Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles--their wavelength--is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.

This Resource Guide is the outcome of a Summer Institute on Methodologies for Housing Justice convened by the Institute on Inequality and Democracy at UCLA Luskin as part of the Housing Justice in Unequal Cities Network, which is supported by the National Science Foundation (BCS 1758774). Held in Los Angeles in August 2019, the Summer Institute brought together participants from cities around the world. As is the case with the overall scope and purpose of the Housing Justice in Unequal Cities Network, it created a shared terrain of scholarship for movement-based and university-based scholars. Dissatisfied with the canonical methods that are in use in housing studies and guided by housing justice movements that are active research communities, the Summer Institute was premised on the assertion that methodology is political. Methodology is rooted in arguments about the world and involves relations of power and knowledge. The method itself – be it countermapping or people’s diaries – does not ensure an ethics of solidarity and a purpose of justice. Such goals require methodologies for liberation. Thus, as is evident in this Resource Guide, our endeavor foregrounds innovative methods that are being used by researchers across academia and activism and explicitly situates such methods in an orientation towards housing justice.

Esta Guía de Recursos es el resultado de un Instituto de Verano sobre Metodologías para la Justicia en la Vivienda convocado por el Instituto sobre Desigualdad y Democracia de UCLA Luskin como parte de la Red de Justicia en la Vivienda en Ciudades Desiguales, que es apoyada por la Fundación Nacional de Ciencias (BCS 1758774). Celebrado en Los Ángeles en agosto de 2019, el Instituto de Verano reunió a participantes de ciudades de todo el mundo. Al igual que el alcance y el propósito general de la Red de Justicia en las Ciudades Desiguales, creó un terreno compartido de para estudiosos del movimiento y académicos de universidades. Con una insatisfacción a los métodos canónicos que se utilizan en los estudios sobre la vivienda y guiado por los movimientos de justicia de la vivienda que son comunidades de investigación activa, el Instituto de verano se basó en la afirmación de que la metodología es política. La metodología se basa en argumentos sobre el mundo e implica relaciones de poder y conocimiento. El método por sí mismo -ya sea el contra ataque al mapeo o los diarios de la genteno asegura una ética de solidaridad y un propósito de justicia. Tales objetivos requieren metodologías para la liberación. Por lo tanto, como es evidente en esta Guía de Recursos, nuestro esfuerzo pone en primer plano los métodos innovadores que están siendo utilizados por los investigadores en todo el mundo académico y el activismo y sitúa explícitamente tales métodos en una orientación hacia la vivienda la justicia.