provided the limit of the denominator exists and is not zero. For example,The Power Law states that the limit of a function...
The Precise Definition of a Limit01:27

The Precise Definition of a Limit

Understanding the formal definition of a limit is essential for precise mathematical analysis. This concept allows us to rigorously determine how a function behaves near a particular point without relying on ambiguous notions such as "getting close." The ε-δ definition plays a foundational role in calculus, ensuring analytical clarity and logical consistency in limit evaluation.The formal definition states that the limit of a function f(x) as x approaches a is L, written asif for every ε >...
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
Types of Limits II01:24

Types of Limits II

When observing how a curve behaves near a specific point along the horizontal axis, there are cases where the curve’s height increases or decreases without limit as the position draws closer to that point. The curve does not settle at any particular value; instead, the values grow more extreme—upward or downward—the nearer they get. No defined value exists exactly at that location, yet the surrounding behavior becomes more dramatic, indicating a sharp change in direction.The values may rise...